Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×SD16×C113 ⋊ C2 |
| Sylow | C113 ⋊ #577 |
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,113|a^2=f,e^2=f,b^a=be,e^a=ef,e^b=ef,d^c=df,g^d=g^112806 conjugacy classes — view the full character table.
| maximal subgroup of | #28402339, #28402340, #28402346, … |
| maximal normal subgroup of | #28402339, #28402340, #28402346, … |
| maximal quotient of | #28399095, #28399102, #28399165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1355);