Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ #428 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,c^b=cf,g^b=g^1121142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28390782, #28390783, #28390787, … |
| maximal normal subgroup of | #28390782, #28390783, #28390787, … |
| maximal quotient of | #28389324, #28389339, #28389357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 589);