| Label |
Name |
Family name |
Order |
Exponent |
Nilp. class |
Der. length |
Comp. length |
Rank |
$\card{\mathrm{conj}(G)}$ |
Subgroups |
Subgroup classes |
Normal subgroups |
Center |
Central quotient |
Commutator |
Abelianization |
$\card{\mathrm{Aut}(G)}$ |
$\card{\mathrm{Out}(G)}$ |
Tr. deg |
Perm. deg |
$\C$-irrep deg |
$\R$-irrep deg |
$\Q$-irrep deg |
$\C$-rep deg |
$\R$-rep deg |
$\Q$-rep deg |
Type - length |
| 120.34 |
$S_5$ |
$\PSOMinus(4,2)$ |
$2^{3} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
7 |
$156$ |
$19$ |
$3$ |
$C_1$ |
$S_5$ |
$A_5$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5$ |
$1$ |
$5$ |
$5$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
Non-Solvable - 2 |
| 360.118 |
$A_6$ |
$\PSOMinus(4,3)$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
7 |
$501$ |
$22$ |
$2$ |
$C_1$ |
$A_6$ |
$A_6$ |
$C_1$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2^{2}$ |
$6$ |
$6$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
Simple |
| 7800.a |
$\PSL(2,25)$ |
$\PSOMinus(4,5)$ |
$2^{3} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{2} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
15 |
$9559$ |
$37$ |
$2$ |
$C_1$ |
$\PSL(2,25)$ |
$\PSL(2,25)$ |
$C_1$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{2}$ |
$26$ |
$26$ |
$13$ |
$13$ |
$13$ |
$13$ |
$13$ |
$13$ |
Simple |
| 8160.a |
$\SOMinus(4,4)$ |
$\PSOMinus(4,4)$ |
$2^{5} \cdot 3 \cdot 5 \cdot 17$ |
$2^{2} \cdot 3 \cdot 5 \cdot 17$ |
$-1$ |
$1$ |
$2$ |
$2$ |
16 |
$10002$ |
$47$ |
$3$ |
$C_1$ |
$\SOMinus(4,4)$ |
$\SL(2,16)$ |
$C_{2}$ |
$2^{6} \cdot 3 \cdot 5 \cdot 17$ |
$2$ |
$17$ |
$17$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
Non-Solvable - 2 |
| 51840.b |
$\SO(5,3)$ |
$\PSOMinus(6,2)$ |
$2^{7} \cdot 3^{4} \cdot 5$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
25 |
|
|
|
$C_1$ |
$\SO(5,3)$ |
$\SU(4,2)$ |
$C_{2}$ |
$2^{7} \cdot 3^{4} \cdot 5$ |
$1$ |
|
$27$ |
$6$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 58800.a |
$\PSL(2,49)$ |
$\PSOMinus(4,7)$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ |
$2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
27 |
$73945$ |
$51$ |
$2$ |
$C_1$ |
$\PSL(2,49)$ |
$\PSL(2,49)$ |
$C_1$ |
$2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ |
$2^{2}$ |
$50$ |
$50$ |
$25$ |
$25$ |
$25$ |
$25$ |
$25$ |
$25$ |
Simple |
| 265680.a |
$\PSL(2,81)$ |
$\PSOMinus(4,9)$ |
$2^{4} \cdot 3^{4} \cdot 5 \cdot 41$ |
$2^{3} \cdot 3 \cdot 5 \cdot 41$ |
$-1$ |
$0$ |
$1$ |
$2$ |
43 |
$433087$ |
$69$ |
$2$ |
$C_1$ |
$\PSL(2,81)$ |
$\PSL(2,81)$ |
$C_1$ |
$2^{7} \cdot 3^{4} \cdot 5 \cdot 41$ |
$2^{3}$ |
$82$ |
$82$ |
$41$ |
$41$ |
$41$ |
$41$ |
$41$ |
$41$ |
Simple |
| 524160.a |
$\SOMinus(4,8)$ |
$\PSOMinus(4,8)$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
46 |
$885500$ |
$127$ |
$3$ |
$C_1$ |
$\SOMinus(4,8)$ |
$\SL(2,64)$ |
$C_{2}$ |
$2^{7} \cdot 3^{3} \cdot 5 \cdot 7 \cdot 13$ |
$3$ |
$65$ |
$65$ |
$64$ |
$64$ |
$64$ |
$64$ |
$64$ |
$64$ |
Non-Solvable - 2 |
| 885720.a |
$\PSL(2,121)$ |
$\PSOMinus(4,11)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 61$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11 \cdot 61$ |
$-1$ |
$0$ |
$1$ |
$2$ |
63 |
$976309$ |
