Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of C3⋊D63 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊Dic63 |
| unambiguous semidirect product | (C2×C3)⋊Dic63 |
| unambiguous semidirect product | (C2×C7)⋊(C3⋊Dic9) |
| unambiguous semidirect product | (C2×C9)⋊Dic21 |
| derived, Hall | C3×C7×C9 ⋊ C2×C4 |
| Sylow | C3×C9 ⋊ C2×Dic7 |
| Sylow | C7 ⋊ C2×C3⋊Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊D63 |
| commutator, hypocenter | C3×C7×C9 | C2×C4 |
| Frattini | C2×C3 | C2×C3⋊D21 |
| Fitting | C22×C3×C7×C9 | C2 |
| socle, prime radical | C22×C32×C7 | D3 |
| cosocle | C2×C3×C7×C9 | C22 |
| LCS | G ▷ C3×C7×C9 | |
| UCS | C1 ◁ C22 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1512 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 410);