Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#16837405 |
| Fitting | C2×#102×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#418 |
1008 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
856 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16837405, #28586465, #28586497, … |
| maximal normal subgroup of | C4×#16837405, #28586465, #28586497, … |
| maximal quotient of | C2×#21422485, C2×#21422537, #28555126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13009);