Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#85562 |
| derived | C22⋊SL(2,𝔽3) ⋊ C4×C5 |
376 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(6,7,8,9)(10,11,13,12)(14,20,19,16,17,15,21,18);(11,12,13)(15,19,16)(18,20,21)150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236998);