Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic67⋊C8 |
| Sylow | C67 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2144 |
Polycyclic presentation:
2^5,67|a^2=d,b^2=c,d^2=e,b^a=bc,f^b=f^66548 conjugacy classes — view the full character table.
| maximal subgroup of | C4⋊C8×D67, C2×Dic67⋊C8, #16863418, … |
| maximal normal subgroup of | C4⋊C8×D67, C2×Dic67⋊C8, #16863418, … |
| maximal quotient of | #16863146, #16863148, #16863150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 75);