Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×#10621882 |
| Fitting | D4×Q8×C43 ⋊ C2 |
| Sylow | C43 ⋊ Q8×D8 |
404 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
560 conjugacy classes — view the full character table.
| maximal subgroup of | #25085967, #25085968, #25085974, … |
| maximal normal subgroup of | #25085967, #25085968, #25085974, … |
| maximal quotient of | Q8×#13063245, Q8×#13063246, C4⋊C4×#10621882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17361);