Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C9 · Schur multiplier (H2) = C4 |
| direct product | C4×C9×C3⋊C8 |
| derived | C3 ⋊ C4×C8×C9 |
| Sylow | C3×C9 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42×C9 | D3 |
| commutator, hypocenter | C3 | C4×C8×C9 |
| Frattini | C2×C3×C4 | C2×C3×D3 |
| Fitting | C3×C42×C9 | C2 |
| socle, prime radical | C22×C32 | C2×C3×C4 |
| cosocle | C2×C32×C4 | C22×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C42×C9 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊C8×C9⋊C8, #13134921, #13134922, … |
| maximal normal subgroup of | C3⋊C8×C9⋊C8, #13134921, #13134922, … |
| maximal quotient of | C8×C9×C3⋊C8, C9×#4455, C4×C9×C3⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 331);