Finite Group DatabasebetaFinite Group Databasebeta| order | 21333 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C547⋊C3)⋊C13 |
| unambiguous semidirect product | (C547⋊C13)⋊C3 |
| Fitting, socle, derived, Sylow | C547 ⋊ C3×C13 |
| Hall | C547⋊C13 ⋊ C3 |
| Hall | C547⋊C3 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C547 | C3×C13 |
| LCS | G ▷ C547 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 547 |
Polycyclic presentation:
3,13,547|c^a=c^40,c^b=c^47553 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21333, 1);