Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×Dic3⋊C8 |
| unambiguous semidirect product | Dic3⋊(C32×C8) |
| Sylow | C33 ⋊ C4⋊C8 |
316 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×Dic3⋊C8, C3×#10590656, C3×#10590643, … |
| maximal normal subgroup of | C3×D3×Dic3⋊C8, C3×#10590656, C3×#10590643, … |
| maximal quotient of | C32×#4479, C32×#4480, C32×Dic3⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2069);