Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| isoclinism | isoclinic class of S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C2×C19×SL(2,ℤ/4) |
| unambiguous semidirect product | (C2×A4)⋊(C4×C19) |
| derived | A4 ⋊ C2×C4×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C19 | S4 |
| commutator, hypocenter | A4 | C2×C4×C19 |
| Frattini | C2 | C2×C19×S4 |
| Fitting, socle | C24×C19 | D3 |
| prime radical | C22×A4×C19 | C2 |
| cosocle | C2×A4 | C22×C19 |
| LCS | G ▷ A4 | |
| UCS | C1 ◁ C22×C19 | |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 456 |
380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 1067);