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 |
---|---|---|---|---|---|---|
216.1 | $C_{27}:C_8$ | $2^{3} \cdot 3^{3}$ | $2^{3} \cdot 3^{3}$ | $60$ | $C_4$ | Solvable - 2 |
216.5 | $C_4\times D_{27}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $60$ | $C_4$ | Solvable - 2 |
216.8 | $C_{27}:D_4$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $57$ | $C_2$ | Solvable - 2 |
216.17 | $\He_3:C_8$ | $2^{3} \cdot 3^{3}$ | $2^{3} \cdot 3$ | $40$ | $C_{12}$ | Solvable - 3 |
216.19 | $C_8\times \He_3$ | $2^{3} \cdot 3^{3}$ | $2^{3} \cdot 3$ | $88$ | $C_{24}$ | Nilpotent - 2 |
216.21 | $C_2^2:D_{27}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $21$ | $C_1$ | Solvable - 3 |
216.26 | $C_6.D_{18}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $33$ | $C_2$ | Solvable - 2 |
216.27 | $C_6.D_{18}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $36$ | $C_2$ | Solvable - 2 |
216.28 | $C_6.D_{18}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $36$ | $C_2$ | Solvable - 2 |
216.29 | $C_3:D_{36}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $33$ | $C_2$ | Solvable - 2 |
216.30 | $C_6.D_{18}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $36$ | $C_2$ | Solvable - 2 |
216.31 | $D_6:D_9$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $33$ | $C_2$ | Solvable - 2 |
216.32 | $C_9:D_{12}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $33$ | $C_2$ | Solvable - 2 |
216.33 | $C_6.S_3^2$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $19$ | $C_2$ | Solvable - 3 |
216.35 | $\He_3:D_4$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $19$ | $C_2$ | Solvable - 3 |
216.36 | $C_6.S_3^2$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $22$ | $C_2$ | Solvable - 3 |
216.40 | $C_3^2.\SL(2,3)$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $63$ | $C_3\times C_6$ | Solvable - 3 |
216.41 | $C_3^2.\SL(2,3)$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $31$ | $C_6$ | Solvable - 3 |
216.42 | $C_3^2:\SL(2,3)$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $31$ | $C_6$ | Solvable - 3 |
216.43 | $C_{36}.C_6$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $63$ | $C_6$ | Solvable - 2 |
216.46 | $C_3\times D_{36}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $63$ | $C_6$ | Solvable - 2 |
216.49 | $\He_3:Q_8$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $31$ | $C_2$ | Solvable - 2 |
216.51 | $C_3^2:D_{12}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $31$ | $C_2$ | Solvable - 2 |
216.55 | $C_{18}:C_{12}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $72$ | $C_2\times C_6$ | Solvable - 2 |
216.59 | $C_6^2.C_6$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $40$ | $C_2^2$ | Solvable - 2 |
216.67 | $C_4\times C_3^2:S_3$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $40$ | $C_{12}$ | Solvable - 3 |
216.72 | $C_6^2:S_3$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $31$ | $C_6$ | Solvable - 3 |
216.76 | $C_{12}:C_{18}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $135$ | $C_3\times C_{18}$ | Nilpotent - 2 |
216.81 | $C_{36}.C_6$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $55$ | $C_6$ | Nilpotent - 2 |
216.82 | $C_3^2:C_{24}$ | $2^{3} \cdot 3^{3}$ | $2^{3} \cdot 3$ | $108$ | $C_3\times C_{12}$ | Solvable - 2 |
216.96 | $D_9:A_4$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $16$ | $C_1$ | Solvable - 2 |
216.97 | $A_4\times D_9$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $24$ | $C_1$ | Solvable - 2 |
216.99 | $C_6^2:C_6$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3$ | $16$ | $C_1$ | Solvable - 2 |
216.101 | $S_3\times D_{18}$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $36$ | $C_2$ | Solvable - 2 |
216.102 | $C_6.S_3^2$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3$ | $22$ | $C_2$ | Solvable - 3 |
216.105 | $C_6^2.C_6$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $72$ | $C_3\times C_6$ | Solvable - 2 |
216.106 | $C_6^2.C_6$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $40$ | $C_6$ | Solvable - 2 |
216.107 | $C_6^2:C_6$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3$ | $40$ | $C_6$ | Solvable - 2 |
216.109 | $D_6\times C_{18}$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $108$ | $C_2\times C_{18}$ | Solvable - 2 |
216.111 | $D_{18}:C_6$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $40$ | $C_2^2$ | Solvable - 2 |
216.117 | $C_3^2:C_{24}$ | $2^{3} \cdot 3^{3}$ | $2^{3} \cdot 3$ | $36$ | $C_6$ | Solvable - 2 |
216.118 | $C_3^3:C_8$ | $2^{3} \cdot 3^{3}$ | $2^{3} \cdot 3$ | $24$ | $C_2$ | Solvable - 2 |
216.120 | $C_6.S_3^2$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $54$ | $C_6$ | Solvable - 2 |
216.121 | $C_3^3:D_4$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $45$ | $C_6$ | Solvable - 2 |
216.123 | $C_3^3:Q_8$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $45$ | $C_6$ | Solvable - 2 |
216.131 | $C_6.S_3^2$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $30$ | $C_2$ | Solvable - 2 |
216.132 | $C_3^2:D_{12}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $27$ | $C_2$ | Solvable - 2 |
216.136 | $C_6.C_6^2$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $108$ | $C_3\times C_{12}$ | Solvable - 2 |
216.139 | $C_6^2:C_6$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $81$ | $C_3\times C_6$ | Solvable - 2 |
216.155 | $C_3:F_9$ | $2^{3} \cdot 3^{3}$ | $2^{3} \cdot 3$ | $15$ | $C_1$ | Solvable - 2 |