Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#709 |
| Fitting | C2×C4×C5×C17 ⋊ C2 |
| Hall | C5×C17 ⋊ #41 |
| Sylow | C5 ⋊ #41×C17 |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 680 |
A minimal faithful permutation representation — 3 generators on 30 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,22,20)(24,28)(27,30);(23,25,26,29)(24,27,28,30);(19,20)(21,22)(23,24)(25,27)(26,28)(29,30)442 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 199);