Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#14582629 |
| Sylow | C43 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 125 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 | #24987193, C4×#14582629, #24987203, … |
| maximal normal subgroup of | #24987193, C4×#14582629, #24987203, … |
| maximal quotient of | C2×#19132417, C2×#19132420, #24984545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2886);