Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #2264 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|b^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,d^b=de,e^b=ef,f^b=fg,h^b=h^42488 conjugacy classes — view the full character table.
| maximal subgroup of | #25017212, #25017215, #25017275, … |
| maximal normal subgroup of | #25017212, #25017215, #25017275, … |
| maximal quotient of | #25017036, #25017043, #25017105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6827);