Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C131 · Schur multiplier (H2) = C26 |
| direct product | C2×#2117×C131 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C131 | C2×D4 |
| commutator | C4 | C23×C8×C131 |
| Frattini, cosocle | C2×C8 | C24×C131 |
| socle | C22×C131 | C2×C22⋊C8 |
| prime radical | C22×#41×C131 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C131 ◁ C23×C8×C131 ◁ G | |
1154 conjugacy classes of subgroups.
| minimal degree | μ(G) = 165 |
| transitive degree | μt(G) = 8384 |
A minimal faithful permutation representation — 4 generators on 165 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165);(3,4,7,13,8,14,22,31,9,11,23,27,6,12,20,29)(5,15,17,32,16,25,33,30,18,28,21,34,19,10,24,26);(3,5)(4,10)(6,19)(7,21)(8,16)(9,18)(11,25)(12,28)(13,30)(14,15)(17,23)(20,33)(22,24)(26,27)(29,32)(31,34);(4,11)(10,25)(12,14)(13,27)(15,28)(26,30)(29,31)(32,34)11528 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 26327);