Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C229 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #11745021 |
| commutator, hypocenter | C229 | C32 |
| Fitting | C8×C229 | C4 |
| socle | C2×C229 | C16 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C8 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^122,f^b=f^228488 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20301038, D229⋊C32, #28412413, … |
| maximal normal subgroup of | C2×#20301038, D229⋊C32, #28412413, … |
| maximal quotient of | #28412320, C2×#20301038 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 196);