Finite Group DatabasebetaFinite Group Databasebeta| order | 2736 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×D3×D19⋊C3 |
| Fitting, socle | C22×C3×C19 ⋊ C22×C3 |
| derived | C3×C19 ⋊ C24×C3 |
| Hall | C3×C19⋊C3 ⋊ C24 |
| Sylow | C19 ⋊ C23×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D19⋊C3 |
| commutator, cosocle, hypocenter | C3×C19 | C24×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C19 | C22×C3 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C22 | |
568 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 228 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×AGL(1,𝔽19), C22×C3⋊D3×D19⋊C3, D3×D4×D19⋊C3, … |
| maximal normal subgroup of | C22×D3×AGL(1,𝔽19), D3×D4×D19⋊C3, D3×A4×D19⋊C3 |
| maximal quotient of | C22×C3⋊D3×D19⋊C3, D3×D4×D19⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.