Finite Group DatabasebetaFinite Group Databasebeta| order | 31654 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C7×C17×D133 |
| unambiguous semidirect product | C7⋊(C7×C17×D19) |
| unambiguous semidirect product | C19⋊(C7×D7×C17) |
| Fitting, socle, Hall | C72×C17×C19 ⋊ C2 |
| derived | C7×C19 ⋊ C2×C7×C17 |
| Hall | C72×C19 ⋊ C2×C17 |
| Hall | C72×C17 ⋊ D19 |
| Hall | C17×C19 ⋊ C7×D7 |
| Sylow | C72 ⋊ C17×D19 |
| Sylow | C19 ⋊ C7×D7×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C17 | D133 |
| commutator, cosocle, hypocenter | C7×C19 | C2×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C72×C17×C19 | C2 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C7×C17 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4522 |
8092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31654, 14);