Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | Q8 ⋊ C27⋊C3 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
3^4,2^3|a^3=c,c^3=d,e^2=g,f^2=g,b^a=bd,e^a=f,f^a=efg,f^e=fg93 conjugacy classes — view the full character table.
| maximal subgroup of | #88390⋊C3, #88391⋊C3, C2×#10619570, … |
| maximal normal subgroup of | #88390⋊C3, #88391⋊C3, C2×#10619570, … |
| maximal quotient of | C2×#10619570, #14515829, C9⋊(Q8⋊C27), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 89);