Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#16837575 |
| Fitting | C2×2−1+4×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#454 |
728 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1018 conjugacy classes — view the full character table.
| maximal subgroup of | #28506028, #28506038, #28507716, … |
| maximal normal subgroup of | #28506028, #28506038, #28507716, … |
| maximal quotient of | C2×#21423025, C2×#21423127, C2×#21423031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13846);