Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C229 ⋊ C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#11745021 |
| commutator | C2×C229 | C2×C8 |
| Fitting | C2×C4×C229 | C4 |
| socle | C22×C229 | C2×C4 |
| hypercenter | C2×C4 | #11745021 |
| hypocenter | C229 | C4⋊C8 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^122,f^b=f^228,f^d=f^228476 conjugacy classes — view the full character table.
| maximal subgroup of | #28412339, #28412340, #28412341, … |
| maximal normal subgroup of | #28412339, #28412340, #28412341, … |
| maximal quotient of | #28412343, #28412345, #28412347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 213);