Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#16837204 |
| Fitting | C22×C16×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#357 |
272 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1900 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28503892, C4×#16837204, #28503902, … |
| maximal normal subgroup of | #28503892, C4×#16837204, #28503902, … |
| maximal quotient of | C2×#21422058, #28498665, #28498717, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6209);