Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D3×(C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | D3×(C3⋊Dic3)⋊C3 |
| unambiguous semidirect product | (D3×C3⋊Dic3)⋊C3 |
| derived | C33 ⋊ C2×C3×C4 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×C4 |
167 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 167 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6196, D3×((C3⋊D3)⋊C3)⋊C4, #13048345, … |
| maximal normal subgroup of | D3×#6196, D3×((C3⋊D3)⋊C3)⋊C4, #13048345, … |
| maximal quotient of | D3×(C3⋊(C3⋊C8))⋊C3, #88786⋊C3, Dic3×(C3⋊Dic3)⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 374);