Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22284 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#22285 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2328 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
772 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(22,33)(23,39,43,53)(24,44)(25,31)(26,32)(27,36)(28,42,54,68)(29,46)(30,45)(34,59,62,48)(35,63)(37,50)(38,57)(40,51,61,76)(41,52,71,77)(47,55)(49,66)(56,73)(58,64)(60,80,82,75)(65,78)(67,83,72,70)(69,79,81,74);(20,22,25,36,26,38,45,37)(21,27,30,33,32,50,31,57)(23,40,68,34,43,61,42,62)(24,35,46,64,47,66,73,65)(28,51,39,48,54,76,53,59)(29,49,44,58,56,63,55,78)(41,69,83,60,71,81,70,82)(52,75,67,74,77,80,72,79);(20,23,26,43)(21,28)(22,34)(24,41,47,71)(25,42,45,68)(27,48,50,59)(29,52)(30,53)(31,39)(32,54)(33,51,57,76)(35,60)(36,40)(37,61)(38,62)(44,72)(46,70,73,83)(49,74,63,79)(55,67)(56,77)(58,75,78,80)(64,69)(65,81)(66,82);(20,24,45,73,26,47,25,46)(21,29,31,55,32,56,30,44)(22,35,37,65,38,66,36,64)(23,41,68,83,43,71,42,70)(27,49,57,78,50,63,33,58)(28,52,39,67,54,77,53,72)(34,60,61,81,62,82,40,69)(48,74,76,80,59,79,51,75)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15273);