$63$ |
$2$ |
$C_1$ |
$\PSL(2,121)$ |
$\PSL(2,121)$ |
$C_1$ |
$2^{5} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 61$ |
$2^{2}$ |
$122$ |
$122$ |
$61$ |
$61$ |
$61$ |
$61$ |
$61$ |
$61$ |
Simple |
| 2413320.a |
$\PSL(2,169)$ |
$\PSOMinus(4,13)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \cdot 17$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
87 |
$2782197$ |
$71$ |
$2$ |
$C_1$ |
$\PSL(2,169)$ |
$\PSL(2,169)$ |
$C_1$ |
$2^{5} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \cdot 17$ |
$2^{2}$ |
$170$ |
$170$ |
$85$ |
$85$ |
$85$ |
$85$ |
$85$ |
$85$ |
Simple |
| 6531840.b |
$\PSOMinus(6,3)$ |
$\PSOMinus(6,3)$ |
$2^{8} \cdot 3^{6} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
34 |
$33884546$ |
$983$ |
$3$ |
$C_1$ |
$\PSOMinus(6,3)$ |
$\PSU(4,3)$ |
$C_{2}$ |
$2^{10} \cdot 3^{6} \cdot 5 \cdot 7$ |
$2^{2}$ |
$112$ |
$112$ |
$21$ |
$21$ |
$21$ |
? |
? |
? |
Non-Solvable - 2 |
| 12068640.a |
$\PSL(2,289)$ |
$\PSOMinus(4,17)$ |
$2^{5} \cdot 3^{2} \cdot 5 \cdot 17^{2} \cdot 29$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 17 \cdot 29$ |
$-1$ |
$0$ |
$1$ |
$2$ |
147 |
$13798153$ |
$82$ |
$2$ |
$C_1$ |
$\PSL(2,289)$ |
$\PSL(2,289)$ |
$C_1$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 17^{2} \cdot 29$ |
$2^{2}$ |
$290$ |
$290$ |
$145$ |
$145$ |
$145$ |
? |
? |
? |
Simple |
| 23522760.a |
$\PSL(2,361)$ |
$\PSOMinus(4,19)$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19^{2} \cdot 181$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \cdot 181$ |
$-1$ |
$0$ |
$1$ |
$2$ |
183 |
$26654969$ |
$89$ |
$2$ |
$C_1$ |
$\PSL(2,361)$ |
$\PSL(2,361)$ |
$C_1$ |
$2^{5} \cdot 3^{2} \cdot 5 \cdot 19^{2} \cdot 181$ |
$2^{2}$ |
$362$ |
$362$ |
$181$ |
$181$ |
$181$ |
? |
? |
? |
Simple |
| 33553920.a |
$\SOMinus(4,16)$ |
$\PSOMinus(4,16)$ |
$2^{9} \cdot 3 \cdot 5 \cdot 17 \cdot 257$ |
$2^{2} \cdot 3 \cdot 5 \cdot 17 \cdot 257$ |
$-1$ |
$1$ |
$2$ |
$2$ |
154 |
|
|
|
$C_1$ |
$\SOMinus(4,16)$ |
$\SL(2,256)$ |
$C_{2}$ |
$2^{11} \cdot 3 \cdot 5 \cdot 17 \cdot 257$ |
$2^{2}$ |
|
$257$ |
$256$ |
$256$ |
$256$ |
? |
? |
? |
Non-Solvable - 2 |
| 74017680.a |
$\PSL(2,529)$ |
$\PSOMinus(4,23)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 23^{2} \cdot 53$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11 \cdot 23 \cdot 53$ |
$-1$ |
$0$ |
$1$ |
$2$ |
267 |
$78076325$ |
$83$ |
$2$ |
$C_1$ |
$\PSL(2,529)$ |
$\PSL(2,529)$ |
$C_1$ |
$2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 23^{2} \cdot 53$ |
$2^{2}$ |
$530$ |
$530$ |
$265$ |
$265$ |
$265$ |
? |
? |
? |
Simple |
| 122070000.a |
$\PSL(2,625)$ |
$\PSOMinus(4,25)$ |
$2^{4} \cdot 3 \cdot 5^{4} \cdot 13 \cdot 313$ |
$2^{3} \cdot 3 \cdot 5 \cdot 13 \cdot 313$ |
$-1$ |
$0$ |
$1$ |
$2$ |
315 |
$164077421$ |
$131$ |
$2$ |
$C_1$ |
$\PSL(2,625)$ |
$\PSL(2,625)$ |
$C_1$ |
$2^{7} \cdot 3 \cdot 5^{4} \cdot 13 \cdot 313$ |
$2^{3}$ |
$626$ |
$626$ |
$313$ |
$313$ |
$313$ |
? |
? |
? |
Simple |
| 193709880.a |
$\PSL(2,729)$ |
$\PSOMinus(4,27)$ |
$2^{3} \cdot 3^{6} \cdot 5 \cdot 7 \cdot 13 \cdot 73$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 73$ |
$-1$ |
$0$ |
$1$ |
$2$ |
367 |
|
|
|
$C_1$ |
$\PSL(2,729)$ |
$\PSL(2,729)$ |
$C_1$ |
