Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#16837484 |
| Fitting | C2×#107×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×C4×D8 |
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
868 conjugacy classes — view the full character table.
| maximal subgroup of | #28503892, #28503902, #28503941, … |
| maximal normal subgroup of | #28503892, #28503902, #28503941, … |
| maximal quotient of | C2×#21422890, C2×#21422924, C2×#21422980, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13260);