Finite Group DatabasebetaFinite Group Databasebeta| order | 31654 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C7 |
| direct product | C19×C7⋊D119 |
| unambiguous semidirect product | C7⋊(C19×D119) |
| unambiguous semidirect product | C17⋊(C19×C7⋊D7) |
| Fitting, socle, Hall | C72×C17×C19 ⋊ C2 |
| derived, Hall | C72×C17 ⋊ C2×C19 |
| Hall | C72×C19 ⋊ D17 |
| Hall | C17×C19 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C19×D17 |
| Sylow | C17 ⋊ C19×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C7⋊D119 |
| commutator, cosocle, hypocenter | C72×C17 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C72×C17×C19 | C2 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C19 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15827 |
7942 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31654, 19);