Finite Group DatabasebetaFinite Group Databasebeta| order | 31148 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C599 ⋊ C2×C13 |
| derived, Sylow | C599 ⋊ C22×C13 |
| Hall | C599⋊C13 ⋊ C22 |
| Hall | C2×D599 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D599⋊C13 |
| commutator, cosocle, hypocenter | C599 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C599 | C2×C13 |
| LCS | G ▷ C599 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1198 |
98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31148, 8);