Finite Group DatabasebetaFinite Group Databasebeta| order | 2736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D4×C3⋊(D19⋊C3) |
| Fitting | C3×D4×C19 ⋊ C2×C3 |
| Hall | C3×C19⋊C3 ⋊ C2×D4 |
| Sylow | C19 ⋊ C3×D3×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×C3⋊(D19⋊C3) |
| commutator, socle, cosocle | C2×C3×C19 | C23×C3 |
| Fitting | C3×D4×C19 | C2×C3 |
| hypercenter | D4 | C3⋊(D19⋊C3) |
| hypocenter | C3×C19 | C2×C3×D4 |
| LCS | G ▷ C2×C3×C19 ▷ C3×C19 | |
| UCS | C1 ◁ C2 ◁ D4 | |
232 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 228 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4×D19⋊C3, D4×C3⋊AGL(1,𝔽19) |
| maximal normal subgroup of | D3×D4×D19⋊C3, D4×C3⋊AGL(1,𝔽19) |
Past the SmallGroups library coverage — no SmallGroups id.