Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1849 |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=f,b^2=d,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^42,c^b=cg872 conjugacy classes — view the full character table.
| maximal subgroup of | #24990989, #24990990, #25000734, … |
| maximal normal subgroup of | #24990989, #24990990, #25000734, … |
| maximal quotient of | #24990346, #24990350, #24990353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4685);