Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#14582686 |
| Sylow | C43 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
614 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#14582686, AΣL(1,𝔽16)×Dic43, #25011744, … |
| maximal normal subgroup of | C4×#14582686, AΣL(1,𝔽16)×Dic43, #25011744, … |
| maximal quotient of | C2×#19132523, C2×#19132543, #25005847, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6142);