Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×C4⋊C8 |
| unambiguous semidirect product | C4⋊(C3×C5×C8) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C22 |
| commutator | C2 | C2×C3×C5×C8 |
| Frattini, cosocle | C2×C4 | C22×C3×C5 |
| socle, prime radical | C22×C3×C5 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ G | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 20 points:
(2,4)(5,6,7,9,8,10,11,12)(13,14,15,16,17)(18,19,20);(1,2,3,4)300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 208);