Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C113 ⋊ #330 |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,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 | #330×D113, C2×#20298340, #28389161, … |
| maximal normal subgroup of | #330×D113, C2×#20298340, #28389161, … |
| maximal quotient of | #28388397, #28388455, C2×#20298340 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 291);