Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#16837222 |
| Sylow | C59 ⋊ C2×#364 |
168 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28504006, C4×#16837222, #28504010, … |
| maximal normal subgroup of | #28504006, C4×#16837222, #28504010, … |
| maximal quotient of | C2×#21422159, #28500233, C2×#21422165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6272);