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×#18422 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3188 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
960 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)(22,32)(23,26)(24,30)(25,39)(27,31)(28,34)(29,41)(33,42)(35,45)(36,48)(37,50)(38,43)(40,44)(46,51)(47,49);(20,22)(21,28)(23,33)(24,34)(25,42)(26,36)(27,37)(29,45)(30,48)(31,47)(32,39)(35,44)(38,50)(40,46)(41,49)(43,51);(20,23,26,21)(22,33,36,28)(24,29,25,38)(27,40,44,31)(30,43,39,41)(32,49,48,51)(34,45,42,50)(35,47,37,46);(20,24,26,25)(21,29,23,38)(22,34,36,42)(27,41,44,43)(28,45,33,50)(30,40,39,31)(32,47,48,46)(35,51,37,49)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11410);