Finite Group DatabasebetaFinite Group Databasebeta| order | 31372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×Dic253 |
| unambiguous semidirect product | C11⋊(C31×Dic23) |
| unambiguous semidirect product | C23⋊(C31×Dic11) |
| derived, Hall | C11×C23 ⋊ C4×C31 |
| Hall | C11×C23×C31 ⋊ C4 |
| Hall | C23×C31 ⋊ Dic11 |
| Hall | C11×C31 ⋊ Dic23 |
| Sylow | C23 ⋊ C31×Dic11 |
| Sylow | C11 ⋊ C31×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D253 |
| commutator, hypocenter | C11×C23 | C4×C31 |
| Frattini | C2 | C31×D253 |
| Fitting, socle, prime radical | C2×C11×C23×C31 | C2 |
| cosocle | C2×C11×C23 | C2×C31 |
| LCS | G ▷ C11×C23 | |
| UCS | C1 ◁ C2×C31 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31372 |
7936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31372, 8);