Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D8×D172 |
| Fitting | C4×D8×C43 ⋊ C2 |
| Sylow | C43 ⋊ D4×D8 |
620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
623 conjugacy classes — view the full character table.
| maximal subgroup of | #25010020, #25010024, #25010048, … |
| maximal normal subgroup of | #25010020, #25010024, #25010048, … |
| maximal quotient of | #25085949, #25085964, #25085979, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16186);