Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×#67717 |
| Hall | C3×C5 ⋊ #1327 |
| Sylow | C3 ⋊ C5×#1327 |
192 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5)(6,7,8)(10,15,18,16)(12,20)(17,22,24,23)(19,21);(7,8)(9,10,12,17,13,16,21,23,14,18,20,24,11,15,19,22)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 3420);