Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×(C2×AGL(1,𝔽5))⋊C4 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊(C4×C11) |
| Fitting | C2×C4×C5×C11 ⋊ C4 |
| Hall | C5×C11 ⋊ #95 |
| Sylow | C5 ⋊ C11×#95 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 440 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15)(17,18,19,20)(22,24);(13,14,15,16)(21,22)(23,24)308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 436);