Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 172032 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C5 |
| multiplicative | (ℤ/1144)ˣ, (ℤ/1155)ˣ, (ℤ/1232)ˣ, (ℤ/1240)ˣ, (ℤ/1400)ˣ, (ℤ/1464)ˣ, (ℤ/1488)ˣ, (ℤ/1540)ˣ, (ℤ/1584)ˣ, (ℤ/1716)ˣ, (ℤ/1800)ˣ, (ℤ/1860)ˣ, (ℤ/1980)ˣ, (ℤ/2100)ˣ, (ℤ/2310)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3×C5 |
| socle, prime radical | C24×C3×C5 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
472 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 18 points:
(1,2,3,4)(11,12,13)(14,15,16,17,18);(5,6);(7,8);(9,10)480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1180);