Finite Group DatabasebetaFinite Group Databasebeta| order | 8172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D9×D227 |
| unambiguous semidirect product | (D9×C227)⋊C2 |
| unambiguous semidirect product | (C9×D227)⋊C2 |
| unambiguous semidirect product | D2043⋊C2 |
| Fitting, derived, Hall | C9×C227 ⋊ C22 |
| Sylow | C227 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D227 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C227 | C22 |
| Frattini | C3 | D3×D227 |
| socle | C3×C227 | C2×D3 |
| LCS | G ▷ C9×C227 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
690 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8172, 6);