Finite Group DatabasebetaFinite Group Databasebeta| order | 1656 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2×C3 |
| direct product | C23×C4⋊(C3⋊D3) |
| unambiguous semidirect product | C4⋊(C3⋊D3×C23) |
| Fitting | C32×C4×C23 ⋊ C2 |
| Hall | C32×C23 ⋊ D4 |
| Sylow | C32 ⋊ D4×C23 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 828 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27)(31,32,33);(25,27)(29,30)(32,33);(28,29,30)483 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1656, 97);