Finite Group DatabasebetaFinite Group Databasebeta| order | 30646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C7×D199⋊C11 |
| unambiguous semidirect product | D199⋊(C7×C11) |
| unambiguous semidirect product | (C199⋊C11)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D199)⋊C11 |
| Fitting, socle, Hall | C7×C199 ⋊ C2×C11 |
| derived, Sylow | C199 ⋊ C2×C7×C11 |
| Hall | C7×C199⋊C11 ⋊ C2 |
| Hall | C7×D199 ⋊ C11 |
| Hall | C199⋊C11 ⋊ C2×C7 |
| Hall | D199 ⋊ C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D199⋊C11 |
| commutator, cosocle, hypocenter | C199 | C2×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C199 | C2×C11 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1393 |
217 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30646, 10);