Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#677 |
| Fitting | C5×C8×C17 ⋊ C2 |
| Hall | C5×C17 ⋊ SD16 |
| Sylow | C5 ⋊ SD16×C17 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 680 |
A minimal faithful permutation representation — 2 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)(23,24,25,27,26,28,29,30);(19,20)(21,22)(24,27)(25,29)(28,30)391 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 54);