Finite Group DatabasebetaFinite Group Databasebeta| order | 14674 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C29 · Schur multiplier (H2) = C1 |
| direct product | C11×C29×D23 |
| Fitting, socle, Hall | C11×C23×C29 ⋊ C2 |
| derived, Sylow | C23 ⋊ C2×C11×C29 |
| Hall | C23×C29 ⋊ C2×C11 |
| Hall | C11×C23 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C29 | D23 |
| commutator, cosocle, hypocenter | C23 | C2×C11×C29 |
| Frattini | C1 | G |
| Fitting, socle | C11×C23×C29 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C11×C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7337 |
4147 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D23×D29, D11×C29×D23, D23×D319, … |
| maximal normal subgroup of | C11×D23×D29, D11×C29×D23, D23×D319, … |
| maximal quotient of | C11×C29×Dic23, C2×C11×C29×D23 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14674, 4);