Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#16837534 |
| Fitting | C22×D8×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#447 |
1048 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
850 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16837534, #28594261, #28594328, … |
| maximal normal subgroup of | C4×#16837534, #28594261, #28594328, … |
| maximal quotient of | C2×#21423012, C2×#21423080, C2×#21423029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13684);