Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11255 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C19 | C23 |
| commutator | C23 | C22×C8×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle, prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C19 ◁ G | |
846 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22)(28,29,31,30)(32,33,34,36,35,37,38,39);(20,21,23,22)(24,25)(26,27)(28,30,31,29);(20,22,23,21)(25,27)(29,30)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4243);