Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#14582640 |
| Sylow | C43 ⋊ C2×#330 |
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
878 conjugacy classes — view the full character table.
| maximal subgroup of | #24987514, C4×#14582640, #24987522, … |
| maximal normal subgroup of | #24987514, C4×#14582640, #24987522, … |
| maximal quotient of | C2×#19132417, C2×#19132419, #24984568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3093);