Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C3×C27 ⋊ Q8 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^3,3^4|a^2=c,b^2=c,d^3=f,f^3=g,b^a=bc,d^a=d^2f^2g^2,e^a=e^2,f^a=f^2g^2,g^a=g^2165 conjugacy classes — view the full character table.
| maximal subgroup of | #13046389, #13046394, #13046400, … |
| maximal normal subgroup of | #13046389, #13046394, #13046400, … |
| maximal quotient of | #13046778, C4⋊(C3⋊Dic27), C2×#10619657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 176);