Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C43×#450 ⋊ C2 |
| Sylow | C43 ⋊ #3211 |
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|b^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^42,c^b=ce,h^b=h^42,f^c=fg431 conjugacy classes — view the full character table.
| maximal subgroup of | #25070612, #25070614, #25070621, … |
| maximal normal subgroup of | #25070612, #25070614, #25070621, … |
| maximal quotient of | #25105919, #25106285, #25107122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15478);