Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#452 ⋊ C2 |
| Sylow | C43 ⋊ #3333 |
398 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=eg,c^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^d=h^42428 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3333, C2×#19146926, #25973547, … |
| maximal normal subgroup of | D43×#3333, C2×#19146926, #25973547, … |
| maximal quotient of | #25112253, #25113044, #25113839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16841);