Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(#4294⋊D19) |
| unambiguous semidirect product | #4294⋊D95 |
| derived, Hall | C5×C192 ⋊ C2×C9 |
| Hall | C5×C19×#4294 ⋊ C2 |
| Hall | C5⋊(C19⋊D19) ⋊ C9 |
| Hall | C19×#4294 ⋊ D5 |
| Sylow | C192 ⋊ C9×D5 |
| Sylow | C5 ⋊ #4294⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊((C19⋊C3)⋊D19) |
| commutator, hypocenter | C5×C192 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C192 | C2×C3 |
| prime radical | C3×C5⋊(C19⋊D19) | C3 |
| LCS | G ▷ C5×C192 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 52 |
| transitive degree | μt(G) = 855 |
A minimal faithful permutation representation — 2 generators on 52 points:
(2,3)(4,5)(6,10,14,8,13,9,11,7,12)(16,20,21,17,18,22)(19,28,25,23,24,30)(26,31,33,32,29,27)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52);(1,2,4,5,3)(15,16,19,25,31,28,32,18,22,27,33,21,20,26,24,29,30,23,17)(34,35,37,39,41,43,45,47,49,51,52,50,48,46,44,42,40,38,36)Polycyclic presentation:
2,3,5,19^2,3|b^3=f,c^a=c^4,d^a=d^18,e^a=e^18,d^b=d^71296 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 60);