Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×C3⋊(C7⋊C8) |
| unambiguous semidirect product | C3⋊(C9×C7⋊C8) |
| derived | C3×C7 ⋊ C8×C9 |
| Hall | C3×C7×C9 ⋊ C8 |
| Sylow | C3×C9 ⋊ C7⋊C8 |
| Sylow | C7 ⋊ C9×C3⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C9 | D21 |
| commutator, hypocenter | C3×C7 | C8×C9 |
| Frattini | C3×C4 | C3×D21 |
| Fitting | C3×C4×C7×C9 | C2 |
| socle, prime radical | C2×C32×C7 | C3×C4 |
| cosocle | C32×C4×C7 | C2×C3 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C4×C9 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 504 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 72);