Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C25 |
| direct product | C131×#25199 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C131 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| prime radical | #3019×C131 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C22×C4×C131 ◁ G | |
990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 163 |
| transitive degree | μt(G) = 4192 |
A minimal faithful permutation representation — 4 generators on 163 points:
(1,2,7,11,8,12,6,22)(3,13,15,9,16,26,23,27)(4,17,19,28,5,20,21,10)(14,25,31,32,18,24,30,29)(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);(1,3,7,15,8,16,6,23)(2,9,11,26,12,27,22,13)(4,18,19,30,5,14,21,31)(10,25,17,32,28,24,20,29);(1,4,8,5)(2,10,12,28)(3,14,16,18)(6,19,7,21)(9,24,27,25)(11,20,22,17)(13,29,26,32)(15,30,23,31);(1,5,8,4)(2,10,12,28)(3,14,16,18)(6,19,7,21)(9,25,27,24)(11,17,22,20)(13,29,26,32)(15,31,23,30)5240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 18187);