Note: Search results may be incomplete due to uncomputed quantities: Outer aut. group order (4830 objects)
Refine search
Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
216.115 | $C_2^3\times \He_3$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3$ | $88$ | $C_2^2\times C_6$ | Nilpotent - 2 |
432.201 | $C_4^2\times \He_3$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $176$ | $C_4\times C_{12}$ | Nilpotent - 2 |
432.398 | $C_6^2.D_6$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $80$ | $C_2^2\times C_6$ | Solvable - 3 |
432.406 | $C_{12}.C_6^2$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $270$ | $C_6\times C_{18}$ | Nilpotent - 2 |
432.407 | $C_{12}.C_6^2$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $110$ | $C_2\times C_6$ | Nilpotent - 2 |
432.463 | $C_{12}^2:C_3$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $72$ | $C_3^2$ | Solvable - 2 |
432.551 | $C_9\times C_2^2:A_4$ | $2^{4} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $72$ | $C_9$ | Solvable - 2 |
432.553 | $C_6^2.A_4$ | $2^{4} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $72$ | $C_3^2$ | Solvable - 2 |
432.555 | $C_6^2:A_4$ | $2^{4} \cdot 3^{3}$ | $2 \cdot 3$ | $56$ | $C_3$ | Solvable - 2 |
432.556 | $C_6^2.D_6$ | $2^{4} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $144$ | $C_2^2\times C_6$ | Solvable - 2 |
432.557 | $C_2\times D_6\times C_{18}$ | $2^{4} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $216$ | $C_2^2\times C_{18}$ | Solvable - 2 |
432.558 | $C_6^2:D_6$ | $2^{4} \cdot 3^{3}$ | $2 \cdot 3$ | $80$ | $C_2^3$ | Solvable - 2 |
432.768 | $C_3:D_6^2$ | $2^{4} \cdot 3^{3}$ | $2 \cdot 3$ | $72$ | $C_2^2$ | Solvable - 2 |
432.770 | $A_4\times C_6^2$ | $2^{4} \cdot 3^{3}$ | $2 \cdot 3$ | $144$ | $C_6^2$ | Solvable - 2 |
648.25 | $C_9^2:C_8$ | $2^{3} \cdot 3^{4}$ | $2^{3} \cdot 3^{2}$ | $168$ | $C_4$ | Solvable - 2 |
648.170 | $C_9^2:Q_8$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $165$ | $C_2$ | Solvable - 2 |
648.171 | $C_{36}:D_9$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $168$ | $C_4$ | Solvable - 2 |
648.172 | $C_9:D_{36}$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $165$ | $C_2$ | Solvable - 2 |
648.192 | $C_{18}^2:C_2$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $165$ | $C_2$ | Solvable - 2 |
648.214 | $D_4\times C_9^2$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $405$ | $C_9\times C_{18}$ | Nilpotent - 2 |
648.336 | $C_6:D_{54}$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3^{3}$ | $168$ | $C_2^2$ | Solvable - 2 |
648.345 | $C_{18}.C_6^2$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3^{3}$ | $264$ | $C_2^2\times C_{18}$ | Nilpotent - 2 |
648.348 | $(C_6\times C_{18}):C_6$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3^{2}$ | $136$ | $C_2^2\times C_6$ | Nilpotent - 3 |
648.349 | $C_2\times C_3^2.C_6^2$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3^{2}$ | $136$ | $C_2^2\times C_6$ | Nilpotent - 3 |
648.512 | $(C_6\times \He_3):C_4$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $84$ | $C_2\times C_6$ | Solvable - 3 |
648.516 | $C_{18}.C_6^2$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $264$ | $C_6\times C_{12}$ | Nilpotent - 2 |
648.519 | $C_3\times D_4\times \He_3$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $165$ | $C_3\times C_6$ | Nilpotent - 2 |
648.527 | $C_3^3:C_{24}$ | $2^{3} \cdot 3^{4}$ | $2^{3} \cdot 3$ | $216$ | $C_3\times C_{12}$ | Solvable - 2 |
648.622 | $D_9\times C_6^2$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3^{2}$ | $216$ | $C_6^2$ | Solvable - 2 |
648.623 | $C_6^2:C_{18}$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3^{2}$ | $324$ | $C_6\times C_{18}$ | Solvable - 2 |
648.628 | $C_6^2:D_9$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3^{2}$ | $180$ | $C_2\times C_6$ | Solvable - 2 |
648.629 | $C_6^2:C_{18}$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3^{2}$ | $216$ | $C_2\times C_{18}$ | Solvable - 2 |
648.631 | $C_3\times C_6^2:S_3$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3$ | $120$ | $C_6^2$ | Solvable - 3 |
648.645 | $C_3^4:C_8$ | $2^{3} \cdot 3^{4}$ | $2^{3} \cdot 3$ | $48$ | $C_2$ | Solvable - 2 |
648.668 | $C_3^3:(C_4\times S_3)$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $72$ | $C_2$ | Solvable - 2 |
648.669 | $C_3^3:(C_4\times S_3)$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $72$ | $C_2$ | Solvable - 2 |
648.670 | $C_3^4:D_4$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $69$ | $C_2$ | Solvable - 2 |
648.671 | $C_3^3:D_{12}$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $69$ | $C_2$ | Solvable - 2 |
648.672 | $C_3^4:Q_8$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $69$ | $C_2$ | Solvable - 2 |
648.684 | $C_3^4:Q_8$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $189$ | $C_3\times C_6$ | Solvable - 2 |
648.685 | $C_3^2\wr C_2\times C_4$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $216$ | $C_3\times C_{12}$ | Solvable - 2 |
648.686 | $C_3^3:D_{12}$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $189$ | $C_3\times C_6$ | Solvable - 2 |
648.688 | $C_3^4:D_4$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $189$ | $C_3\times C_6$ | Solvable - 2 |
648.745 | $C_2\times C_3^4:C_4$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $48$ | $C_2$ | Solvable - 2 |
648.750 | $C_3^4:C_2^3$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3$ | $72$ | $C_2$ | Solvable - 2 |
864.87 | $C_4^2\times D_{27}$ | $2^{5} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $240$ | $C_4^2$ | Solvable - 2 |
864.90 | $C_4:D_{108}$ | $2^{5} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $222$ | $C_2^2$ | Solvable - 2 |
864.136 | $C_{108}.C_2^3$ | $2^{5} \cdot 3^{3}$ | $2^{3} \cdot 3^{3}$ | $240$ | $C_2^2\times C_4$ | Solvable - 2 |
864.138 | $C_{54}:C_4^2$ | $2^{5} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $240$ | $C_2^2\times C_4$ | Solvable - 2 |
864.141 | $C_2^2.D_{108}$ | $2^{5} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $228$ | $C_2^3$ | Solvable - 2 |