Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33469 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33469 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#442 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3414 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
646 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)(21,26,28,41)(22,30)(23,33)(24,37)(27,43,44,51)(29,34,38,42)(31,48)(32,35)(36,39)(40,47,45,46);(20,21)(22,27)(23,34)(24,38)(25,28)(26,39)(29,37)(30,47)(31,44)(32,43)(33,41)(35,51)(36,42)(40,49)(45,50)(46,48);(20,22,24,30,25,31,37,48)(21,27,38,47,28,44,29,46)(23,35,33,50,36,32,39,49)(26,40,34,51,41,45,42,43);(22,31)(27,44)(30,48)(32,35)(40,45)(43,51)(46,47)(49,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26457);