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Results (1-50 of 904 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
96.3 $C_2^3.A_4$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ $12$ $C_2$ $C_4^2:C_3$ $C_2.C_4^2$ $C_{3}$ Solvable - 3
96.66 $\SL(2,3):C_4$ $2^{5} \cdot 3$ $2^{3} \cdot 3$ $16$ $C_2^2$ $S_4$ $\SL(2,3)$ $C_{4}$ Solvable - 4
96.67 $\GU(2,3)$ $2^{5} \cdot 3$ $2^{3} \cdot 3$ $16$ $C_4$ $S_4$ $\SL(2,3)$ $C_{4}$ Solvable - 4
96.69 $C_4\times \SL(2,3)$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ $28$ $C_2\times C_4$ $A_4$ $Q_8$ $C_{12}$ Solvable - 3
96.74 $C_8.A_4$ $2^{5} \cdot 3$ $2^{3} \cdot 3$ $28$ $C_8$ $A_4$ $Q_8$ $C_{12}$ Solvable - 3
96.188 $C_2^2.S_4$ $2^{5} \cdot 3$ $2^{3} \cdot 3$ $16$ $C_2^2$ $S_4$ $\SL(2,3)$ $C_{2}^{2}$ Solvable - 4
96.189 $C_2\times \GL(2,3)$ $2^{5} \cdot 3$ $2^{3} \cdot 3$ $16$ $C_2^2$ $S_4$ $\SL(2,3)$ $C_{2}^{2}$ Solvable - 4
96.190 $\GL(2,3):C_2$ $2^{5} \cdot 3$ $2^{3} \cdot 3$ $13$ $C_2$ $C_2\times S_4$ $\SL(2,3)$ $C_{2}^{2}$ Solvable - 4
96.191 $C_4.S_4$ $2^{5} \cdot 3$ $2^{3} \cdot 3$ $13$ $C_2$ $C_2\times S_4$ $\SL(2,3)$ $C_{2}^{2}$ Solvable - 4
96.192 $\GL(2,3):C_2$ $2^{5} \cdot 3$ $2^{3} \cdot 3$ $16$ $C_4$ $S_4$ $\SL(2,3)$ $C_{2}^{2}$ Solvable - 4
96.193 $\GL(2,3):C_2$ $2^{5} \cdot 3$ $2^{3} \cdot 3$ $13$ $C_2$ $C_2\times S_4$ $\SL(2,3)$ $C_{2}^{2}$ Solvable - 4
96.198 $C_2^2\times \SL(2,3)$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ $28$ $C_2^3$ $A_4$ $Q_8$ $C_{2} \times C_{6}$ Solvable - 3
96.200 $\SL(2,3):C_2^2$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ $28$ $C_2\times C_4$ $A_4$ $Q_8$ $C_{2} \times C_{6}$ Solvable - 3
96.201 $\SL(2,3):C_2^2$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ $19$ $C_2$ $C_2^2\times A_4$ $Q_8$ $C_{2} \times C_{6}$ Solvable - 3
96.202 $D_4.A_4$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ $19$ $C_2$ $C_2^2\times A_4$ $Q_8$ $C_{2} \times C_{6}$ Solvable - 3
96.203 $Q_8:A_4$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ $12$ $C_2$ $C_2^2:A_4$ $C_2^2\times Q_8$ $C_{3}$ Solvable - 3
160.199 $C_2.C_2^4:C_5$ $2^{5} \cdot 5$ $2^{2} \cdot 5$ $13$ $C_2$ $C_2^4:C_5$ $C_4.C_2^3$ $C_{5}$ Solvable - 3
192.4 $C_2^3.\SL(2,3)$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $18$ $C_4$ $C_4^2:C_3$ $C_4.C_4^2$ $C_{3}$ Solvable - 3
192.180 $C_2^3.S_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $15$ $C_2$ $C_4^2:S_3$ $C_2^3.A_4$ $C_{2}$ Solvable - 4
192.181 $C_2^3.S_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $15$ $C_2$ $C_4^2:S_3$ $C_2^3.A_4$ $C_{2}$ Solvable - 4
192.183 $\SL(2,3):C_8$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $32$ $C_2\times C_4$ $S_4$ $\SL(2,3)$ $C_{8}$ Solvable - 4
192.187 $C_8.S_4$ $2^{6} \cdot 3$ $2^{4} \cdot 3$ $32$ $C_8$ $S_4$ $\SL(2,3)$ $C_{8}$ Solvable - 4
192.189 $C_2^3.\SL(2,3)$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ $24$ $C_2^2$ $C_4^2:C_3$ $C_2.C_4^2$ $C_{6}$ Solvable - 3
192.190 $C_2^3.(C_2\times A_4)$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ $24$ $C_4$ $C_4^2:C_3$ $C_2.C_4^2$ $C_{6}$ Solvable - 3
192.194 $C_2^3.(C_2\times A_4)$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ $18$ $C_2$ $C_4^2:C_6$ $C_2.C_4^2$ $C_{6}$ Solvable - 3
192.195 $C_2^3:\SL(2,3)$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ $18$ $C_2$ $C_2^3:A_4$ $C_2^2\times Q_8$ $C_{6}$ Solvable - 3
