Finite Group DatabasebetaFinite Group Databasebeta| order | 31372 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D253⋊D31 |
| unambiguous semidirect product | D341⋊D23 |
| unambiguous semidirect product | D713⋊D11 |
| Fitting, socle, derived, Hall | C11×C23×C31 ⋊ C22 |
| Hall | C23×C31 ⋊ C2×D11 |
| Hall | C11×C31 ⋊ C2×D23 |
| Hall | C11×C23 ⋊ C2×D31 |
| Sylow | C31 ⋊ D11×D23 |
| Sylow | C23 ⋊ D11×D31 |
| Sylow | C11 ⋊ D23×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C23×C31 | C22 |
| LCS | G ▷ C11×C23×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7843 |
Polycyclic presentation:
2^2,11,23,31|d^a=d^22,e^a=e^30,c^b=c^10,d^b=d^222011 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31372, 25);