Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16837832 |
| Fitting | C2×#135×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #28505736, #28505737, #28505739, … |
| maximal normal subgroup of | #28505736, #28505737, #28505739, … |
| maximal quotient of | C2×#21425801, C2×#21425803, C2×#21425878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17626);