Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of C3⋊#1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊#1088 |
| unambiguous semidirect product | C3⋊(C5×#1088) |
| Fitting, Hall | C3×C5×H(3,𝔽3) ⋊ C4 |
| derived, Sylow | C3×H(3,𝔽3) ⋊ C4×C5 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 90 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3,4,5)(6,7)(8,14,15,22)(9,18)(10,13)(11,19,12,17)(16,20,23,21);(6,16,23)(7,18,13)(8,15,10)(9,17,19)(12,21,22)120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 294);