Finite Group DatabasebetaFinite Group Databasebeta| order | 31372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C31⋊(Dic23⋊C11) |
| unambiguous semidirect product | (C23⋊C11)⋊Dic31 |
| unambiguous semidirect product | Dic713⋊C11 |
| derived, Hall | C23×C31 ⋊ C4×C11 |
| Hall | C31×C23⋊C11 ⋊ C4 |
| Hall | Dic713 ⋊ C11 |
| Hall | C23⋊C11 ⋊ Dic31 |
| Sylow | C31 ⋊ Dic23⋊C11 |
| Sylow | C23 ⋊ C11×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C31⋊AGL(1,𝔽23) |
| commutator, hypocenter | C23×C31 | C4×C11 |
| Fitting, socle, cosocle | C2×C23×C31 | C2×C11 |
| prime radical | C2×C31×C23⋊C11 | C2 |
| LCS | G ▷ C23×C31 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2852 |
Polycyclic presentation:
2,11,23,31,2|a^2=e,c^a=c^22,d^a=d^30,c^b=c^2436 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31372, 12);