Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3396 |
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=g,b^2=eg,c^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,h^b=h^42,f^c=fg623 conjugacy classes — view the full character table.
| maximal subgroup of | #25010111, #25010115, #25010139, … |
| maximal normal subgroup of | #25010111, #25010115, #25010139, … |
| maximal quotient of | #25113409, #25115441, #25116351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17520);