Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C22×C42 |
| direct product | C131×#33249 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C131 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ #376×C131 ◁ G | |
838 conjugacy classes of subgroups.
| minimal degree | μ(G) = 175 |
| transitive degree | μt(G) = 33536 |
A minimal faithful permutation representation — 4 generators on 175 points:
(2,4)(5,6)(7,10)(8,9)(11,12)(13,14,19,24)(15,25,30,43)(16,31,32,22)(17,21,34,40)(18,35,26,23)(20,36,39,29)(27,42,44,37)(28,41,33,38)(45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175);(6,9)(10,12)(13,15,26,36,19,30,18,29)(14,20,35,43,24,39,23,25)(16,27,34,28,32,44,17,33)(21,37,22,41,40,42,31,38);(1,2,3,4)(13,16,26,34,19,32,18,17)(14,21,35,22,24,40,23,31)(15,27,36,28,30,44,29,33)(20,37,43,41,39,42,25,38);(5,7,8,11)(6,10,9,12)(13,17,18,32,19,34,26,16)(14,22,23,21,24,31,35,40)(15,28,29,27,30,33,36,44)(20,38,25,42,39,41,43,37)6812 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 26237);