Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#16837573 |
| Fitting | C2×AGL(1,ℤ/8)×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#454 |
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
670 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16837573, #28594588, #28594625, … |
| maximal normal subgroup of | C4×#16837573, #28594588, #28594625, … |
| maximal quotient of | C2×#21423022, C2×#21423024, C2×#21423124, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13844);