Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×#65190 |
| Fitting | C2×C3×C5×C16 ⋊ C2 |
| Hall | C3×C5 ⋊ #504 |
| Sylow | C5 ⋊ C3×#504 |
168 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,2,3)(4,5,7,8,6)(9,11,12,19,13,20,22,31,14,21,23,32,24,33,34,39)(10,16,17,28,18,29,30,38,15,25,26,35,27,36,37,40);(10,15)(16,25)(17,26)(18,27)(28,35)(29,36)(30,37)(38,40);(5,6)(7,8)(9,10)(11,16)(12,17)(13,18)(14,15)(19,28)(20,29)(21,25)(22,30)(23,26)(24,27)(31,38)(32,35)(33,36)(34,37)(39,40)312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10598086, C3×#10598094, #14279284, … |
| maximal normal subgroup of | C3×#10598086, C3×#10598094, #14279284, … |
| maximal quotient of | C3×#10599844, C3×#10602192, C3×#10599900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3993);