Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×#4508 |
| Fitting | C2×C3×C5×C16 ⋊ C2 |
| Hall | C3×C5 ⋊ #350 |
| Sylow | C3 ⋊ C5×#350 |
112 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 54 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 — 2 generators on 40 points:
(1,2,3,4,5)(6,7,8)(9,11,12,21,14,23,27,37,15,24,28,38,13,22,26,36)(10,16,17,30,18,20,32,33,19,31,25,39,29,34,40,35);(7,8)(9,10)(11,20)(12,25)(13,29)(14,18)(15,19)(16,22)(17,28)(21,35)(23,31)(24,34)(26,32)(27,40)(30,37)(33,38)(36,39)300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×#350, C2×C5×#4508, D5×#4508, … |
| maximal normal subgroup of | C5×D3×#350, C2×C5×#4508, D5×#4508, … |
| maximal quotient of | C5×#67523, C5×#67525, C5×#67503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 402);