Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×#73071 |
| derived | SL(2,𝔽3) ⋊ C2×C5×C8 |
236 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5)(14,26,23,19,24,29,18,20,25,15,16,28)(17,21,22,27);(6,7,8,10,9,11,12,13)(15,19)(16,22)(17,24)(20,21)(23,25)(26,27)260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236493);