Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#14582720 |
| Sylow | C43 ⋊ C2×#364 |
168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24983480, #24983481, #24983482, … |
| maximal normal subgroup of | #24983480, #24983481, #24983482, … |
| maximal quotient of | C2×#19132659, #25008142, C2×#19132665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6273);