Finite Group DatabasebetaFinite Group Databasebeta| order | 32526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#24925708 |
| Fitting, socle, derived | C3×C13×C139 ⋊ C2×C3 |
| Hall | C3×#19129429 ⋊ 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)(76,89,101)(79,96,98)(82,99,95)(85,102,93)(87,105,90)(92,110,125)(94,111,122)(97,115,119)(100,117,116)(103,120,114)(106,123,112)(108,126,109)(113,129,138)(118,132,133)(121,134,131)(124,136,130)(127,139,128)(135,144,143)(137,145,142)(140,147,141)(146,151,150)(148,152,149)(153,155,154);(1,2,3)(4,5,8,7,11,14,13,15,16,10,9,12,6)(17,18,20,24,31,41,54,70,89,56,30,39,50,63,79,97,107,125,138,110,69,87,106,124,137,146,147,123,84,51,64,80,98,116,131,142,149,151,134,99,62,36,21,25,32,42,55,71,90,109,115,75,43,23,29,37,47,60,76,94,113,129,91,53,68,85,103,121,135,139,105,67,83,101,119,133,143,150,154,155,145,120,81,49,28,35,45,58,74,93,112,128,132,96,59,33,19,22,27,34,44,57,73,92,111,72,40,52,66,82,100,118,126,86,104,122,88,108,127,140,148,153,152,136,102,65,38,48,61,77,95,114,130,141,144,117,78,46,26)Polycyclic presentation:
2,3^2,13,139|c^a=c^2,d^a=d^12,d^b=d^3,e^b=e^96981 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32526, 48);