Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#468 ⋊ C2 |
| Sylow | C43 ⋊ #3319 |
414 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=eg,b^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^42,h^d=h^42365 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3319, C2×#19146746, #25973360, … |
| maximal normal subgroup of | D43×#3319, C2×#19146746, #25973360, … |
| maximal quotient of | #25112147, #25112895, #25113671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16661);