Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#554 ⋊ C2 |
| Sylow | C43 ⋊ #3370 |
358 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|b^2=e,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,c^b=cg,d^b=de,f^c=fg554 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3370, C2×#19147348, #25976413, … |
| maximal normal subgroup of | D43×#3370, C2×#19147348, #25976413, … |
| maximal quotient of | #25113268, #25113477, #25115581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17263);