Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C24 |
| direct product | C131×#24930 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C131 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| prime radical | #3013×C131 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C22×C4×C131 ◁ G | |
862 conjugacy classes of subgroups.
| minimal degree | μ(G) = 171 |
| transitive degree | μt(G) = 8384 |
A minimal faithful permutation representation — 4 generators on 171 points:
(1,2)(3,5)(4,6)(7,8)(9,10)(11,20)(12,25)(13,15)(14,19)(16,24)(17,26)(18,29)(21,30)(22,37)(23,32)(27,34)(28,33)(31,39)(35,36)(38,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171);(1,3,4,7)(2,5,6,8)(10,15)(11,21)(13,29)(17,25)(18,19)(22,36)(23,24)(26,28)(30,32)(33,34)(37,40)(38,39);(2,6)(5,8)(9,11)(10,16)(12,22)(13,23)(14,24)(15,30)(17,31)(18,32)(19,20)(21,29)(25,40)(26,36)(27,38)(28,39)(33,35)(34,37);(9,12,14,27)(10,17,19,33)(11,22,24,38)(13,28,29,26)(15,25,18,34)(16,31,20,35)(21,36,23,39)(30,40,32,37)5633 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 17918);