Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#14583303 |
| Sylow | C43 ⋊ C2×#500 |
424 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #25015167, #25015171, #25015184, … |
| maximal normal subgroup of | #25015167, #25015171, #25015184, … |
| maximal quotient of | C2×#19134753, C2×#19135326, C2×#19135327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15017);