Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#465 ⋊ C2 |
| Sylow | C43 ⋊ #3257 |
358 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^42,c^b=ce,d^b=dg,f^c=fg,h^c=h^42,h^d=h^42488 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3257, C2×#19146009, #25969576, … |
| maximal normal subgroup of | D43×#3257, C2×#19146009, #25969576, … |
| maximal quotient of | #25106574, #25106579, #25107006, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15924);