Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#20266599 |
| Fitting, socle, derived, Hall | C5×C192 ⋊ C2×C9 |
| Hall | C5×#15692433 ⋊ C2 |
| Hall | C5⋊(C19⋊D19) ⋊ C9 |
| Hall | #15692433 ⋊ D5 |
| Sylow | C192 ⋊ C9×D5 |
| Sylow | C5 ⋊ #20266599 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C192 | C2×C9 |
| prime radical | C5⋊#14524206 | C3 |
| cosocle | C5×#11762245 | C2×C3 |
| LCS | G ▷ C5×C192 | |
| UCS | C1 | |
264 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1805 |
A minimal faithful permutation representation — 3 generators on 43 points:
(2,3)(4,5)(7,22,16,13,24,21,17,12,19,8,15,20,10,23,14,18,9,11)(26,41,35,32,43,40,36,31,38,27,34,39,29,42,33,37,28,30);(1,2,4,5,3)(25,26,30,40,28,35,43,29,37,34,41,36,32,42,39,31,33,38,27);(6,7,11,21,9,16,24,10,18,15,22,17,13,23,20,12,14,19,8)Polycyclic presentation:
2,3^2,5,19^2|b^3=c,d^a=d^4,e^a=e^18,f^a=f^18,e^b=e^4,f^b=f^4,e^c=e^7,f^c=f^7136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 130);