Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C43 ⋊ #2165 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,h^a=h^42,e^b=eg,e^c=eg872 conjugacy classes — view the full character table.
| maximal subgroup of | #24983657, #24983658, #24983660, … |
| maximal normal subgroup of | #24983657, #24983658, #24983660, … |
| maximal quotient of | #25011613, #25011663, #25011931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6322);