Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×C8×C9 |
| Fitting | C2×C3×C8×C9 ⋊ C2 |
| derived | C3 ⋊ C22×C8×C9 |
| Sylow | C3×C9 ⋊ C22×C8 |
250 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D3)⋊(C9⋊C16), C9×(C2×D3)⋊C16, C2×D3×C9⋊C16, … |
| maximal normal subgroup of | (C2×D3)⋊(C9⋊C16), C9×(C2×D3)⋊C16, C2×D3×C9⋊C16, … |
| maximal quotient of | C8×C9×Dic6, C4×D3×C8×C9, C9×#4685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1459);