Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16837795 |
| Fitting | C22×Q16×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#497 |
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
844 conjugacy classes — view the full character table.
| maximal subgroup of | #28597237, C4×#16837795, #28597258, … |
| maximal normal subgroup of | #28597237, C4×#16837795, #28597258, … |
| maximal quotient of | C2×#21423719, C2×#21423720, C2×#21423727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14949);