Finite Group DatabasebetaFinite Group Databasebeta| order | 31234 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C97 · Schur multiplier (H2) = C1 |
| direct product | C97×D161 |
| unambiguous semidirect product | C7⋊(D23×C97) |
| unambiguous semidirect product | C23⋊(D7×C97) |
| Fitting, socle, Hall | C7×C23×C97 ⋊ C2 |
| derived, Hall | C7×C23 ⋊ C2×C97 |
| Hall | C23×C97 ⋊ D7 |
| Hall | C7×C97 ⋊ D23 |
| Sylow | C23 ⋊ D7×C97 |
| Sylow | C7 ⋊ D23×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | D161 |
| commutator, cosocle, hypocenter | C7×C23 | C2×C97 |
| Frattini | C1 | G |
| Fitting, socle | C7×C23×C97 | C2 |
| LCS | G ▷ C7×C23 | |
| UCS | C1 ◁ C97 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15617 |
7954 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31234, 7);