Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×#2982⋊C3 |
| unambiguous semidirect product | #2982⋊(C3×C5) |
| unambiguous semidirect product | (C5×#2982)⋊C3 |
| Fitting, Hall | C5×#2982 ⋊ C3 |
| Sylow | #2982 ⋊ C3×C5 |
252 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 76 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)(15,19)(16,22,17)(20,29,21,26,28,27)(23,25,24);(6,7,8,10,9,11,12,13)(14,28,18,29)(15,22,19,23)(16,21,24,27)(17,26,25,20)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236675);