Finite Group DatabasebetaFinite Group Databasebeta| order | 32526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#24925709 |
| Fitting, socle, derived | C3×C13×C139 ⋊ C2×C3 |
| Hall | C3×#19129428 ⋊ C2 |
| Hall | C13×C139 ⋊ C3×D3 |
| Sylow | C139 ⋊ C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ D3×C139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C139 | C2×C3 |
| LCS | G ▷ C3×C13×C139 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 155 |
| transitive degree | μt(G) = 5421 |
A minimal faithful permutation representation — 2 generators on 155 points:
(2,3)(5,9,10,6,7,11)(8,15,14,12,13,16)(18,19,21)(20,23,28)(22,26,25)(24,30,38)(27,33,35)(29,36,32)(31,40,51)(34,43,48)(37,46,45)(39,49,42)(41,53,67)(44,56,64)(47,59,61)(50,62,58)(52,65,55)(54,69,86)(57,72,83)(60,75,80)(63,78,77)(66,81,74)(68,84,71)(70,88,107)(73,91,104)(76,94,102)(79,97,99)(82,100,96)(85,89,93)(87,105,90)(92,110,125)(95,113,123)(98,116,121)(101,119,118)(103,111,115)(106,124,112)(108,126,109)(114,129,139)(117,131,138)(120,134,136)(122,130,133)(127,140,128)(132,141,148)(135,143,147)(137,142,145)(144,149,153)(146,150,152)(151,154,155);(1,2,3)(4,5,8,7,11,14,13,15,16,10,9,12,6)(17,18,20,24,31,41,54,70,89,65,38,48,61,77,96,115,88,108,127,126,86,104,123,138,147,152,141,113,72,40,52,66,82,101,120,135,144,150,134,97,59,33,19,22,27,34,44,57,73,92,111,81,49,28,35,45,58,74,93,112,128,140,105,67,83,102,121,136,145,129,91,53,68,85,103,122,137,146,151,154,143,116,75,43,23,29,37,47,60,76,95,114,130,100,62,36,21,25,32,42,55,71,90,109,124,84,51,64,80,99,118,133,110,69,87,106,107,125,139,148,153,155,149,131,94,56,30,39,50,63,79,98,117,132,142,119,78,46,26)Polycyclic presentation:
2,3^2,13,139|c^a=c^2,d^a=d^12,d^b=d^3,e^b=e^42981 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32526, 47);