Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C113 ⋊ C2 |
| Sylow | C113 ⋊ #508 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^112,d^b=de,e^b=ef,g^b=g^112,g^c=g^112638 conjugacy classes — view the full character table.
| maximal subgroup of | #28392882, #28392884, #28392888, … |
| maximal normal subgroup of | #28392882, #28392884, #28392888, … |
| maximal quotient of | #28392280, #28392355, #28392420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 982);