Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C67 ⋊ C2 |
| Sylow | C67 ⋊ #117 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1072 |
Polycyclic presentation:
2^5,67|a^2=e,c^2=d,b^a=bd,f^b=f^66548 conjugacy classes — view the full character table.
| maximal subgroup of | #16863350, #16863353, #16863411, … |
| maximal normal subgroup of | #16863350, #16863353, #16863411, … |
| maximal quotient of | #16863242, C4×(C2×D67)⋊C4, C4×Dic67⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 103);