Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×M16×C113 ⋊ C2 |
| Sylow | C113 ⋊ #468 |
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,113|b^2=d,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^112,c^b=cf1136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #468×D113, C2×#20298844, #28400178, … |
| maximal normal subgroup of | #468×D113, C2×#20298844, #28400178, … |
| maximal quotient of | #28390039, #28390046, #28390073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 795);