Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C173 ⋊ C2 |
| Sylow | C173 ⋊ #99 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,173|a^2=d,b^a=bc,c^a=ce,d^b=de,f^b=f^172871 conjugacy classes — view the full character table.
| maximal subgroup of | #99×D173, C2×#19149593, #26011463, … |
| maximal normal subgroup of | #99×D173, C2×#19149593, #26011463, … |
| maximal quotient of | #26011214, #26011216, #26011224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 60);