Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24985 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#24985 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | #2420 |
| prime radical | C19×#3067 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ 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)(20,21)(22,34)(23,38)(24,28)(25,32)(26,31)(27,33)(29,41)(30,37)(35,50)(36,45)(39,47)(40,46)(42,48)(43,49)(44,51);(20,22,26,36,27,37,25,24)(21,28,32,30,33,45,31,34)(23,39,41,35,43,40,42,51)(29,46,38,50,48,47,49,44);(20,23)(21,29)(22,35)(24,40)(25,41)(26,42)(27,43)(28,44)(30,47)(31,38)(32,49)(33,48)(34,46)(36,39)(37,51)(45,50);(20,24,25,37,27,36,26,22)(21,30,31,28,33,34,32,45)(23,40,41,51,43,39,42,35)(29,47,38,44,48,46,49,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17973);