Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#16837536 |
| Fitting | C23×D4×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#447 |
1048 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28483823, #28483829, #28485134, … |
| maximal normal subgroup of | #28483823, #28483829, #28485134, … |
| maximal quotient of | C2×#21423014, C2×#21423082, C2×#21423031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13686);