Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C131 · Schur multiplier (H2) = C2×C4 |
| direct product | C131×#11405 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C131 | C42 |
| commutator | C4 | C2×C4×C8×C131 |
| Frattini, cosocle | C4×C8 | C23×C131 |
| socle | C22×C131 | C2×#97 |
| prime radical | C23×C131 | #97 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C131 ◁ G | |
282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 171 |
| transitive degree | μt(G) = 16768 |
A minimal faithful permutation representation — 3 generators on 171 points:
(9,10,12,16,13,18,24,32,14,17,25,31,26,33,39,40)(11,19,21,35,22,28,37,30,20,34,23,38,36,15,27,29)(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);(1,2,3,5,4,6,7,8)(9,11)(10,15,17,28)(12,23)(13,22)(14,20)(16,30,31,29)(18,19,33,34)(21,25)(24,27)(26,36)(32,38,40,35)(37,39);(11,20)(15,28)(19,34)(21,23)(22,36)(27,37)(29,30)(35,38)11528 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 4393);