Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#16837137 |
| Fitting | C2×C22⋊C8×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#327 |
388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 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 | #28479562, C4×#16837137, #28479572, … |
| maximal normal subgroup of | #28479562, C4×#16837137, #28479572, … |
| maximal quotient of | C2×#21421916, C2×#21421918, #28476649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2988);