Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#13063345 |
| Fitting | C22×#41×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×#135 |
1504 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1504 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.
896 conjugacy classes — view the full character table.
| maximal subgroup of | #25003410, #25003411, #25003415, … |
| maximal normal subgroup of | #25003410, #25003411, #25003415, … |
| maximal quotient of | C22×#14582893, C22×#14582895, C22×#14582935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 19236);