Finite Group DatabasebetaFinite Group Databasebeta| order | 31654 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C7 |
| direct product | C17×C7⋊D133 |
| unambiguous semidirect product | C7⋊(C17×D133) |
| unambiguous semidirect product | C19⋊(C17×C7⋊D7) |
| Fitting, socle, Hall | C72×C17×C19 ⋊ C2 |
| derived, Hall | C72×C19 ⋊ C2×C17 |
| Hall | C72×C17 ⋊ D19 |
| Hall | C17×C19 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C17×D19 |
| Sylow | C19 ⋊ C17×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C7⋊D133 |
| commutator, cosocle, hypocenter | C72×C19 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C72×C17×C19 | C2 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C17 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15827 |
7939 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31654, 18);