Finite Group DatabasebetaFinite Group Databasebeta| order | 1998 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C37⋊#272 |
| Fitting, derived, Hall | H(3,𝔽3)×C37 ⋊ C2 |
| Sylow | C37 ⋊ #272 |
| Sylow | H(3,𝔽3) ⋊ D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C3⋊D111 |
| commutator, Fitting, cosocle, hypocenter | H(3,𝔽3)×C37 | C2 |
| socle | C3×C37 | C3⋊D3 |
| LCS | G ▷ H(3,𝔽3)×C37 | |
| UCS | C1 ◁ C3 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 333 |
Polycyclic presentation:
2,3^2,37,3|b^a=b^2,c^a=c^2,d^a=d^36,c^b=ce208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1998, 45);