Finite Group DatabasebetaFinite Group Databasebeta| order | 2133 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊(C79⋊C3) |
| unambiguous semidirect product | C79⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×C79⋊C3)⋊C3 |
| Fitting | C32×C79 ⋊ C3 |
| Sylow | C79 ⋊ H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C79⋊C3 |
| commutator, socle, cosocle | C3×C79 | C32 |
| Fitting | C32×C79 | C3 |
| hypercenter | C32 | C79⋊C3 |
| hypocenter | C79 | H(3,𝔽3) |
| LCS | G ▷ C3×C79 ▷ C79 | |
| UCS | C1 ◁ C3 ◁ C32 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 711 |
Polycyclic presentation:
3^3,79|b^a=bc,d^b=d^23245 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2133, 9);