Finite Group DatabasebetaFinite Group Databasebeta| order | 30338 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D197⋊C7 |
| unambiguous semidirect product | D197⋊(C7×C11) |
| unambiguous semidirect product | (C197⋊C7)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D197)⋊C7 |
| Fitting, socle, Hall | C11×C197 ⋊ C2×C7 |
| derived, Sylow | C197 ⋊ C2×C7×C11 |
| Hall | C11×C197⋊C7 ⋊ C2 |
| Hall | C11×D197 ⋊ C7 |
| Hall | C197⋊C7 ⋊ C2×C11 |
| Hall | D197 ⋊ C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D197⋊C7 |
| commutator, cosocle, hypocenter | C197 | C2×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C197 | C2×C7 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2167 |
308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30338, 10);