Finite Group DatabasebetaFinite Group Databasebeta| order | 30646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(D199⋊C11) |
| unambiguous semidirect product | (C199⋊C11)⋊D7 |
| unambiguous semidirect product | D1393⋊C11 |
| Fitting, socle, derived, Hall | C7×C199 ⋊ C2×C11 |
| Hall | C7×C199⋊C11 ⋊ C2 |
| Hall | D1393 ⋊ C11 |
| Hall | C199⋊C11 ⋊ D7 |
| Sylow | C199 ⋊ C11×D7 |
| Sylow | C7 ⋊ D199⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C199 | C2×C11 |
| LCS | G ▷ C7×C199 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1393 |
Polycyclic presentation:
2,7,11,199|b^a=b^6,d^a=d^198,d^c=d^125118 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30646, 12);