Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#16837541 |
| Fitting | C23×Q8×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#448 |
792 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28483809, #28483815, #28485155, … |
| maximal normal subgroup of | #28483809, #28483815, #28485155, … |
| maximal quotient of | C2×#21423019, C2×#21423087, C2×#21423036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13698);