Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C229 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#11745021 |
| commutator, socle | C2×C229 | C2×C8 |
| Fitting | C8×C229 | C4 |
| hypercenter | C8 | #11745021 |
| hypocenter | C229 | M32 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C4 ◁ C8 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^122,f^b=f^228,f^c=f^228476 conjugacy classes — view the full character table.
| maximal subgroup of | #28412371, #28412372, #28412397, … |
| maximal normal subgroup of | #28412371, #28412372, #28412397, … |
| maximal quotient of | #28412370, #28412376, #28412402, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 221);