Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C23×C113 ⋊ C8 |
| Sylow | C113 ⋊ #323 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,d^2=f,b^a=bc,c^a=ce,g^a=g^18,d^b=de,g^d=g^98,g^f=g^112134 conjugacy classes — view the full character table.
| maximal subgroup of | #28407599, #28407600, #28407612, … |
| maximal normal subgroup of | #28407599, #28407600, #28407612, … |
| maximal quotient of | #28407573, #28407575, #28407583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1634);