Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#69417 |
| Hall | C3×C5 ⋊ #1443 |
| Sylow | C3 ⋊ C5×#1443 |
952 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)(14,16)(17,19,20,18)(21,22)(23,24);(7,8)(13,14)(15,16)(17,18)(19,20)(21,22,23,24);(9,10,11,12)(18,19)(21,22,23,24)420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5909);