Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C67 ⋊ #108 |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1072 |
Polycyclic presentation:
2^5,67|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^b=f^66344 conjugacy classes — view the full character table.
| maximal subgroup of | #108×D67, C2×#14523978, #16863443, … |
| maximal normal subgroup of | #108×D67, C2×#14523978, #16863443, … |
| maximal quotient of | #16863146, #16863148, #16863160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 81);