Finite Group DatabasebetaFinite Group Databasebeta| order | 21306 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3551 |
| unambiguous semidirect product | C53⋊(C3×D67) |
| Fitting, socle, Hall | C3×C53×C67 ⋊ C2 |
| derived, Hall | C53×C67 ⋊ C2×C3 |
| Hall | C3×C67 ⋊ D53 |
| Hall | C3×C53 ⋊ D67 |
| Sylow | C67 ⋊ C3×D53 |
| Sylow | C53 ⋊ C3×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3551 |
| commutator, cosocle, hypocenter | C53×C67 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C53×C67 | C2 |
| LCS | G ▷ C53×C67 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10653 |
5331 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21306, 5);