Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#542 ⋊ C2 |
| Sylow | C43 ⋊ #3125 |
384 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,f^c=fg,h^c=h^42494 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3125, C2×#19144866, #25964959, … |
| maximal normal subgroup of | D43×#3125, C2×#19144866, #25964959, … |
| maximal quotient of | #25096701, #25099682, #25099697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 14781);