Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of (C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C8×(C3⋊D3)⋊C3 |
| unambiguous semidirect product | (C2×C8×C3⋊D3)⋊C3 |
| Fitting | C2×C8×H(3,𝔽3) ⋊ C2 |
| derived | C32 ⋊ C22×C3×C8 |
| Sylow | H(3,𝔽3) ⋊ C22×C8 |
288 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #13135085, #10589373⋊C3, #13138715, … |
| maximal normal subgroup of | #13135085, #10589373⋊C3, #13138715, … |
| maximal quotient of | C8×#634⋊C3, C4×C8×(C3⋊D3)⋊C3, #10592384⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1467);