Finite Group DatabasebetaFinite Group Databasebeta| order | 18430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D485 |
| unambiguous semidirect product | C5⋊(C19×D97) |
| unambiguous semidirect product | C97⋊(D5×C19) |
| Fitting, socle, Hall | C5×C19×C97 ⋊ C2 |
| derived, Hall | C5×C97 ⋊ C2×C19 |
| Hall | C19×C97 ⋊ D5 |
| Sylow | C97 ⋊ D5×C19 |
| Hall | C5×C19 ⋊ D97 |
| Sylow | C5 ⋊ C19×D97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D485 |
| commutator, cosocle, hypocenter | C5×C97 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C97 | C2 |
| LCS | G ▷ C5×C97 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9215 |
4636 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#14515595, C19×#14515594, C19⋊#14515595, … |
| maximal normal subgroup of | C19×#14515595, C19×#14515594, C19⋊#14515595, … |
| maximal quotient of | C19×Dic485, C2×C19×D485 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18430, 6);