Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #64945 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#64960 |
| Fitting | C3×C5×#95 ⋊ C2 |
| Hall | C3×C5 ⋊ #392 |
| Sylow | C5 ⋊ C3×#392 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C3 | C22×D5 |
| commutator, cosocle | C23×C5 | C23×C3 |
| Frattini | C23 | C22×C3×D5 |
| Fitting | C3×C5×#95 | C2 |
| socle | C23×C3×C5 | C23 |
| hypercenter | C3×#95 | D5 |
| hypocenter | C5 | C3×#392 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23×C3 ◁ C3×#95 | |
644 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 138 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)(4,5,7,8,6)(14,16)(17,18,19,20);(9,10,11,12)(13,14)(15,16);(5,6)(7,8)(10,12)(18,20)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598495, #14278083, C3×#10599077, … |
| maximal normal subgroup of | C3×#10598495, #14278083, C3×#10599077, … |
| maximal quotient of | C3×#10600219, C3×#10600220, C3×#10600212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3763);