Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | D13×#11925897 |
| Fitting, socle, derived, Hall | C112×C13 ⋊ C22×C5 |
| Hall | C13×#10597244 ⋊ C22 |
| Hall | C11×D11×D13 ⋊ C5 |
| Hall | #10597244 ⋊ C2×D13 |
| Sylow | C112 ⋊ C2×C5×D13 |
| Sylow | C13 ⋊ C2×#11925897 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C13 | C22×C5 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1430 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 126);