Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16837211 |
| Fitting | C2×#106×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#360 |
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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 | #28503936, C4×#16837211, #28503979, … |
| maximal normal subgroup of | #28503936, C4×#16837211, #28503979, … |
| maximal quotient of | C2×#21422062, C2×#21422065, #28498458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6241);