Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #3162 |
348 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=e,c^2=f,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,c^b=cg872 conjugacy classes — view the full character table.
| maximal subgroup of | #24991550, #24997587, #24997588, … |
| maximal normal subgroup of | #24991550, #24997587, #24997588, … |
| maximal quotient of | #25097020, #25099950, #25101174, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15034);