Finite Group DatabasebetaFinite Group Databasebeta| order | 1971 |
| isoclinism | isoclinic class of C73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C32×C73⋊C3 |
| unambiguous semidirect product | C73⋊C33 |
| unambiguous semidirect product | (C3×C73)⋊C32 |
| Fitting, socle | C32×C73 ⋊ C3 |
| derived, Sylow | C73 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C33 |
| Frattini | C1 | G |
| Fitting, socle | C32×C73 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C32 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 657 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1971, 13);