Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C113 ⋊ C4 |
| Sylow | C113 ⋊ #344 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^15,d^b=df,g^b=g^98,g^d=g^112,g^e=g^112302 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20299481, #28406286, #28406331, … |
| maximal normal subgroup of | C2×#20299481, #28406286, #28406331, … |
| maximal quotient of | #28405413, #28405415, #28405420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1432);