Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | H(3,𝔽3) ⋊ C3×C8 |
| Sylow | AΣL(1,𝔽27) ⋊ C8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2,3,2^2,3^3|a^2=c,c^2=d,e^a=e^2,f^a=f^2g,e^b=ef,f^e=fg88 conjugacy classes — view the full character table.
| maximal subgroup of | #4183⋊C8, #4175⋊C8, #13046410, … |
| maximal normal subgroup of | #4183⋊C8, #4175⋊C8, #13046410, … |
| maximal quotient of | #13046317, C2×#10619500, #14515619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 19);