Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#108 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | D4 |
| commutator | C4 | C2×C3×C4×C5 |
| Frattini, cosocle | C2×C4 | C22×C3×C5 |
| socle | C2×C3×C5 | C4⋊C4 |
| prime radical | C22×C3×C5 | Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C2×C3×C4×C5 ◁ G | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,5,8,6,9,4,14)(3,10,12,15,13,16,11,7)(17,18,19,20,21)(22,23,24);(1,3,4,11,6,13,5,12)(2,7,8,10,9,15,14,16)210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 211);