Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C24 |
| direct product | C131×#19812 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C131 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C131 |
| prime radical | C2×D4×C131 | C2×D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C42×C131 ◁ G | |
616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 155 |
| transitive degree | μt(G) = 16768 |
A minimal faithful permutation representation — 4 generators on 155 points:
(2,5)(3,8)(6,7)(9,10,13,16)(11,17,19,24)(12,20,22,15)(14,21,23,18)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155);(1,2,4,7)(3,6,8,5);(9,11,13,19)(10,14,16,23)(12,21,22,18)(15,24,20,17);(2,6)(3,8)(5,7)5240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 12800);