Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#16837153 |
| Sylow | C59 ⋊ C2×#334 |
200 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475562, #28475563, #28475566, … |
| maximal normal subgroup of | #28475562, #28475563, #28475566, … |
| maximal quotient of | C2×#21421931, C4×#16837153, #28481524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3251);