Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #104×Dic43 |
| Sylow | C43 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
644 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#104×D43, C2×#104×Dic43, #25094319, … |
| maximal normal subgroup of | C4×#104×D43, C2×#104×Dic43, #25094319, … |
| maximal quotient of | D4⋊C8×Dic43, Q8⋊C8×Dic43, #24987211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4317);