Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C113 ⋊ C4 |
| Sylow | C113 ⋊ #365 |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^15,d^b=df,g^d=g^112464 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20299523, D113⋊#365, #28406921, … |
| maximal normal subgroup of | C2×#20299523, D113⋊#365, #28406921, … |
| maximal quotient of | #28405599, #28405600, #28405639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1474);