Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C113 ⋊ #329 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,c^2=f,d^2=e,b^a=bc,c^a=ce,g^a=g^112,c^b=cf,d^b=def803 conjugacy classes — view the full character table.
| maximal subgroup of | #28388721, #28388722, #28388724, … |
| maximal normal subgroup of | #28388721, #28388722, #28388724, … |
| maximal quotient of | #28388395, #28388400, #28388455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 289);