Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#13063249 |
| Sylow | C43 ⋊ C22×#103 |
816 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 389 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 | #25002166, #25002168, #25002864, … |
| maximal normal subgroup of | #25002166, #25002168, #25002864, … |
| maximal quotient of | C22×Q8⋊(C43⋊C8), C2×#19133024, C2×#19132998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13000);