$2^{5} \cdot 3^{7} \cdot 5 \cdot 7 \cdot 13 \cdot 73$ |
$2^{2} \cdot 3$ |
|
$730$ |
$365$ |
$365$ |
? |
? |
? |
? |
Simple |
| 297411240.a |
$\PSL(2,841)$ |
$\PSOMinus(4,29)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29^{2} \cdot 421$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 29 \cdot 421$ |
$-1$ |
$0$ |
$1$ |
$2$ |
423 |
$349672921$ |
$111$ |
$2$ |
$C_1$ |
$\PSL(2,841)$ |
$\PSL(2,841)$ |
$C_1$ |
$2^{5} \cdot 3 \cdot 5 \cdot 7 \cdot 29^{2} \cdot 421$ |
$2^{2}$ |
$842$ |
$842$ |
$421$ |
$421$ |
$421$ |
? |
? |
? |
Simple |
| 394813440.a |
$\SOMinus(8,2)$ |
$\PSOMinus(8,2)$ |
$2^{13} \cdot 3^{4} \cdot 5 \cdot 7 \cdot 17$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17$ |
$-1$ |
$1$ |
$2$ |
$2$ |
60 |
|
|
|
$C_1$ |
$\SOMinus(8,2)$ |
$\OmegaMinus(8,2)$ |
$C_{2}$ |
$2^{13} \cdot 3^{4} \cdot 5 \cdot 7 \cdot 17$ |
$1$ |
|
$119$ |
$34$ |
$34$ |
$34$ |
? |
? |
? |
Non-Solvable - 2 |
| 443751360.a |
$\PSL(2,961)$ |
$\PSOMinus(4,31)$ |
$2^{6} \cdot 3 \cdot 5 \cdot 13 \cdot 31^{2} \cdot 37$ |
$2^{5} \cdot 3 \cdot 5 \cdot 13 \cdot 31 \cdot 37$ |
$-1$ |
$0$ |
$1$ |
$2$ |
483 |
|
|
|
$C_1$ |
$\PSL(2,961)$ |
$\PSL(2,961)$ |
$C_1$ |
$2^{8} \cdot 3 \cdot 5 \cdot 13 \cdot 31^{2} \cdot 37$ |
$2^{2}$ |
|
$962$ |
$481$ |
$481$ |
? |
? |
? |
? |
Simple |
| 2036736000.a |
$\SOMinus(6,4)$ |
$\PSOMinus(6,4)$ |
$2^{13} \cdot 3^{2} \cdot 5^{3} \cdot 13 \cdot 17$ |
$2^{3} \cdot 3 \cdot 5 \cdot 13 \cdot 17$ |
$-1$ |
$1$ |
$2$ |
$2$ |
86 |
|
|
|
$C_1$ |
$\SOMinus(6,4)$ |
$\SU(4,4)$ |
$C_{2}$ |
$2^{14} \cdot 3^{2} \cdot 5^{3} \cdot 13 \cdot 17$ |
$2$ |
|
$325$ |
$52$ |
$52$ |
$52$ |
? |
? |
? |
Non-Solvable - 2 |
| 14742000000.a |
$\PSU(4,5)$ |
$\PSOMinus(6,5)$ |
$2^{7} \cdot 3^{4} \cdot 5^{6} \cdot 7 \cdot 13$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
97 |
|
|
$2$ |
$C_1$ |
$\PSU(4,5)$ |
$\PSU(4,5)$ |
$C_1$ |
$2^{9} \cdot 3^{4} \cdot 5^{6} \cdot 7 \cdot 13$ |
$2^{2}$ |
$756$ |
$756$ |
$104$ |
$105$ |
$105$ |
? |
? |
? |
Simple |
| 2331144345600.b |
$\PSOMinus(6,7)$ |
$\PSOMinus(6,7)$ |
$2^{11} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 43$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 43$ |
$-1$ |
$1$ |
$2$ |
$2$ |
226 |
|
|
$3$ |
$C_1$ |
$\PSOMinus(6,7)$ |
$\PSU(4,7)$ |
$C_{2}$ |
$2^{13} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 43$ |
$2^{2}$ |
|
$2752$ |
$300$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 10151968619520.a |
$\OmegaMinus(8,3)$ |
$\PSOMinus(8,3)$ |
$2^{10} \cdot 3^{12} \cdot 5 \cdot 7 \cdot 13 \cdot 41$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 41$ |
$-1$ |
$0$ |
$1$ |
$2$ |
112 |
|
|
|
$C_1$ |
$\OmegaMinus(8,3)$ |
$\OmegaMinus(8,3)$ |
$C_1$ |
$2^{12} \cdot 3^{12} \cdot 5 \cdot 7 \cdot 13 \cdot 41$ |
$2^{2}$ |
|
$1066$ |
$246$ |
? |
? |
? |
? |
? |
Simple |
| 69387579555840.a |
$\SOMinus(6,8)$ |
$\PSOMinus(6,8)$ |
$2^{19} \cdot 3^{7} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 19$ |
$2^{3} \cdot 3^{3} \cdot 5 \cdot 7 \cdot 13 \cdot 19$ |
$-1$ |
$1$ |
$2$ |
$2$ |
424 |
|
|
|
$C_1$ |
$\SOMinus(6,8)$ |
$\SU(4,8)$ |
$C_{2}$ |
$2^{19} \cdot 3^{8} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 19$ |
$3$ |
|
$4617$ |
$456$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
