Finite Group DatabasebetaFinite Group Databasebeta| order | 30226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D17×C127⋊C7 |
| unambiguous semidirect product | C17⋊(C2×C127⋊C7) |
| unambiguous semidirect product | (D17×C127)⋊C7 |
| Fitting, socle, derived, Hall | C17×C127 ⋊ C2×C7 |
| Hall | C17×C127⋊C7 ⋊ C2 |
| Hall | D17×C127 ⋊ C7 |
| Sylow | C127 ⋊ C7×D17 |
| Sylow | C17 ⋊ C2×C127⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C127 | C2×C7 |
| LCS | G ▷ C17×C127 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2159 |
250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30226, 11);