Finite Group DatabasebetaFinite Group Databasebeta| order | 31694 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(D53⋊C13) |
| unambiguous semidirect product | (C53⋊C13)⋊D23 |
| unambiguous semidirect product | D1219⋊C13 |
| Fitting, socle, derived, Hall | C23×C53 ⋊ C2×C13 |
| Hall | C23×C53⋊C13 ⋊ C2 |
| Hall | D1219 ⋊ C13 |
| Hall | C53⋊C13 ⋊ D23 |
| Sylow | C53 ⋊ C13×D23 |
| Sylow | C23 ⋊ D53⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C53 | C2×C13 |
| LCS | G ▷ C23×C53 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1219 |
Polycyclic presentation:
2,13,23,53|c^a=c^22,d^a=d^52,d^b=d^16215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31694, 12);