Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊Q8×C113 ⋊ C2 |
| Sylow | C113 ⋊ #461 |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^112803 conjugacy classes — view the full character table.
| maximal subgroup of | #28389750, #28389752, #28389771, … |
| maximal normal subgroup of | #28389750, #28389752, #28389771, … |
| maximal quotient of | #28389946, #28389960, #28389970, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 751);