Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#13063271 |
| Sylow | C43 ⋊ C4×Q32 |
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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 | #25008328, C8×#13063271, #25008340, … |
| maximal normal subgroup of | #25008328, C8×#13063271, #25008340, … |
| maximal quotient of | C8×#13063271, #25008511, #25008513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6367);