Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C131 · Schur multiplier (H2) = C24 |
| direct product | C131×#21606 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C131 | C24 |
| commutator | C23 | C23×C4×C131 |
| Frattini, cosocle | C22×C4 | C24×C131 |
| socle | C23×C131 | C23×C4 |
| prime radical | C24×C131 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C131 ◁ G | |
834 conjugacy classes of subgroups.
| minimal degree | μ(G) = 159 |
| transitive degree | μt(G) = 16768 |
A minimal faithful permutation representation — 4 generators on 159 points:
(1,2)(3,4)(5,6)(7,12)(8,10)(9,11)(13,14,18,21,17,20,27,16)(15,22,25,26,23,19,28,24)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159);(5,7,9,8)(6,10,11,12)(13,15,17,23)(14,19,20,22)(16,26,21,24)(18,25,27,28);(2,4)(14,20)(15,23)(16,21)(25,28);(5,8,9,7)(6,10,11,12)(13,16,27,20,17,21,18,14)(15,24,28,19,23,26,25,22)9956 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 14594);