Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D229⋊C8 |
| unambiguous semidirect product | D229⋊(C2×C8) |
| derived, Sylow | C229 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11745021 |
| commutator, hypocenter | C229 | C22×C8 |
| Frattini | C2 | C22×#11745021 |
| Fitting | C2×C4×C229 | C4 |
| socle | C22×C229 | C2×C4 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
488 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#11745021)⋊C8, #28412354, #28412356, … |
| maximal normal subgroup of | (C2×#11745021)⋊C8, #28412354, #28412356, … |
| maximal quotient of | C2×C4×#14270087, C4×D229⋊C8, D229⋊(C22⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 229);