Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#14583248 |
| Sylow | C43 ⋊ C2×#487 |
424 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
632 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#14583248, #25104570, #25104615, … |
| maximal normal subgroup of | C4×#14583248, #25104570, #25104615, … |
| maximal quotient of | C2×#19134721, C2×#19135268, C2×#19135269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 14819);