Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×#69814 |
| Hall | C3×C5 ⋊ #1776 |
| Sylow | C3 ⋊ C5×#1776 |
544 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(13,15,16,14)(18,23)(22,24);(7,8)(9,10,11,12)(18,22)(19,20)(23,24);(13,14,16,15)(17,18,20,22,21,23,19,24)420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 22353);