Finite Group DatabasebetaFinite Group Databasebeta| order | 1971 |
| isoclinism | isoclinic class of #10620323 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×#10620323 |
| unambiguous semidirect product | (C73⋊C3)⋊C9 |
| Fitting, socle | C3×C73 ⋊ C9 |
| derived, Sylow | C73 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10620323 |
| commutator, hypocenter | C73 | C3×C9 |
| Frattini | C1 | G |
| Fitting, socle | C3×C73 | C9 |
| prime radical | C3×C73⋊C3 | C3 |
| cosocle | C73⋊C3 | C32 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 219 |
51 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10620323⋊C2, D3×#10620323, #72276533 |
| maximal normal subgroup of | C3×#10620323⋊C2, D3×#10620323, #72276533 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1971, 15);