Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C229 ⋊ C4 |
| Sylow | C229 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#11745021 |
| commutator, socle | C2×C229 | C42 |
| Fitting | C8×C229 | C4 |
| hypercenter | C8 | #11745021 |
| hypocenter | C229 | #97 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C4 ◁ C8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^122,f^d=f^228476 conjugacy classes — view the full character table.
| maximal subgroup of | #28412371, #28412372, C2×#20301042, … |
| maximal normal subgroup of | #28412371, #28412372, C2×#20301042, … |
| maximal quotient of | #28412322, #14270087⋊C8, (C2×#11745021)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 200);