Finite Group DatabasebetaFinite Group Databasebeta| order | 21054 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C3×C29×D121 |
| unambiguous semidirect product | C121⋊(C2×C3×C29) |
| Fitting, Hall | C3×C29×C121 ⋊ C2 |
| derived, Sylow | C121 ⋊ C2×C3×C29 |
| Hall | C29×C121 ⋊ C2×C3 |
| Hall | C3×C121 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C29 | D121 |
| commutator, cosocle, hypocenter | C121 | C2×C3×C29 |
| Frattini | C11 | C3×D11×C29 |
| Fitting | C3×C29×C121 | C2 |
| socle | C3×C11×C29 | D11 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C3×C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10527 |
5394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21054, 3);