Finite Group DatabasebetaFinite Group Databasebeta| order | 31314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D307⋊C3 |
| unambiguous semidirect product | (C17×D307)⋊C3 |
| Fitting, socle, Hall | C17×C307 ⋊ C2×C3 |
| derived, Sylow | C307 ⋊ C2×C3×C17 |
| Hall | C17×C307⋊C3 ⋊ C2 |
| Hall | C17×D307 ⋊ C3 |
| Hall | C307⋊C3 ⋊ C2×C17 |
| Hall | D307 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D307⋊C3 |
| commutator, cosocle, hypocenter | C307 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C307 | C2×C3 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5219 |
969 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31314, 15);