Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #106×C113 ⋊ C2 |
| Sylow | C113 ⋊ #427 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,b^2=d,c^2=f,d^2=f,b^a=bd,d^a=df,g^c=g^112812 conjugacy classes — view the full character table.
| maximal subgroup of | #28392308, #28392345, #427×D113, … |
| maximal normal subgroup of | #28392308, #28392345, #427×D113, … |
| maximal quotient of | #28389319, #28389334, #28389351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 584);