Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#5018 |
| Hall | C3×C5 ⋊ #440 |
| Sylow | C3 ⋊ C5×#440 |
240 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 240 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) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(6,7,8)(9,10,11,12)(13,15,16,17)(14,19,20,18);(14,18)(15,17)(19,20);(7,8)(13,14,16,20)(15,19,17,18)210 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#440, C2×C5×#5018, D5×#5018, … |
| maximal normal subgroup of | C5×D3×#440, C2×C5×#5018, D5×#5018, … |
| maximal quotient of | C5×#70839, C5×#70843, C5×#70865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4712);