Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#106×D43 |
| Fitting | C2×#106×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×#106 |
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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 | D43×#1383, D43×#1386, #25013152, … |
| maximal normal subgroup of | D43×#1383, D43×#1386, #25013152, … |
| maximal quotient of | C2×#334×D43, D43×#1566, C2×#19133349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13080);