Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C24×C42 |
| direct product | C4×C19×#391 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C19 | C23 |
| commutator | C22 | C22×C42×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| socle, prime radical | C24×C19 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C19 ◁ G | |
2110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(6,8)(9,10,12,11)(15,19)(17,20);(5,6,7,8)(9,11,12,10)(13,14,16,18)(15,17,19,20);(13,15,16,19)(14,17,18,20)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6756);