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 |
| direct product | C3×C5×#126 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C3×C5 |
| prime radical | C23×C3×C5 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7)(8,10)(9,11)(12,13)(14,15)(16,20)(17,18)(19,21)(22,23,24);(6,8,9,12)(7,10,11,13)(15,18)(19,20);(7,11)(10,13)(14,16,17,21)(15,19,18,20)210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 931);