Finite Group DatabasebetaFinite Group Databasebeta| order | 9226 |
| automorphism | Aut(G) order 18212124 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4613 |
| unambiguous semidirect product | C7⋊D659 |
| unambiguous semidirect product | C659⋊D7 |
| Fitting, socle, derived, Hall | C7×C659 ⋊ C2 |
| Sylow | C659 ⋊ D7 |
| Sylow | C7 ⋊ D659 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C659 | C2 |
| LCS | G ▷ C7×C659 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,659|b^a=b^6,c^a=c^6582308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D659, C2×D4613, C3×D4613, … |
| maximal normal subgroup of | D7×D659, C2×D4613, C3×D4613, … |
| maximal quotient of | Dic4613, C2×D4613, C3×D4613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9226, 5);