Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C113 ⋊ #419 |
150 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,b^2=f,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^112,c^b=cf,d^b=df1142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28390546, #28390549, #28390945, … |
| maximal normal subgroup of | #28390546, #28390549, #28390945, … |
| maximal quotient of | #28388969, #28388995, #28389021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 558);