Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C9⋊C8 |
| derived | C9 ⋊ C3×C7×C8 |
| Hall | C3×C7×C9 ⋊ C8 |
| Sylow | C3×C9 ⋊ C7×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4×C7 | D9 |
| commutator, hypocenter | C9 | C3×C7×C8 |
| Frattini | C3×C4 | C3×D3×C7 |
| Fitting | C3×C4×C7×C9 | C2 |
| socle, prime radical | C2×C32×C7 | Dic3 |
| cosocle | C4×C9 | C2×C3×C7 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C3×C4×C7 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 504 |
504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 67);