Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C210 |
| direct product | C22×C19×#399 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C19 | C23 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| prime radical | C26×C19 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C19 ◁ G | |
5838 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(3,4);(9,10,11,12)(15,19)(17,20);(6,8)(10,12)(13,14,16,18)(15,20,19,17);(5,6)(7,8)(9,10)(11,12)(13,15)(14,17)(16,19)(18,20)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27528);