Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×C5×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C22 |
| commutator, Frattini, cosocle | C2 | C24×C3×C5 |
| socle | C22×C3×C5 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ G | |
328 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 18 points:
(1,2)(3,4,5)(6,7,8,9,10);(12,15)(16,18);(11,12)(13,16)(14,15)(17,18);(1,2)(11,13,14,17)(12,16,15,18)300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1183);