G |
Aut(G) |
Order of G |
Number of involutions |
Number of Polytopes |
Alt(5) = PSL(2,4) = PSL(2,5) |
Sym(5) |
60 |
15 |
2 |
Sym(5) |
Sym(5) |
120 |
25 |
5 = 4+1 |
PSL(3,2) = PSL(2,7) |
PΓL(2,7) |
168 |
21 |
0 |
PGL(2,7) = PΓL(2,7) |
PΓL(2,7) |
336 |
49 |
16 |
Alt(6) = PSL(2,9) |
PΓL(2,9) |
360 |
45 |
0 |
PGL(2,9) |
PΓL(2,9) |
720 |
81 |
14 |
PΣL(2,9) |
PΓL(2,9) |
720 |
75 |
7 = 2+4+1 |
M10 |
PΓL(2,9) |
720 |
45 |
0 |
PΓL(2,9) |
PΓL(2,9) |
1440 |
111 |
12 |
PSL(2,8) = PGL(2,8) |
PΓL(2,8) |
504 |
63 |
7 |
PΓL(2,8) = PΣL(2,8) |
PΓL(2,8) |
1512 |
63 |
0 |
PSL(2,11) = PΣL(2,11) |
PΓL(2,11) |
660 |
55 |
4 = 3+1 |
PGL(2,11) = PΓL(2,11) |
PΓL(2,11) |
1320 |
121 |
42 |
PSL(2,13) = PΣL(2,13) |
PΓL(2,13) |
1092 |
91 |
11 |
PGL(2,13) = PΓL(2,13) |
PΓL(2,13) |
2184 |
169 |
59 |
PSL(2,17) = PΣL(2,17) |
PΓL(2,17) |
2448 |
153 |
16 |
PGL(2,17) = PΓL(2,17) |
PΓL(2,17) |
4896 |
289 |
110 |
PSL(2,19) = PΣL(2,19) |
PΓL(2,19) |
3420 |
171 |
18 = 17+1 |
PGL(2,19) = PΓL(2,19) |
PΓL(2,19) |
6840 |
361 |
140 |
PSL(2,16) = PGL(2,16) |
PΓL(2,16) |
4080 |
255 |
27 |
PSL(2,16):2 |
PΓL(2,16) |
8160 |
323 |
26 = 21+5 |
PΓL(2,16) = PΣL(2,16) |
PΓL(2,16) |
16320 |
323 |
0 |
PSL(3,3) = PGL(3,3) = PΣL(3,3) = PΓL(3,3) |
PSL(3,3):2 |
5616 |
117 |
0 |
PSL(3,3):2 |
PSL(3,3):2 |
11232 |
351 |
68 = 67+1 |
PSL(2,23) = PΣL(2,23) |
PΓL(2,23) |
6072 |
253 |
28 |
PGL(2,23) = PΓL(2,23) |
PΓL(2,23) |
12144 |
529 |
212 |
PSL(2,25) |
PΓL(2,25) |
7800 |
325 |
17 |
PGL(2,25) |
PΓL(2,25) |
15600 |
625 |
127 |
PΣL(2,25) |
PΓL(2,25) |
15600 |
455 |
51 = 34+17 |
PSL(2,25).2 |
PΓL(2,25) |
7800 |
325 |
0 |
PΓL(2,25) |
PΓL(2,25) |
31200 |
755 |
64 |
PSL(2,27) |
PΓL(2,27) |
9828 |
351 |
14 |
PGL(2,27) |
PΓL(2,27) |
19656 |
729 |
98 |
PΣL(2,27) |
PΓL(2,27) |
29484 |
351 |
0 |
PΓL(2,27) |
PΓL(2,27) |
58968 |
729 |
0 |
PSL(2,29) = PΣL(2,29) |
PΓL(2,29) |
12180 |
435 |
50 |
PGL(2,29) = PΓL(2,29) |
PΓL(2,29) |
24360 |
841 |
337 |
PSL(2,31) = PΣL(2,31) |
PΓL(2,31) |
14880 |
465 |
51 |
PGL(2,31) = PΓL(2,31) |
PΓL(2,31) |
29760 |
961 |
394 |
PSL(3,4) |
PSL(3,4).D12 |
20160 |
315 |
0 |
PSL(3,4).21 |
PSL(3,4).D12 |
40320 |
595 |
4 |
PSL(3,4).3 = PGL(3,4) |
PSL(3,4).D12 |
60480 |
315 |
0 |
PSL(3,4).3.23 |
PSL(3,4).D12 |
120960 |
1323 |
52 = 50+2 |
PSL(3,4).3.22 = PΓL(3,4) |
PSL(3,4).D12 |
120960 |
675 |
0 |
PSL(3,4).6 |
PSL(3,4).D12 |
120960 |
595 |
0 |
PSL(3,4).D12 |
PSL(3,4).D12 |
241920 |
1963 |
119 = 100+16+3 |
PSL(3,4).23 |
PSL(3,4).22 |
40320 |
651 |
53 = 44+9 |
PSL(3,4).22 = PΣL(3,4) |
PSL(3,4).22 |
40320 |
435 |
0 |
PSL(3,4).22 |
PSL(3,4).22 |
80640 |
1051 |
147 = 88+59 |
PSL(2,32) = PGL(2,32) |
PΓL(2,32) |
32736 |
1023 |
93 |
PΓL(2,32) = PΣL(2,32) |
PΓL(2,32) |
163680 |
1023 |
0 |
PSL(3,5) = PΣL(3,5) = PGL(3,5) = PΓL(3,5) |
PSL(3,5):2 |
372000 |
775 |
0 |
PSL(3,5):2 |
PSL(3,5):2 |
744000 |
3875 |
498 = 496+2 |
PSL(4,3) |
PGL(4,3):2 |
6065280 |
7371 |
18 = 9+9 |