Finite Group DatabasebetaFinite Group Databasebeta| order | 8172 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C227 · Schur multiplier (H2) = C2 |
| direct product | C22⋊C9×C227 |
| unambiguous semidirect product | C22⋊(C9×C227) |
| unambiguous semidirect product | (C22×C227)⋊C9 |
| derived, Sylow | C22 ⋊ C9×C227 |
| Hall | C22×C227 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C227 | A4 |
| commutator, hypocenter | C22 | C9×C227 |
| Frattini | C3 | A4×C227 |
| Fitting, socle | C22×C3×C227 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C227 | |
16 conjugacy classes of subgroups.
2724 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8172, 7);