Finite Group DatabasebetaFinite Group Databasebeta| order | 9226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D659⋊C7 |
| unambiguous semidirect product | (C659⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C659 ⋊ C2×C7 |
| Hall | C659⋊C7 ⋊ C2 |
| Hall | D659 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C659 | C2×C7 |
| LCS | G ▷ C659 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,659|c^a=c^658,c^b=c^30761 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D659⋊C7, C3×D659⋊C7, C3⋊(D659⋊C7) |
| maximal normal subgroup of | C2×D659⋊C7, C3×D659⋊C7 |
| maximal quotient of | Dic659⋊C7, C2×D659⋊C7, C3×D659⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9226, 1);