Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #1537 |
194 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=f,c^2=g,d^2=g,e^2=f,b^a=bd,c^a=cg,d^a=df,h^a=h^42,d^b=dg,e^b=efg614 conjugacy classes — view the full character table.
| maximal subgroup of | #24988855, #24988858, #24988860, … |
| maximal normal subgroup of | #24988855, #24988858, #24988860, … |
| maximal quotient of | #24984698, #24984721, #24984898, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3148);