Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C43×M64 ⋊ C2 |
| Sylow | C43 ⋊ #1418 |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,c^2=efg,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^42,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^42866 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1418, C2×#19132783, #25017058, … |
| maximal normal subgroup of | D43×#1418, C2×#19132783, #25017058, … |
| maximal quotient of | #24984054, #24984057, #24984153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2698);