Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C131 · Schur multiplier (H2) = C23 |
| direct product | C131×#13400 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C131 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C131 |
| prime radical | #3060×C131 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C22×C4×C131 ◁ C2×#131×C131 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 163 |
| transitive degree | μt(G) = 4192 |
A minimal faithful permutation representation — 3 generators on 163 points:
(1,2)(3,12)(4,18)(5,10)(6,24)(7,11)(8,15)(9,22)(13,20)(14,29)(16,30)(17,26)(19,21)(23,32)(25,31)(27,28)(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);(1,2)(3,13)(4,19)(5,24)(6,10)(7,11)(8,16)(9,23)(12,28)(14,27)(15,26)(17,25)(18,21)(20,29)(22,32)(30,31);(1,3,6,16,7,14,5,17)(2,8,10,27,11,25,24,13)(4,20,22,31,23,28,21,15)(9,26,18,29,19,30,32,12)4454 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 6388);