Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ #102 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1072 |
Polycyclic presentation:
2^5,67|a^2=d,c^2=e,b^a=bc,c^a=ce,f^a=f^66,c^b=ce,f^b=f^66542 conjugacy classes — view the full character table.
| maximal subgroup of | #102×D67, C2×#14523965, #16863391, … |
| maximal normal subgroup of | #102×D67, C2×#14523965, #16863391, … |
| maximal quotient of | #16863125, #16863131, #16863139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 68);