Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#20521 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C22 | C22×C42×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle, prime radical | C23×C19 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25)(26,30)(27,31)(28,29)(32,33,37,40,36,39,45,35)(34,41,44,43,42,38,46,47);(20,21,23,22)(25,29)(30,31)(32,34,36,42)(33,38,39,41)(35,43,40,47)(37,44,45,46);(20,22,23,21)(24,26,28,27)(25,30,29,31)(33,39)(34,42)(35,40)(44,46);(24,27,28,26)(25,31,29,30)(32,35,45,39,36,40,37,33)(34,43,46,41,42,47,44,38)1900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13509);