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) = C2 |
| direct product | C3×C5×#101 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | C22⋊C4 |
| commutator | C22 | C2×C3×C4×C5 |
| Frattini, cosocle | C2×C4 | C22×C3×C5 |
| prime radical | C22×C3×C5 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ G | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5)(6,7,9,13,10,12,18,20)(8,14,15,21,16,11,17,19)(22,23,24);(6,8,10,16)(7,11,12,14)(9,17,18,15)(13,21,20,19)165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 204);