Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C67 ⋊ C2 |
| Sylow | C67 ⋊ #99 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 536 |
Polycyclic presentation:
2^5,67|a^2=d,b^a=bc,c^a=ce,d^b=de,f^b=f^66341 conjugacy classes — view the full character table.
| maximal subgroup of | #99×D67, C2×#14523957, #16863368, … |
| maximal normal subgroup of | #99×D67, C2×#14523957, #16863368, … |
| maximal quotient of | #16863119, #16863121, #16863129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 60);