Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×D8×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3169 |
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^42632 conjugacy classes — view the full character table.
| maximal subgroup of | #25006570, #25006588, #25006601, … |
| maximal normal subgroup of | #25006570, #25006588, #25006601, … |
| maximal quotient of | #25097133, #25100813, #25100815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15086);