Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×#73056 |
244 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 244 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) = 320 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5)(14,24,26)(15,20,29,19,25,28)(16,23,18)(21,22);(6,7,8,10,9,11,12,13)(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, 236478);