Finite Group DatabasebetaFinite Group Databasebeta| order | 1392 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#204 |
| Fitting | C3×C8×C29 ⋊ C2 |
| Hall | C3×C29 ⋊ SD16 |
| Sylow | C3 ⋊ SD16×C29 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 696 |
A minimal faithful permutation representation — 2 generators on 40 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31,32)(33,34,35,37,36,38,39,40);(31,32)(34,37)(35,39)(38,40)435 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1392, 51);