Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C131 · Schur multiplier (H2) = C23 |
| direct product | C131×#13370 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C131 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C131 |
| prime radical | C23×C131 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C22×C4×C131 ◁ #405×C131 ◁ G | |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 171 |
| transitive degree | μt(G) = 16768 |
A minimal faithful permutation representation — 3 generators on 171 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,20)(12,26)(13,18)(14,31)(15,19)(16,22)(17,29)(21,36)(23,33)(24,40)(25,38)(27,35)(28,34)(30,37)(32,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171);(1,3,4,8)(2,5,6,7)(9,10)(11,21)(12,17)(13,31)(14,18)(15,19)(16,23)(20,36)(22,33)(24,32)(25,35)(26,29)(27,38)(28,37)(30,34)(39,40);(9,11,15,25)(10,16,19,32)(12,27,30,36)(13,24,14,23)(17,33,34,40)(18,35,31,21)(20,37,38,26)(22,28,39,29)5240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 6358);