Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C229 ⋊ C4 |
| Sylow | C229 ⋊ #107 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C4⋊#11745021 |
| commutator | C4×C229 | C2×C4 |
| Frattini | C4 | C2×#11745021 |
| Fitting | C8×C229 | C4 |
| socle | C2×C229 | C4⋊C4 |
| hypercenter | C8 | #11745021 |
| hypocenter | C229 | #107 |
| LCS | G ▷ C4×C229 ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|a^2=d,b^2=ce,c^2=e,b^a=bc,c^a=ce,f^a=f^122,f^d=f^228470 conjugacy classes — view the full character table.
| maximal subgroup of | #28412393, #28412394, #28412407, … |
| maximal normal subgroup of | #28412393, #28412394, #28412407, … |
| maximal quotient of | #28412344, #28412345, #28412355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 215);