Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C5⋊#14524206) |
| unambiguous semidirect product | C5⋊(C3⋊#14524206) |
| Fitting, socle, derived | C3×C5×C192 ⋊ C2×C3 |
| Hall | C3×C5×#11762245 ⋊ C2 |
| Hall | C3×#11762245 ⋊ D5 |
| Hall | C5×C192 ⋊ C3×D3 |
| Sylow | C192 ⋊ C3×D15 |
| Sylow | C5 ⋊ C3⋊#14524206 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C192 | C2×C3 |
| LCS | G ▷ C3×C5×C192 | |
| UCS | C1 | |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 5415 |
A minimal faithful permutation representation — 3 generators on 46 points:
(2,3)(5,6)(7,8)(10,14,15,11,12,16)(13,22,19,17,18,24)(20,25,27,26,23,21)(29,33,34,30,31,35)(32,41,38,36,37,43)(39,44,46,45,42,40);(1,2,3)(4,5,7,8,6)(28,29,32,38,44,41,45,31,35,40,46,34,33,39,37,42,43,36,30);(9,10,13,19,25,22,26,12,16,21,27,15,14,20,18,23,24,17,11)Polycyclic presentation:
2,3^2,5,19^2|c^a=c^2,d^a=d^4,e^a=e^18,f^a=f^18,e^b=e^7,f^b=f^7927 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 196);