Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1736 |
448 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=f,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^42,c^b=cg,h^b=h^42884 conjugacy classes — view the full character table.
| maximal subgroup of | #25001926, #25001927, #25001960, … |
| maximal normal subgroup of | #25001926, #25001927, #25001960, … |
| maximal quotient of | #24986060, #24986070, #24986082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4231);