Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #107×C113 ⋊ C2 |
| Sylow | C113 ⋊ C4×D8 |
134 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,c^2=e,d^2=f,b^a=bd,d^a=df,d^b=df,g^b=g^112,g^c=g^112812 conjugacy classes — view the full character table.
| maximal subgroup of | #28392418, #28392420, #28392423, … |
| maximal normal subgroup of | #28392418, #28392420, #28392423, … |
| maximal quotient of | #28389368, #28389402, #28389458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 631);