Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C113 ⋊ #350 |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^18,c^b=cf,d^b=df,g^b=g^112,g^d=g^98,g^e=g^11298 conjugacy classes — view the full character table.
| maximal subgroup of | #28407754, C2×#20299699, #28407757, … |
| maximal normal subgroup of | #28407754, C2×#20299699, #28407757, … |
| maximal quotient of | #28407598, #28407609, #28407617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1650);