Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#16814669 |
| derived, Sylow | C229 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11745021 |
| commutator, hypocenter | C229 | C2×C16 |
| Frattini | C4 | C2×#11745021 |
| Fitting | C2×C4×C229 | C4 |
| socle | C22×C229 | C8 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C2×C4 | |
28 conjugacy classes of subgroups.
488 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16814669, #28412367, #28412369, … |
| maximal normal subgroup of | C4×#16814669, #28412367, #28412369, … |
| maximal quotient of | C4×#16814669, C22⋊#16814669, C4⋊#16814669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 218);