Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×C5×#124 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C3×C5 |
| prime radical | C2×C3×C5×D4 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(7,8)(10,11)(12,14)(13,15)(16,17)(18,19,20);(6,7,9,8)(10,12,13,16)(11,14,15,17);(6,8,9,7)(11,15)(14,17)210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 929);