Finite Group DatabasebetaFinite Group Databasebeta| order | 2052 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C32×D19⋊C3 |
| Fitting, socle | C2×C32×C19 ⋊ C2×C3 |
| derived, Sylow | C19 ⋊ C22×C33 |
| Hall | C32×C19⋊C3 ⋊ C22 |
| Hall | C2×D19 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C22×C33 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C19 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C32 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 342 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊D3×D19⋊C3, C22×C32×D19⋊C3, C2×C32×AGL(1,𝔽19) |
| maximal normal subgroup of | C2×C3⋊D3×D19⋊C3, C22×C32×D19⋊C3, C2×C32×AGL(1,𝔽19) |
| maximal quotient of | C22×C32×D19⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.