Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22×AΣL(1,𝔽27) ⋊ C2 |
| Sylow | AΣL(1,𝔽27) ⋊ D4 |
138 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 24 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:
2^2,3,2,3^3|b^a=bd,e^a=e^2,f^a=f^2g,e^c=ef,f^e=fg61 conjugacy classes — view the full character table.
| maximal subgroup of | #13047188, #13047191, #13047197, … |
| maximal normal subgroup of | #13047188, #13047191, #13047197, … |
| maximal quotient of | #13046632, #13046637, #13046677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 160);