Finite Group DatabasebetaFinite Group Databasebeta| order | 9338 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C23 · Schur multiplier (H2) = C1 |
| direct product | C7×C23×D29 |
| Fitting, socle, Hall | C7×C23×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C7×C23 |
| Hall | C23×C29 ⋊ C2×C7 |
| Hall | C7×C29 ⋊ C2×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C23 | D29 |
| commutator, hypocenter | C29 | C2×C7×C23 |
| Frattini | C1 | G |
| Fitting, socle | C7×C23×C29 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C7×C23 | |
16 conjugacy classes of subgroups.
2576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C23×#1181, C7×C23⋊#1181, C7×D23×D29, … |
| maximal normal subgroup of | C7×C23×#1181, C7×C23⋊#1181, C7×D23×D29, … |
| maximal quotient of | C7×C23×Dic29, C2×C7×C23×D29, C3×C7×C23×D29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9338, 3);