Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#14270087 |
| Sylow | C229 ⋊ C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#11745021 |
| commutator | C2×C229 | C2×C8 |
| Fitting | C23×C229 | C4 |
| socle | C22×C229 | C2×C4 |
| hypercenter | C23 | #11745021 |
| hypocenter | C229 | C22⋊C8 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C22 ◁ C23 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|a^2=d,d^2=e,b^a=bc,f^a=f^122,f^d=f^228476 conjugacy classes — view the full character table.
| maximal subgroup of | #28412324, #28412325, #28412326, … |
| maximal normal subgroup of | #28412324, #28412325, #28412326, … |
| maximal quotient of | #28412324, #28412326, D4⋊#14270087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 202);