Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of #157×D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | #157×D21 |
| Fitting, socle, derived, Hall | C33×C7 ⋊ C2×C4 |
| Sylow | C33 ⋊ C4×D7 |
| Sylow | C7 ⋊ D3×#157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C33×C7 | C2×C4 |
| prime radical | C3⋊D3×D21 | C2 |
| cosocle | C3×C7×C3⋊D3 | C22 |
| LCS | G ▷ C33×C7 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 817);