Finite Group DatabasebetaFinite Group Databasebeta| order | 35334 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26044505 |
| Fitting, socle, derived | C3×C13×C151 ⋊ C2×C3 |
| Hall | C3×#20238114 ⋊ C2 |
| Hall | C13×C151 ⋊ C3×D3 |
| Sylow | C151 ⋊ C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ C3⋊(D151⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C151 | C2×C3 |
| LCS | G ▷ C3×C13×C151 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 167 |
| transitive degree | μt(G) = 5889 |
A minimal faithful permutation representation — 2 generators on 167 points:
(2,3)(5,9,10,6,7,11)(8,15,14,12,13,16)(18,22,23,19,20,24)(21,30,31,25,26,40)(27,43,44,33,34,57)(28,42,38,36,32,29)(35,62,63,46,47,80)(37,60,61,49,45,54)(39,41,59,51,52,55)(48,85,86,65,66,109)(50,83,84,68,64,77)(53,58,82,70,71,78)(56,98,96,74,75,73)(67,114,115,88,89,143)(69,112,113,91,87,106)(72,81,111,93,94,107)(76,127,128,99,100,102)(79,132,125,103,104,97)(90,147,148,117,118,166)(92,146,119,120,116,140)(95,110,145,122,123,141)(101,156,153,129,130,136)(105,159,157,133,134,131)(108,161,154,137,138,126)(121,167,151,150,149,164)(124,144,160,152,135,165)(139,163,155,142,162,158);(1,2,3)(4,5,8,7,11,14,13,15,16,10,9,12,6)(17,18,21,27,35,48,67,90,119,86,111,132,127,112,85,110,142,137,94,47,64,75,78,80,106,136,152,122,93,70,51,38,23,22,28,37,50,69,92,121,151,115,145,161,159,156,146,114,144,133,103,71,34,45,55,57,77,102,131,158,154,125,96,61,31,42,30,41,56,76,101,118,149,148,160,162,163,165,166,167,147,129,99,74,52,26,32,40,54,73,97,126,155,157,128,84,44,59,60,43,58,79,105,135,89,116,130,134,138,141,143,164,150,120,91,68,49,36,20,24,29,39,53,72,95,124,153,113,63,82,98,83,62,81,108,139,123,66,87,100,104,107,109,140,117,88,65,46,33,25,19)Polycyclic presentation:
2,3^2,13,151|c^a=c^2,d^a=d^12,e^a=e^150,d^b=d^3,e^b=e^118990 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35334, 46);