Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C3×C42×C3⋊D3 |
| Fitting | C33×C42 ⋊ C2 |
| derived | C32 ⋊ C2×C3×C42 |
| Sylow | C33 ⋊ C2×C42 |
768 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 258 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10590151, #13157168, C3×#10590256, … |
| maximal normal subgroup of | C3×#10590151, #13157168, C3×#10590256, … |
| maximal quotient of | C3×#10592365, C3×#10592347, C3×#10592348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3793);