Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×Dic3×H(3,𝔽3) |
| unambiguous semidirect product | (C2×C3)⋊(C4×H(3,𝔽3)) |
| unambiguous semidirect product | (C2×C32×Dic3)⋊C3 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×C4 |
261 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×(C3⋊Dic3)⋊C3, #88807⋊C3, #88806⋊C3, … |
| maximal normal subgroup of | Dic3×(C3⋊Dic3)⋊C3, #88807⋊C3, #88806⋊C3, … |
| maximal quotient of | C2×C3⋊C8×H(3,𝔽3), H(3,𝔽3)×#208, C4×Dic3×H(3,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 462);