Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×C19⋊C8 |
| derived, Sylow | C19 ⋊ C22×C3×C8 |
| Hall | C3×C19 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C4 | D19 |
| commutator, hypocenter | C19 | C22×C3×C8 |
| Frattini | C4 | C22×C3×D19 |
| Fitting | C22×C3×C4×C19 | C2 |
| socle, prime radical | C23×C3×C19 | C4 |
| cosocle | C4×C19 | C23×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C22×C3×C4 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1824 |
528 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 813);