Finite Group DatabasebetaFinite Group Databasebeta| order | 21021 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11×C13 · Schur multiplier (H2) = C1 |
| direct product | C11×C13×C49⋊C3 |
| unambiguous semidirect product | C49⋊(C3×C11×C13) |
| unambiguous semidirect product | (C11×C49)⋊(C3×C13) |
| Fitting, Hall | C11×C13×C49 ⋊ C3 |
| derived, Sylow | C49 ⋊ C3×C11×C13 |
| Hall | C13×C49 ⋊ C3×C11 |
| Hall | C11×C49 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C13 | C49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C3×C11×C13 |
| Frattini | C7 | C11×C13×ΓL(1,𝔽8) |
| Fitting | C11×C13×C49 | C3 |
| socle | C7×C11×C13 | ΓL(1,𝔽8) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C11×C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7007 |
2717 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21021, 3);