Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C4 |
| direct product | C5×#73063 |
| derived | SL(2,𝔽3) ⋊ C42×C5 |
354 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 84 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)(10,11,12,13)(14,24,26)(15,20,29,19,25,28)(16,23,18)(21,22);(6,7,8,9)(14,15)(16,22)(17,25)(18,19)(20,27)(21,24)(23,29)(26,28)260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236485);