Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#14582986 |
| Fitting | C2×#106×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×C4×SD16 |
552 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
644 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#14582986, #25095086, #25095115, … |
| maximal normal subgroup of | C4×#14582986, #25095086, #25095115, … |
| maximal quotient of | C2×#19133394, C2×#19133437, C2×#19133430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13266);