Finite Group DatabasebetaFinite Group Databasebeta| order | 31314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D307⋊C17) |
| unambiguous semidirect product | D921⋊C17 |
| unambiguous semidirect product | (C307⋊C17)⋊D3 |
| Fitting, socle, derived, Hall | C3×C307 ⋊ C2×C17 |
| Hall | C3×C307⋊C17 ⋊ C2 |
| Hall | C307⋊C17 ⋊ D3 |
| Hall | D921 ⋊ C17 |
| Sylow | C307 ⋊ D3×C17 |
| Sylow | C3 ⋊ D307⋊C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C307 | C2×C17 |
| LCS | G ▷ C3×C307 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 921 |
Polycyclic presentation:
2,3,17,307|b^a=b^2,d^a=d^306,d^c=d^8178 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31314, 14);