Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #97 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2144 |
Polycyclic presentation:
2^5,67|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^66548 conjugacy classes — view the full character table.
| maximal subgroup of | #16863173, #97×D67, C2×#14523953, … |
| maximal normal subgroup of | #16863173, #97×D67, C2×#14523953, … |
| maximal quotient of | #16863117, #16863118, #16863150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 56);