Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16837762 |
| Fitting | C2×#97×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#489 |
436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28483603, #28483605, #28489987, … |
| maximal normal subgroup of | #28483603, #28483605, #28489987, … |
| maximal quotient of | C2×#21424230, C2×#21424786, C2×#21424793, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14839);