Finite Group DatabasebetaFinite Group Databasebeta| order | 3036 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | D3×C11×D23 |
| Fitting, socle, Hall | C3×C11×C23 ⋊ C22 |
| derived, Hall | C3×C23 ⋊ C22×C11 |
| Hall | C11×C23 ⋊ C2×D3 |
| Hall | C3×C11 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D3×C11 |
| Sylow | C3 ⋊ C2×C11×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D3×D23 |
| commutator, cosocle, hypocenter | C3×C23 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C23 | C22 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C11 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 759 |
429 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D23×C11⋊C5, C5×D3×C11×D23, C11×D15×D23, … |
| maximal normal subgroup of | D3×D23×C11⋊C5, C5×D3×C11×D23, D3×C7×C11×D23, … |
| maximal quotient of | C5×D3×C11×D23, C11×D15×D23, D3×C11×D115, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3036, 21);