Finite Group DatabasebetaFinite Group Databasebeta| order | 20475 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C5 |
| abelian | C32×C52×C7×C13 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
192 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 20475 |
A minimal faithful permutation representation — 2 generators on 36 points:
(1,2,3)(7,8,9,10,11)(17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36);(4,5,6)(12,13,14,15,16)20475 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20475, 22);