Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#14582643 |
| Sylow | C43 ⋊ C2×#331 |
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 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.
626 conjugacy classes — view the full character table.
| maximal subgroup of | #24984335, #24984336, C4×#14582643, … |
| maximal normal subgroup of | #24984335, #24984336, C4×#14582643, … |
| maximal quotient of | C2×#19132416, #24984572, #24984874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3151);