Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C43×#447 ⋊ C2 |
| Sylow | C43 ⋊ D4×D8 |
620 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,e^d=eg,h^d=h^42434 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D8×D43, C2×#19146265, #25971885, … |
| maximal normal subgroup of | D4×D8×D43, C2×#19146265, #25971885, … |
| maximal quotient of | #25085937, #25085942, #25085947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16180);