Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18425 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3536 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,26,23)(22,32,36,46)(24,30,25,38)(27,31,43,39)(28,41,33,34)(29,42,37,40)(35,48,50,44)(45,51,49,47);(20,22,26,36)(21,28,23,33)(24,34,25,41)(27,35,43,50)(29,44,37,48)(30,46,38,32)(31,45,39,49)(40,47,42,51);(20,23,26,21)(22,33,36,28)(24,29,25,37)(27,39,43,31)(30,42,38,40)(32,47,46,51)(34,44,41,48)(35,49,50,45);(20,24,26,25)(21,29,23,37)(22,34,36,41)(27,40,43,42)(28,44,33,48)(30,39,38,31)(32,45,46,49)(35,47,50,51)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11413);