Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C26 |
| direct product | C131×#24422 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C131 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C22×C4×C131 ◁ G | |
1300 conjugacy classes of subgroups.
| minimal degree | μ(G) = 163 |
| transitive degree | μt(G) = 4192 |
A minimal faithful permutation representation — 4 generators on 163 points:
(1,2,7,11,6,4,8,12)(3,9,16,24,15,18,17,13)(5,10,21,25,20,19,22,26)(14,23,29,27,28,31,30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163);(1,3,6,15)(2,9,4,18)(5,14,20,28)(7,17,8,16)(10,23,19,31)(11,13,12,24)(21,30,22,29)(25,32,26,27);(1,4)(2,6)(3,13)(5,19)(7,11)(8,12)(9,17)(10,20)(14,27)(15,24)(16,18)(21,25)(22,26)(23,29)(28,32)(30,31);(1,5)(2,10)(3,14)(4,19)(6,20)(7,22)(8,21)(9,23)(11,26)(12,25)(13,27)(15,28)(16,30)(17,29)(18,31)(24,32)5240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 17410);