Finite Group DatabasebetaFinite Group Databasebeta| order | 1368 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C4×D19⋊C3 |
| unambiguous semidirect product | D19⋊(C32×C4) |
| unambiguous semidirect product | (C4×D19)⋊C32 |
| unambiguous semidirect product | (C3×C4×D19)⋊C3 |
| Fitting | C3×C4×C19 ⋊ C2×C3 |
| derived, Sylow | C19 ⋊ C2×C32×C4 |
| Hall | C3×C19⋊C3 ⋊ C2×C4 |
| Hall | C4×D19 ⋊ C32 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 228 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D4×D19⋊C3, C4×D3×D19⋊C3, D12×D19⋊C3, … |
| maximal normal subgroup of | C3×D4×D19⋊C3, C4×D3×D19⋊C3, D12×D19⋊C3, … |
| maximal quotient of | D19⋊C3×AGL(1,𝔽13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1368, 85);