G |
Aut(G) |
Order of G |
Number of Polytopes |
Alt(5) = PSL(2,4) = PSL(2,5) |
Sym(5) |
60 |
0 |
Sym(5) = PGL(2,5) |
Sym(5) |
120 |
6 = 0 + 6 |
PSL(3,2) = PSL(2,7) |
PΓL(2,7) |
168 |
0 |
PGL(2,7) = PΓL(2,7) |
PΓL(2,7) |
336 |
10 = 0 + 10 |
Alt(6) = PSL(2,9) |
PΓL(2,9) |
360 |
0 |
PGL(2,9) |
PΓL(2,9) |
720 |
2 = 0 + 2 |
Sym(6) = PΣL(2,9) |
PΓL(2,9) |
720 |
4 = 2 + 0 + 2 |
M10 |
PΓL(2,9) |
720 |
0 |
PΓL(2,9) |
PΓL(2,9) |
1440 |
28 = 8 + 20 |
PSL(2,8) = PGL(2,8) |
PΓL(2,8) |
504 |
2 = 0 + 2 |
PΓL(2,8) = PΣL(2,8) |
PΓL(2,8) |
1512 |
28 = 28 |
PSL(2,11) = PΣL(2,11) |
PΓL(2,11) |
660 |
0 |
PGL(2,11) = PΓL(2,11) |
PΓL(2,11) |
1320 |
24 = 0 + 24 |
PSL(2,13) = PΣL(2,13) |
PΓL(2,13) |
1092 |
6 = 0 + 6 |
PGL(2,13) = PΓL(2,13) |
PΓL(2,13) |
2184 |
14 = 0 + 14 |
PSL(2,17) = PΣL(2,17) |
PΓL(2,17) |
2448 |
10 = 0 + 10 |
PGL(2,17) = PΓL(2,17) |
PΓL(2,17) |
4896 |
8 = 0 + 8 |
PSL(2,19) = PΣL(2,19) |
PΓL(2,19) |
3420 |
4 = 0 + 4 |
PGL(2,19) = PΓL(2,19) |
PΓL(2,19) |
6840 |
28 = 0 + 28 |
PSL(2,16) = PGL(2,16) |
PΓL(2,16) |
4080 |
2 = 0 + 2 |
PSL(2,16):2 |
PΓL(2,16) |
8160 |
48 = 32 + 16 |
PΓL(2,16) = PΣL(2,16) |
PΓL(2,16) |
16320 |
122 = 122 |
PSL(3,3) = PGL(3,3) = PΣL(3,3) = PΓL(3,3) |
PSL(3,3):2 |
5616 |
0 |
PSL(3,3):2 |
PSL(3,3):2 |
11232 |
168 = 136 + 32 |
PSL(2,23) = PΣL(2,23) |
PΓL(2,23) |
6072 |
0 |
PGL(2,23) = PΓL(2,23) |
PΓL(2,23) |
12144 |
10 = 0 + 10 |
PSL(2,25) |
PΓL(2,25) |
7800 |
2 = 0 + 2 |
PGL(2,25) |
PΓL(2,25) |
15600 |
6 = 0 + 6 |
PΣL(2,25) |
PΓL(2,25) |
15600 |
62 = 38 + 24 |
PSL(2,25).2 |
PΓL(2,25) |
15600 |
30 = 30 |
PΓL(2,25) |
PΓL(2,25) |
31200 |
152 = 108 + 44 |
PSL(2,27) |
PΓL(2,27) |
9828 |
0 |
PGL(2,27) |
PΓL(2,27) |
19656 |
4 = 0 + 4 |
PΣL(2,27) |
PΓL(2,27) |
29484 |
108 = 108 |
PΓL(2,27) |
PΓL(2,27) |
58968 |
324 = 324 |
PSL(2,29) = PΣL(2,29) |
PΓL(2,29) |
12180 |
10 = 0 + 10 |
PGL(2,29) = PΓL(2,29) |
PΓL(2,29) |
24360 |
26 = 0 + 26 |
PSL(2,31) = PΣL(2,31) |
PΓL(2,31) |
14880 |
6 = 0 + 6 |
PGL(2,31) = PΓL(2,31) |
PΓL(2,31) |
29760 |
46 = 0 + 46 |
PSL(3,4) |
PSL(3,4).D12 |
20160 |
0 |
PSL(3,4).21 |
PSL(3,4).D12 |
40320 |
28 = 24 + 4 |
PSL(3,4).3 = PGL(3,4) |
PSL(3,4).D12 |
60480 |
0 |
PSL(3,4).3.23 |
PSL(3,4).D12 |
120960 |
262 = 224 + 38 |
PSL(3,4).3.22 = PΓL(3,4) |
PSL(3,4).D12 |
120960 |
24 = 24 |
PSL(3,4).6 |
PSL(3,4).D12 |
120960 |
60 = 60 |
PSL(3,4).D12 |
PSL(3,4).D12 |
241920 |
392 = 296 + 88 + 8 |
PSL(3,4).23 |
PSL(3,4).22 |
40320 |
138 = 102 + 36 |
PSL(3,4).22 = PΣL(3,4) |
PSL(3,4).22 |
40320 |
30 = 26 + 4 |
PSL(3,4).22 |
PSL(3,4).22 |
80640 |
216 = 164 + 52 |
PSL(2,32) = PGL(2,32) |
PΓL(2,32) |
32736 |
6 = 0 + 6 |
PΓL(2,32) = PΣL(2,32) |
PΓL(2,32) |
163680 |
744 |
PSL(3,5) = PΣL(3,5) = PGL(3,5) = PΓL(3,5) |
PSL(3,5):2 |
372000 |
2 = 0 + 2 |
PSL(3,5):2 |
PSL(3,5):2 |
744000 |
2668 = 2494 + 174 |