Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #103 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2144 |
Polycyclic presentation:
2^5,67|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^66,c^b=ce344 conjugacy classes — view the full character table.
| maximal subgroup of | #103×D67, C2×#14523967, #16863391, … |
| maximal normal subgroup of | #103×D67, C2×#14523967, #16863391, … |
| maximal quotient of | Q8⋊(C67⋊C8), #16863133, #16863142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 70);