Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C173 ⋊ C2 |
| Sylow | C173 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,173|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^172,d^b=de871 conjugacy classes — view the full character table.
| maximal subgroup of | #26011657, #26011658, #26011662, … |
| maximal normal subgroup of | #26011657, #26011658, #26011662, … |
| maximal quotient of | #26011490, #26011496, #26011531, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 172);