Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D229⋊M16 |
| Sylow | C229 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×#11745021 |
| commutator, socle | C2×C229 | C22×C4 |
| Frattini | C2 | C22×#11745021 |
| Fitting | C2×C4×C229 | C4 |
| hypercenter | C2×C4 | #11745021 |
| hypocenter | C229 | C2×M16 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|a^2=d,d^2=e,b^a=be,f^a=f^122,f^c=f^228,f^d=f^228476 conjugacy classes — view the full character table.
| maximal subgroup of | #28412348, #28412350, #28412352, … |
| maximal normal subgroup of | #28412348, #28412350, #28412352, … |
| maximal quotient of | #28412440, C4×#16814675, C4×#16814676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 231);