Finite Group DatabasebetaFinite Group Databasebeta| order | 9338 |
| automorphism | Aut(G) order 17256624 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4669 |
| unambiguous semidirect product | C7⋊D667 |
| unambiguous semidirect product | C23⋊D203 |
| unambiguous semidirect product | C29⋊D161 |
| Fitting, socle, derived, Hall | C7×C23×C29 ⋊ C2 |
| Hall | C23×C29 ⋊ D7 |
| Hall | C7×C29 ⋊ D23 |
| Hall | C7×C23 ⋊ D29 |
| Sylow | C29 ⋊ D161 |
| Sylow | C23 ⋊ D203 |
| Sylow | C7 ⋊ D667 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C23×C29 | C2 |
| LCS | G ▷ C7×C23×C29 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,23,29|b^a=b^6,c^a=c^22,d^a=d^282336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×D161, D23×D203, D7×D667, … |
| maximal normal subgroup of | D29×D161, D23×D203, D7×D667, … |
| maximal quotient of | Dic4669, C2×D4669, C3×D4669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9338, 9);