Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊C4×C113 ⋊ C4 |
| Sylow | C113 ⋊ #340 |
114 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,c^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^b=g^98,g^e=g^112308 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20299471, #28406259, #28406261, … |
| maximal normal subgroup of | C2×#20299471, #28406259, #28406261, … |
| maximal quotient of | #28405403, #28405408, #28405410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1422);