Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C4×C113 ⋊ C4 |
| Sylow | C113 ⋊ #328 |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=ce,g^a=g^98,c^b=cf,d^b=def,g^d=g^112299 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20299451, D113⋊#328, #28405945, … |
| maximal normal subgroup of | C2×#20299451, D113⋊#328, #28405945, … |
| maximal quotient of | #28405392, #28405395, #28405447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1402);