Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C43×#346 ⋊ C2 |
| Sylow | C43 ⋊ #1333 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,c^2=e,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^42,c^b=ceg,d^b=dg,e^b=eg,h^b=h^42872 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1333, C2×#19132563, #25006362, … |
| maximal normal subgroup of | D43×#1333, C2×#19132563, #25006362, … |
| maximal quotient of | #24983253, #24983265, #24983365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2478);