Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C27×C4 |
| direct product | C4×C19×#555 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| socle | C23×C19 | C25 |
| prime radical | C2×C19×#555 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
2564 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(5,6)(7,11)(8,12)(9,10)(14,15)(18,19);(6,10)(8,11)(13,14,17,15)(16,19,20,18);(5,7,9,12)(6,11,10,8)(13,15,17,14)(16,19,20,18);(5,8,9,11)(6,12,10,7)(13,16,17,20)(14,18,15,19)1900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27153);