Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C229 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#11745021 |
| commutator, socle | C2×C229 | C22×C4 |
| Fitting | Q8×C229 | C4 |
| hypercenter | Q8 | #11745021 |
| hypocenter | C229 | #131 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|a^2=d,d^2=e,f^a=f^122,c^b=ce,f^b=f^228,f^c=f^228,f^d=f^228305 conjugacy classes — view the full character table.
| maximal subgroup of | #28412524, #28412525, #28412526, … |
| maximal normal subgroup of | #28412524, #28412525, #28412526, … |
| maximal quotient of | #28412446, #28412456, #28412488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 234);