Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | Aut(G) = C22×C4×#41 (order 256) · Inn(G) = C22 · Out(G) = C24×C4 |
| homology | Abelianization (H1) = C2×C3×C5×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C5×C8 | C22 |
| commutator | C2 | C2×C3×C5×C8 |
| Frattini, cosocle | C8 | C22×C3×C5 |
| socle | C2×C3×C5 | C2×C8 |
| prime radical | C22×C3×C5 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C5×C8 ◁ G | |
52 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)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24);(10,18)(12,20)(14,22)(16,24)300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 213);