Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C9 · Schur multiplier (H2) = C26×C3 |
| direct product | C23×C9×C3⋊D3 |
| Fitting | C23×C32×C9 ⋊ C2 |
| derived | C32 ⋊ C24×C9 |
| Sylow | C32×C9 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C9 | C3⋊D3 |
| commutator, hypocenter | C32 | C24×C9 |
| Frattini | C3 | C23×C3×C3⋊D3 |
| Fitting | C23×C32×C9 | C2 |
| socle | C23×C33 | C2×C3 |
| prime radical | C23×C3×C3⋊D3 | C3 |
| cosocle | C33 | C24×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23×C9 | |
1462 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4×C9×C3⋊D3, C23×D9×C3⋊D3, C2×C3⋊D3×#611, … |
| maximal normal subgroup of | C2×D4×C9×C3⋊D3, C23×D9×C3⋊D3, C2×C3⋊D3×#611, … |
| maximal quotient of | C2×D4×C9×C3⋊D3, C22×C3⋊D3×AGL(1,𝔽19) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3069);