Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11302 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #397 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1443 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
532 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)(20,21,25,31,26,29,24,30)(22,27,35,44,33,43,34,42)(23,36,38,45,39,46,40,28)(32,47,48,51,37,50,49,41);(20,22,24,35,26,33,25,34)(21,27,31,42,29,43,30,44)(23,37,38,48,39,32,40,49)(28,41,46,47,45,51,36,50);(20,23)(21,28,29,45)(22,32,33,37)(24,38)(25,40)(26,39)(27,41)(30,36,31,46)(34,48,35,49)(42,47)(43,51)(44,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4290);