Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C4×C113 ⋊ C4 |
| Sylow | C113 ⋊ #342 |
142 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,b^a=bc,c^a=cf,g^a=g^98,d^b=df,g^d=g^112470 conjugacy classes — view the full character table.
| maximal subgroup of | #28405552, #28405553, #28405554, … |
| maximal normal subgroup of | #28405552, #28405553, #28405554, … |
| maximal quotient of | #28405412, #28405416, #28405422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1427);