Finite Group DatabasebetaFinite Group Databasebeta| order | 23214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C53⋊(D73⋊C3) |
| unambiguous semidirect product | (C73⋊C3)⋊D53 |
| unambiguous semidirect product | D3869⋊C3 |
| Fitting, socle, derived, Hall | C53×C73 ⋊ C2×C3 |
| Hall | C53×C73⋊C3 ⋊ C2 |
| Hall | D3869 ⋊ C3 |
| Hall | C73⋊C3 ⋊ D53 |
| Sylow | C73 ⋊ C3×D53 |
| Sylow | C53 ⋊ D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C53×C73 | C2×C3 |
| LCS | G ▷ C53×C73 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3869 |
Polycyclic presentation:
2,3,53,73|c^a=c^52,d^a=d^72,d^b=d^8720 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23214, 12);