Finite Group DatabasebetaFinite Group Databasebeta| order | 1368 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | C4×#4294⋊C2 |
| derived, Sylow | C19 ⋊ C2×C4×C9 |
| Hall | #4294 ⋊ C2×C4 |
| Hall | C4×D19 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | D19⋊C3 |
| commutator, hypocenter | C19 | C2×C4×C9 |
| Frattini | C2×C3 | C2×D19⋊C3 |
| Fitting | C3×C4×C19 | C2×C3 |
| socle, cosocle | C2×C3×C19 | C22×C3 |
| prime radical | C2×C3×D19 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C4 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 684 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1368, 8);