Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C113 ⋊ C8 |
| Sylow | C113 ⋊ #324 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,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 | #28407601, #28407602, #28407610, … |
| maximal normal subgroup of | #28407601, #28407602, #28407610, … |
| maximal quotient of | #28407574, #28407583, #28407607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1635);