Finite Group DatabasebetaFinite Group Databasebeta| order | 31372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic341 |
| unambiguous semidirect product | C11⋊(C23×Dic31) |
| unambiguous semidirect product | C31⋊(C23×Dic11) |
| derived, Hall | C11×C31 ⋊ C4×C23 |
| Hall | C11×C23×C31 ⋊ C4 |
| Hall | C23×C31 ⋊ Dic11 |
| Hall | C11×C23 ⋊ Dic31 |
| Sylow | C31 ⋊ C23×Dic11 |
| Sylow | C11 ⋊ C23×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D341 |
| commutator, hypocenter | C11×C31 | C4×C23 |
| Frattini | C2 | C23×D341 |
| Fitting, socle, prime radical | C2×C11×C23×C31 | C2 |
| cosocle | C2×C11×C31 | C2×C23 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C2×C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31372 |
7912 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31372, 7);