Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | Q8⋊C8×D43 |
| Fitting | C43×Q8⋊C8 ⋊ C2 |
| Sylow | C43 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 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 | C2×Q8⋊C8×D43, D43×#1476, D43×#1479, … |
| maximal normal subgroup of | C2×Q8⋊C8×D43, D43×#1476, D43×#1479, … |
| maximal quotient of | D43×#1271, D43×#1272, #24984541, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2885);