192.196 $C_2^3.(C_2\times A_4)$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ $18$ $C_2$ $C_2^3:A_4$ $C_2^2\times Q_8$ $C_{6}$ Solvable - 3
192.197 $C_2^3.\SL(2,3)$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ $18$ $C_2$ $C_4^2:C_6$ $C_2.C_4^2$ $C_{6}$ Solvable - 3
192.198 $C_2^3.\SL(2,3)$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ $18$ $C_2$ $C_4^2:C_6$ $C_2.C_4^2$ $C_{6}$ Solvable - 3
192.199 $C_2^3.(C_2\times A_4)$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ $18$ $C_2$ $C_4^2:C_6$ $C_2.C_4^2$ $C_{6}$ Solvable - 3
192.200 $C_8\times \SL(2,3)$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $56$ $C_2\times C_8$ $A_4$ $Q_8$ $C_{24}$ Solvable - 3
192.204 $C_{16}.A_4$ $2^{6} \cdot 3$ $2^{4} \cdot 3$ $56$ $C_{16}$ $A_4$ $Q_8$ $C_{24}$ Solvable - 3
192.945 $\SL(2,3):Q_8$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $23$ $C_2^2$ $C_2\times S_4$ $C_2\times \SL(2,3)$ $C_{2}^{2}$ Solvable - 4
192.946 $C_4\times C_2.S_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $32$ $C_2\times C_4$ $S_4$ $\SL(2,3)$ $C_{2} \times C_{4}$ Solvable - 4
192.947 $(C_2\times C_4).S_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $26$ $C_2^2$ $C_2\times S_4$ $\SL(2,3)$ $C_{2} \times C_{4}$ Solvable - 4
192.948 $\SL(2,3).Q_8$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $23$ $C_2^2$ $C_2\times S_4$ $C_2\times \SL(2,3)$ $C_{2}^{2}$ Solvable - 4
192.949 $Q_8.D_{12}$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $23$ $C_2^2$ $C_2\times S_4$ $C_2\times \SL(2,3)$ $C_{2}^{2}$ Solvable - 4
192.950 $\SL(2,3):Q_8$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $23$ $C_2^2$ $C_2\times S_4$ $C_2\times \SL(2,3)$ $C_{2}^{2}$ Solvable - 4
192.951 $C_4\times \GL(2,3)$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $32$ $C_2\times C_4$ $S_4$ $\SL(2,3)$ $C_{2} \times C_{4}$ Solvable - 4
192.952 $C_4:\GL(2,3)$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $23$ $C_2^2$ $C_2\times S_4$ $C_2\times \SL(2,3)$ $C_{2}^{2}$ Solvable - 4
192.953 $\GL(2,3):C_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $26$ $C_2^2$ $C_2\times S_4$ $\SL(2,3)$ $C_{2} \times C_{4}$ Solvable - 4
192.954 $Q_8.D_{12}$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $23$ $C_2^2$ $C_2\times S_4$ $C_2\times \SL(2,3)$ $C_{2}^{2}$ Solvable - 4
192.962 $C_8.S_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $20$ $C_2$ $C_4:S_4$ $\SL(2,3):C_2$ $C_{2}^{2}$ Solvable - 4
192.963 $\GL(2,3):C_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $32$ $C_8$ $S_4$ $\SL(2,3)$ $C_{2} \times C_{4}$ Solvable - 4
192.964 $\GL(2,3):C_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $26$ $C_4$ $C_2\times S_4$ $\SL(2,3)$ $C_{2} \times C_{4}$ Solvable - 4
192.965 $C_8.S_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $20$ $C_2$ $C_4:S_4$ $\SL(2,3):C_2$ $C_{2}^{2}$ Solvable - 4
192.966 $C_8.S_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $20$ $C_2$ $C_4:S_4$ $\SL(2,3):C_2$ $C_{2}^{2}$ Solvable - 4
192.977 $C_2^3.S_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $32$ $C_2^3$ $S_4$ $\SL(2,3)$ $C_{2} \times C_{4}$ Solvable - 4
192.978 $C_2.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $23$ $C_2^2$ $C_2\times S_4$ $C_2\times \SL(2,3)$ $C_{2}^{2}$ Solvable - 4
192.979 $C_2^3.S_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ $26$ $C_2^2$ $C_2\times S_4$ $\SL(2,3)$ $C_{2} \times C_{4}$ Solvable - 4
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