Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C43 ⋊ #1369 |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,b^2=c,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^42,d^b=dg872 conjugacy classes — view the full character table.
| maximal subgroup of | #24984068, #24984069, #24984071, … |
| maximal normal subgroup of | #24984068, #24984069, #24984071, … |
| maximal quotient of | #24983335, #24983483, C2×#19132663 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2578);