Finite Group DatabasebetaFinite Group Databasebeta| order | 31372 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | D11×C23×D31 |
| unambiguous semidirect product | (D11×C31)⋊(C2×C23) |
| unambiguous semidirect product | (C11×D31)⋊(C2×C23) |
| unambiguous semidirect product | D341⋊(C2×C23) |
| Fitting, socle, Hall | C11×C23×C31 ⋊ C22 |
| derived, Hall | C11×C31 ⋊ C22×C23 |
| Hall | C23×C31 ⋊ C2×D11 |
| Hall | C11×C23 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×D11×C23 |
| Sylow | C11 ⋊ C2×C23×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D11×D31 |
| commutator, cosocle, hypocenter | C11×C31 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C11×C23×C31 | C22 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C23 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7843 |
2737 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31372, 20);