Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #127×C113 ⋊ C2 |
| Sylow | C113 ⋊ #453 |
168 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,g^b=g^112,d^c=df800 conjugacy classes — view the full character table.
| maximal subgroup of | #28388718, #28388720, #28392558, … |
| maximal normal subgroup of | #28388718, #28388720, #28392558, … |
| maximal quotient of | #28389491, #28389496, #28389518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 716);