Finite Group DatabasebetaFinite Group Databasebeta| order | 14674 |
| isoclinism | isoclinic class of AGL(1,𝔽23) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×AGL(1,𝔽23) |
| unambiguous semidirect product | D23⋊(C11×C29) |
| unambiguous semidirect product | (C23⋊C11)⋊(C2×C29) |
| unambiguous semidirect product | (C29×D23)⋊C11 |
| Fitting, socle, Hall | C23×C29 ⋊ C2×C11 |
| derived, Sylow | C23 ⋊ C2×C11×C29 |
| Hall | C29×C23⋊C11 ⋊ C2 |
| Hall | C29×D23 ⋊ C11 |
| Hall | C23⋊C11 ⋊ C2×C29 |
| Hall | D23 ⋊ C11×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | AGL(1,𝔽23) |
| commutator, cosocle, hypocenter | C23 | C2×C11×C29 |
| Frattini | C1 | G |
| Fitting, socle | C23×C29 | C2×C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 667 |
667 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×AGL(1,𝔽23), C2×C29×AGL(1,𝔽23) |
| maximal normal subgroup of | D29×AGL(1,𝔽23), C2×C29×AGL(1,𝔽23) |
| maximal quotient of | C29×Dic23⋊C11, C2×C29×AGL(1,𝔽23) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14674, 11);