Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#13063266 |
| Fitting | C4×D8×C43 ⋊ C2 |
| Sylow | C43 ⋊ C4×D16 |
174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 174 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 | #25008316, C8×#13063266, #25008345, … |
| maximal normal subgroup of | #25008316, C8×#13063266, #25008345, … |
| maximal quotient of | C8×#13063266, #25008490, #25008492, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6355);