Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16837806 |
| Sylow | C59 ⋊ C2×#500 |
424 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #28507259, #28507263, #28507276, … |
| maximal normal subgroup of | #28507259, #28507263, #28507276, … |
| maximal quotient of | C2×#21424254, C2×#21424827, C2×#21424828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15017);