Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of C3⋊D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C3 |
| direct product | C3×C3⋊(C3⋊(C7⋊C8)) |
| unambiguous semidirect product | C3⋊(C3×C3⋊(C7⋊C8)) |
| derived | C32×C7 ⋊ C3×C8 |
| Hall | C33×C7 ⋊ C8 |
| Sylow | C33 ⋊ C7⋊C8 |
| Sylow | C7 ⋊ C3×C3⋊(C3⋊C8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C3⋊D21 |
| commutator, hypocenter | C32×C7 | C3×C8 |
| Frattini | C4 | C3×C3⋊D21 |
| Fitting | C33×C4×C7 | C2 |
| socle, prime radical | C2×C33×C7 | C4 |
| cosocle | C32×C4×C7 | C2×C3 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C3×C4 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 433);