Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#14273645 |
| Sylow | C59 ⋊ C4×#101 |
296 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28479251, C8×#14273645, #28479261, … |
| maximal normal subgroup of | #28479251, C8×#14273645, #28479261, … |
| maximal quotient of | C4×#16837127, #28479204, #28479208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4307);