Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13030 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13031 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1879 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,31,50,53,48,30,27,33,47,64,26,32,24,46)(22,34,37,28,51,55,36,65,39,68,75,57,38,62,49,56)(23,40,43,61,52,63,41,60,45,58,78,29,44,59,42,66)(35,54,71,67,76,83,70,79,73,82,74,77,72,81,69,80);(20,22,26,51,27,39,50,38)(21,28,53,56,33,57,32,65)(23,35,52,72,45,73,44,76)(24,37,47,36,48,75,25,49)(29,54,60,83,61,82,66,81)(30,62,64,68,46,55,31,34)(40,77,59,80,58,67,63,79)(41,74,78,70,42,71,43,69);(20,23)(21,29)(22,35)(24,43)(25,42)(26,52)(27,45)(28,54)(30,63)(31,58)(32,66)(33,61)(34,67)(36,74)(37,69)(38,76)(39,73)(40,64)(41,47)(44,50)(46,59)(48,78)(49,71)(51,72)(53,60)(55,80)(56,83)(57,82)(62,79)(65,81)(68,77)(70,75)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6019);