Finite Group DatabasebetaFinite Group Databasebeta| order | 13846 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D23×C43⋊C7 |
| unambiguous semidirect product | C23⋊(C2×C43⋊C7) |
| unambiguous semidirect product | (C43×D23)⋊C7 |
| Fitting, socle, derived, Hall | C23×C43 ⋊ C2×C7 |
| Hall | C23×C43⋊C7 ⋊ C2 |
| Hall | C43×D23 ⋊ C7 |
| Sylow | C43 ⋊ C7×D23 |
| Sylow | C23 ⋊ C2×C43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C43 | C2×C7 |
| LCS | G ▷ C23×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 989 |
169 conjugacy classes — view the full character table.
| maximal subgroup of | D23×D43⋊C7, C2×D23×C43⋊C7 |
| maximal normal subgroup of | D23×D43⋊C7, C2×D23×C43⋊C7 |
| maximal quotient of | Dic23×C43⋊C7, C2×D23×C43⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13846, 11);