Finite Group DatabasebetaFinite Group Databasebeta| order | 3230 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D323 |
| unambiguous semidirect product | C17⋊(C5×D19) |
| unambiguous semidirect product | C19⋊(C5×D17) |
| Fitting, socle, Hall | C5×C17×C19 ⋊ C2 |
| derived, Hall | C17×C19 ⋊ C2×C5 |
| Hall | C5×C19 ⋊ D17 |
| Hall | C5×C17 ⋊ D19 |
| Sylow | C19 ⋊ C5×D17 |
| Sylow | C17 ⋊ C5×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D323 |
| commutator, cosocle, hypocenter | C17×C19 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C19 | C2 |
| LCS | G ▷ C17×C19 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1615 |
815 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×D323, C5×D1615, C52×D323, … |
| maximal normal subgroup of | C25×D323, C52×D323, C5×C7×D323, … |
| maximal quotient of | C25×D323, C5×D1615, C52×D323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3230, 4);