Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C229 ⋊ C4 |
| Sylow | C229 ⋊ #104 |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^122,c^b=ce,f^b=f^228,f^d=f^228299 conjugacy classes — view the full character table.
| maximal subgroup of | D229⋊#104, C2×#20301053, #28412478, … |
| maximal normal subgroup of | D229⋊#104, C2×#20301053, #28412478, … |
| maximal quotient of | #28412329, Q8⋊#14270087, #28412333, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 211);