Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C43 ⋊ #1296 |
188 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^42,c^b=cg878 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1296, C2×#19132479, #24986682, … |
| maximal normal subgroup of | D43×#1296, C2×#19132479, #24986682, … |
| maximal quotient of | #24983149, #24983165, #24983166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2394);