Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#14524206⋊C5) |
| unambiguous semidirect product | (C3⋊#14524206)⋊C5 |
| unambiguous semidirect product | (C3⋊((C19⋊D19)⋊C5))⋊C3 |
| Fitting, socle, derived | C3×C192 ⋊ C2×C3×C5 |
| Hall | C3×#11762245⋊C5 ⋊ C2 |
| Hall | C3⋊#14524206 ⋊ C5 |
| Hall | C3×#11762245 ⋊ C2×C5 |
| Hall | C192⋊C5 ⋊ C3×D3 |
| Sylow | C192 ⋊ C3×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C192 | C2×C3×C5 |
| LCS | G ▷ C3×C192 | |
| UCS | C1 | |
72 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)(4,5,7,14,35)(6,25,38,42,69,30,12,41,68,75,11,56,31,67,92,10,29,15,37,91,28,27,40,39,71,26,58,16,36,73)(8,64,80,96,32,46,19,72,94,62,18,55,47,95,61,17,43,70,79,13,45,44,77,93,87,34,54,78,97,33)(9,60,82,66,86,20,24,74,65,88,23,48,53,90,57,22,52,76,84,59,21,51,81,89,63,50,49,83,98,85);(1,2,3)(4,6,13,33,63,87,86,28,26,57,85,11,30,59,62,88,61,32,10)(5,8,20,22,12,23,29,45,34,58,56,18,46,25,50,27,9,21,17)(7,15,19,43,48,55,51,41,31,60,52,16,40,24,54,49,64,44,38)(14,36,70,78,81,77,82,37,39,53,83,68,42,76,72,74,47,80,67)(35,65,75,91,97,92,94,98,66,79,96,84,90,93,73,95,69,71,89)Polycyclic presentation:
2,3,5,3,19^2|d^a=d^2,e^a=e^18,f^a=f^18,e^b=e^11,f^b=f^11,e^c=e^9f^8,f^c=e^15f^581 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 88);