Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16837786 |
| Fitting | C2×C4×C8×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#495 |
592 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1900 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28488230, #28488232, #28488254, … |
| maximal normal subgroup of | #28488230, #28488232, #28488254, … |
| maximal quotient of | C2×#21423688, C2×#21423693, C2×#21423697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14931);