Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#13063351 |
| Fitting | C23×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×AGL(1,ℤ/8) |
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
884 conjugacy classes — view the full character table.
| maximal subgroup of | #25003324, #25003328, #25003337, … |
| maximal normal subgroup of | #25003324, #25003328, #25003337, … |
| maximal quotient of | C22×#14582904, C22×#14582898, C22×#14582939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 19243);