Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #117×C113 ⋊ C2 |
| Sylow | C113 ⋊ #418 |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,c^b=cf,d^b=df,g^b=g^1121142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28390542, #28390543, #28390950, … |
| maximal normal subgroup of | #28390542, #28390543, #28390950, … |
| maximal quotient of | #28388964, #28388990, #28389016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 553);