Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×C3×#1094 |
| Sylow | C23 ⋊ C3×3−1+2 |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#1094⋊C4, C3⋊(#1094⋊C4), Dic3×#1094, … |
| maximal normal subgroup of | C3×#1094⋊C4, C3⋊(#1094⋊C4), Dic3×#1094, … |
| maximal quotient of | C3×C4×#1094, C2×C3×#6204, C3×#88691, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 620);