Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C113 ⋊ C2 |
| Sylow | C113 ⋊ #486 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^112,g^b=g^112,g^c=g^112806 conjugacy classes — view the full character table.
| maximal subgroup of | #28389663, #28389664, #28389670, … |
| maximal normal subgroup of | #28389663, #28389664, #28389670, … |
| maximal quotient of | #28390701, #28391256, #28391379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 897);