Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#4183 |
| Fitting | C4×AΣL(1,𝔽27) ⋊ C2 |
| Sylow | AΣL(1,𝔽27) ⋊ D4 |
160 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^3,3^4|b^2=c,b^a=bc,d^a=d^2,e^a=e^2,f^a=fg^2,g^a=g^2,e^d=ef,f^d=fg43 conjugacy classes — view the full character table.
| maximal subgroup of | #13046413, #13046415, #13046416, … |
| maximal normal subgroup of | #13046413, #13046415, #13046416, … |
| maximal quotient of | #13046743, #13046746, #13046747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 181);