Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C113 ⋊ #365 |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^112,d^b=df,g^b=g^112800 conjugacy classes — view the full character table.
| maximal subgroup of | #365×D113, C2×#20298422, #28392345, … |
| maximal normal subgroup of | #365×D113, C2×#20298422, #28392345, … |
| maximal quotient of | #28388639, #28388674, C2×#20298422 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 373);