Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #107×C113 ⋊ C2 |
| Sylow | C113 ⋊ #440 |
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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=e,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^b=g^112,g^c=g^112806 conjugacy classes — view the full character table.
| maximal subgroup of | #440×D113, C2×#20298697, #28399369, … |
| maximal normal subgroup of | #440×D113, C2×#20298697, #28399369, … |
| maximal quotient of | #28389385, #28389430, #28389451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 648);