Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| isoclinism | isoclinic class of D19⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic19⋊A4 |
| unambiguous semidirect product | (C2×Dic19)⋊A4 |
| unambiguous semidirect product | (C2×C22⋊(C19⋊C3))⋊C4 |
| derived | C22×C19 ⋊ C2×C3×C4 |
| Hall | C23×Dic19 ⋊ C3 |
| Sylow | C19 ⋊ C2×C4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D19⋊A4 |
| commutator, hypocenter | C22×C19 | C2×C3×C4 |
| Frattini | C2 | C2×D19⋊A4 |
| Fitting, socle | C24×C19 | C2×C3 |
| prime radical | C22×C22⋊(C19⋊C3) | C2 |
| cosocle | C23×C19 | C22×C3 |
| LCS | G ▷ C22×C19 | |
| UCS | C1 ◁ C22 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 456 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 1115);