Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #3237 |
322 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^2=e,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,h^b=h^42,f^c=fg425 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3237, C2×#19145806, #25968768, … |
| maximal normal subgroup of | D43×#3237, C2×#19145806, #25968768, … |
| maximal quotient of | #25106117, #25106354, #25107164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15721);