Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #101×C113 ⋊ C2 |
| Sylow | C113 ⋊ #413 |
150 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,c^2=f,e^2=f,b^a=bd,d^a=df,e^b=ef,g^b=g^112,g^c=g^112638 conjugacy classes — view the full character table.
| maximal subgroup of | #28392256, #28392258, #28392264, … |
| maximal normal subgroup of | #28392256, #28392258, #28392264, … |
| maximal quotient of | #28388887, #28388891, #28388907, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 532);