Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C113 ⋊ #368 |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=ce,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^b=g^112806 conjugacy classes — view the full character table.
| maximal subgroup of | #368×D113, C2×#20298427, #28392367, … |
| maximal normal subgroup of | #368×D113, C2×#20298427, #28392367, … |
| maximal quotient of | #28388645, #28388647, #28388667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 378);