Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C43 ⋊ #3046 |
472 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^42,f^c=fg620 conjugacy classes — view the full character table.
| maximal subgroup of | #25134668, #25134673, #25134683, … |
| maximal normal subgroup of | #25134668, #25134673, #25134683, … |
| maximal quotient of | #25082061, #25082072, #25082083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 14058);