Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10690 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10690 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #401 |
| commutator, Frattini, cosocle | C25 | C23×C19 |
| prime radical | C25×C19 | C23 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C25×C19 ◁ G | |
372 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 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)(22,31,34,42)(23,35,50,44)(24,28)(25,30)(26,33,41,49)(27,37,45,38)(29,39)(32,46,47,43)(36,40,48,51);(20,22)(21,26,30,42)(23,36,37,47)(24,34)(25,33)(27,43,45,51)(28,41,29,31)(32,38,48,50)(35,46,44,40)(39,49);(20,23)(21,27,28,44)(22,32,33,47)(24,37)(25,38)(26,40,31,46)(29,45,30,35)(34,48,49,36)(39,50)(41,43,42,51)475 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3678);