Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16837195 |
| Sylow | C59 ⋊ C2×#353 |
368 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
838 conjugacy classes — view the full character table.
| maximal subgroup of | #28476428, #28476429, #28476452, … |
| maximal normal subgroup of | #28476428, #28476429, #28476452, … |
| maximal quotient of | C2×#21422028, C2×#21422042, #28497959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6168);