Finite Group DatabasebetaFinite Group Databasebeta| order | 31314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D307⋊C3)⋊C17 |
| unambiguous semidirect product | (D307⋊C17)⋊C3 |
| unambiguous semidirect product | ((C307⋊C3)⋊C17)⋊C2 |
| Fitting, socle, derived, Sylow | C307 ⋊ C2×C3×C17 |
| Hall | (C307⋊C3)⋊C17 ⋊ C2 |
| Hall | D307⋊C17 ⋊ C3 |
| Hall | C307⋊C17 ⋊ C2×C3 |
| Hall | D307⋊C3 ⋊ C17 |
| Hall | C307⋊C3 ⋊ C2×C17 |
| Hall | D307 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C307 | C2×C3×C17 |
| LCS | G ▷ C307 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 307 |
Polycyclic presentation:
2,3,17,307|d^a=d^306,d^b=d^289,d^c=d^81105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31314, 18);