Note: Search results may be incomplete due to uncomputed quantities: Automorphism group order (4830 objects)
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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
32.46 | $C_2^2\times D_4$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2^3$ | Nilpotent - 2 |
48.50 | $C_2^2:A_4$ | $2^{4} \cdot 3$ | $2 \cdot 3$ | $8$ | $C_1$ | Solvable - 2 |
48.51 | $C_2^2\times D_6$ | $2^{4} \cdot 3$ | $2 \cdot 3$ | $24$ | $C_2^3$ | Solvable - 2 |
54.7 | $C_3:D_9$ | $2 \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $15$ | $C_1$ | Solvable - 2 |
64.62 | $C_2^3.D_4$ | $2^{6}$ | $2^{2}$ | $28$ | $C_2^3$ | Nilpotent - 2 |
64.63 | $C_4^2:C_4$ | $2^{6}$ | $2^{2}$ | $28$ | $C_2^3$ | Nilpotent - 2 |
64.64 | $C_4^2:C_4$ | $2^{6}$ | $2^{2}$ | $28$ | $C_2^3$ | Nilpotent - 2 |
64.73 | $C_2^3:D_4$ | $2^{6}$ | $2^{2}$ | $22$ | $C_2^3$ | Nilpotent - 2 |
64.74 | $C_2^3:Q_8$ | $2^{6}$ | $2^{2}$ | $22$ | $C_2^3$ | Nilpotent - 2 |
64.76 | $C_2^3.C_2^3$ | $2^{6}$ | $2^{2}$ | $22$ | $C_2^3$ | Nilpotent - 2 |
64.80 | $C_2^3.Q_8$ | $2^{6}$ | $2^{2}$ | $22$ | $C_2^3$ | Nilpotent - 2 |
64.174 | $C_4:D_8$ | $2^{6}$ | $2^{3}$ | $22$ | $C_2^2$ | Nilpotent - 3 |
64.175 | $C_4:Q_{16}$ | $2^{6}$ | $2^{3}$ | $22$ | $C_2^2$ | Nilpotent - 3 |
64.195 | $C_4^2:C_2^2$ | $2^{6}$ | $2^{2}$ | $40$ | $C_2^2\times C_4$ | Nilpotent - 2 |
64.196 | $C_4^2:C_2^2$ | $2^{6}$ | $2^{2}$ | $40$ | $C_2^2\times C_4$ | Nilpotent - 2 |
64.198 | $C_4^2.C_2^2$ | $2^{6}$ | $2^{2}$ | $40$ | $C_4^2$ | Nilpotent - 2 |
64.199 | $C_4^2:C_2^2$ | $2^{6}$ | $2^{2}$ | $34$ | $C_2^2$ | Nilpotent - 2 |
64.201 | $C_4^2.C_2^2$ | $2^{6}$ | $2^{2}$ | $34$ | $C_2^2$ | Nilpotent - 2 |
64.203 | $C_2^3:D_4$ | $2^{6}$ | $2^{2}$ | $28$ | $C_2^3$ | Nilpotent - 2 |
64.204 | $C_2^3:Q_8$ | $2^{6}$ | $2^{2}$ | $28$ | $C_2^3$ | Nilpotent - 2 |
64.205 | $C_2^3.D_4$ | $2^{6}$ | $2^{2}$ | $28$ | $C_2^3$ | Nilpotent - 2 |
64.207 | $C_4^2:C_2^2$ | $2^{6}$ | $2^{2}$ | $28$ | $C_2^3$ | Nilpotent - 2 |
64.208 | $C_4^2.C_2^2$ | $2^{6}$ | $2^{2}$ | $28$ | $C_2^3$ | Nilpotent - 2 |
64.209 | $C_4^2:C_2^2$ | $2^{6}$ | $2^{2}$ | $28$ | $C_2^3$ | Nilpotent - 2 |
64.224 | $C_2^3:Q_8$ | $2^{6}$ | $2^{2}$ | $22$ | $C_2^2$ | Nilpotent - 2 |
64.230 | $D_4\times Q_8$ | $2^{6}$ | $2^{2}$ | $25$ | $C_2^2$ | Nilpotent - 2 |
64.231 | $Q_8:D_4$ | $2^{6}$ | $2^{2}$ | $25$ | $C_2^2$ | Nilpotent - 2 |
64.238 | $Q_8:Q_8$ | $2^{6}$ | $2^{2}$ | $25$ | $C_2^2$ | Nilpotent - 2 |
64.247 | $C_2^2\times \OD_{16}$ | $2^{6}$ | $2^{3}$ | $40$ | $C_2^2\times C_4$ | Nilpotent - 2 |
64.251 | $C_2^2\times \SD_{16}$ | $2^{6}$ | $2^{3}$ | $28$ | $C_2^3$ | Nilpotent - 3 |
72.31 | $C_3^2:Q_8$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $21$ | $C_2$ | Solvable - 2 |
72.33 | $C_3:D_{12}$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $21$ | $C_2$ | Solvable - 2 |
72.34 | $C_6.D_6$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $24$ | $C_2^2$ | Solvable - 2 |
80.43 | $C_2^2.D_{10}$ | $2^{4} \cdot 5$ | $2^{2} \cdot 5$ | $32$ | $C_2^3$ | Solvable - 2 |
81.13 | $C_9:C_3^2$ | $3^{4}$ | $3^{2}$ | $33$ | $C_3^2$ | Nilpotent - 2 |
88.11 | $C_2\times D_{22}$ | $2^{3} \cdot 11$ | $2 \cdot 11$ | $28$ | $C_2^2$ | Solvable - 2 |
94.1 | $D_{47}$ | $2 \cdot 47$ | $2 \cdot 47$ | $25$ | $C_1$ | Solvable - 2 |
96.76 | $C_{12}:Q_8$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $30$ | $C_2^2$ | Solvable - 2 |
96.78 | $S_3\times C_4^2$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $48$ | $C_4^2$ | Solvable - 2 |
96.127 | $C_{12}.C_2^3$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $48$ | $C_2^2\times C_4$ | Solvable - 2 |
96.129 | $C_6:C_4^2$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $48$ | $C_2^2\times C_4$ | Solvable - 2 |
96.132 | $C_2^2.D_{12}$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $36$ | $C_2^3$ | Solvable - 2 |
96.152 | $C_3:C_4\times Q_8$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $30$ | $C_2^2$ | Solvable - 2 |
96.159 | $C_2^3.D_6$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $36$ | $C_2^3$ | Solvable - 2 |
96.160 | $C_2^4:S_3$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $30$ | $C_2^2$ | Solvable - 2 |
96.174 | $C_{12}:D_4$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $42$ | $C_2\times C_6$ | Nilpotent - 2 |
96.212 | $Q_8\times D_6$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $30$ | $C_2^2$ | Solvable - 2 |
96.213 | $Q_8:D_6$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $30$ | $C_2^2$ | Solvable - 2 |
96.214 | $Q_8.D_6$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $27$ | $C_2$ | Solvable - 2 |
96.221 | $C_{12}:C_2^3$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $60$ | $C_2^2\times C_6$ | Nilpotent - 2 |