Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,b^2=f,c^2=ef,d^2=f,b^a=bd,d^a=df,d^b=df,g^c=g^112812 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Q16×D113, C2×#20298690, #28399342, … |
| maximal normal subgroup of | C4×Q16×D113, C2×#20298690, #28399342, … |
| maximal quotient of | #28389378, #28389421, #28389427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 641);