Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C11 |
| direct product | C13×#14559075 |
| Fitting, socle, Hall | C112×C13 ⋊ Dic5 |
| derived, Hall | #10597245 ⋊ C4×C13 |
| Hall | C13×#10597245 ⋊ C4 |
| Sylow | C112 ⋊ C13×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #14559075 |
| commutator, hypocenter | #10597245 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C112×C13 | Dic5 |
| prime radical | C13×#11925893 | C2 |
| cosocle | #11925893 | C2×C13 |
| LCS | G ▷ #10597245 | |
| UCS | C1 ◁ C13 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 286 |
182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 92);