Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#16813380⋊C3) |
| unambiguous semidirect product | (C3⋊#16813380)⋊C3 |
| Fitting, socle | C3×C192 ⋊ C3×D5 |
| derived | C3×C192⋊C5 ⋊ C2×C3 |
| Hall | C3×#11762245⋊C5 ⋊ C2 |
| Hall | C3×#11762245 ⋊ D5 |
| Hall | C192⋊C5 ⋊ C3×D3 |
| Sylow | C192 ⋊ C3×D15 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C192⋊C5 | C2×C3 |
| Fitting, socle | C3×C192 | C3×D5 |
| LCS | G ▷ C3×C192⋊C5 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 98 |
| transitive degree | μt(G) = 285 |
A minimal faithful permutation representation — 2 generators on 98 points:
(2,3)(4,6,29)(5,52,35,19,20,7)(8,98,55,97,75,92)(9,60,27,57,10,36)(11,69,62)(12,15,59,74,64,68)(13,78,28)(14,54,42,32,38,33)(16,47,66,17,45,50)(18,87,21,84,80,44)(22,88,71,24,25,61)(23,79,77,40,65,30)(26,95,73,90,67,85)(31,89,46,48,82,43)(34,94,76)(37,41,96)(39,53)(49,93,86,56,58,91)(63,72)(70,83,81);(1,2,3)(4,5,8,16,7)(6,12,31,72,30)(9,21,56,19,51)(10,26,66,24,62)(11,23,18,48,60)(13,35,80,84,79)(14,37,20,55,89)(15,41,39,82,93)(17,45,40,83,59)(22,58,95,57,94)(25,63,97,61,96)(27,49,92,68,28)(29,71,73,87,42)(32,47,91,74,70)(33,75,43,52,76)(34,77,50,85,38)(36,81,54,67,98)(44,88,69,64,86)(46,90,53,78,65)Polycyclic presentation:
2,3^2,5,19^2|c^a=c^2,d^a=d^4,e^a=ef^16,f^a=f^18,e^b=e^11,f^b=f^11,e^d=e^16f^4,f^d=e^6f^1772 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 87);