Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C113 ⋊ #362 |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=f,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^112,c^b=cef,d^b=df,e^b=ef800 conjugacy classes — view the full character table.
| maximal subgroup of | #362×D113, C2×#20298414, #28392322, … |
| maximal normal subgroup of | #362×D113, C2×#20298414, #28392322, … |
| maximal quotient of | #28388544, #28388592, #28388623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 365);