Finite Group DatabasebetaFinite Group Databasebeta| order | 1368 |
| isoclinism | isoclinic class of D3×D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic3×D19⋊C3 |
| unambiguous semidirect product | D19⋊(C3×Dic3) |
| unambiguous semidirect product | (C3×D19⋊C3)⋊C4 |
| unambiguous semidirect product | (Dic3×D19)⋊C3 |
| derived | C3×C19 ⋊ C2×C3×C4 |
| Hall | C3×C19⋊C3 ⋊ C2×C4 |
| Sylow | C19 ⋊ C2×C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D19⋊C3 |
| commutator, hypocenter | C3×C19 | C2×C3×C4 |
| Fitting, socle, cosocle | C2×C3×C19 | C22×C3 |
| prime radical | C2×C3×D19⋊C3 | C2 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C2 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 228 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | #67×D19⋊C3, C4×D3×D19⋊C3, Dic3×AGL(1,𝔽19) |
| maximal normal subgroup of | #67×D19⋊C3, C4×D3×D19⋊C3, Dic3×AGL(1,𝔽19) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1368, 72);