Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#99 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | C22⋊C4 |
| commutator | C22 | C2×C3×C4×C5 |
| Frattini, cosocle | C23 | C22×C3×C5 |
| prime radical | C2×C3×C5×D4 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C23×C3×C5 ◁ G | |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,2,3,4,5)(6,7)(8,12,13,10)(9,11)(14,15,16);(6,8)(7,10)(9,13)(11,12)165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 202);