Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×SD16×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3360 |
350 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|b^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,d^b=de,f^c=fg,h^d=h^42623 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3360, C2×#19147245, #25976234, … |
| maximal normal subgroup of | D43×#3360, C2×#19147245, #25976234, … |
| maximal quotient of | #25113194, #25113394, #25115556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17160);