Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C131 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#1746×C131 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C131 | C23 |
| commutator | C22 | C22×C42×C131 |
| Frattini, cosocle | C22×C4 | C24×C131 |
| socle, prime radical | C24×C131 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C131 ◁ G | |
1134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 33536 |
A minimal faithful permutation representation — 4 generators on 161 points:
(1,2)(31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161);(7,8)(9,12)(10,11)(13,14)(15,16,18,21,19,22,25,28)(17,20,24,27,23,26,29,30);(3,4,5,6)(8,11)(12,14)(15,17)(16,20)(18,24)(19,23)(21,27)(22,26)(25,29)(28,30);(7,9,10,13)(8,12,11,14)(17,23)(20,26)(24,29)(27,30)14672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 13351);