Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13406 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #2034 |
| prime radical | C19×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
390 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)(22,33)(23,39)(24,31)(25,47)(26,32)(27,35)(28,42)(29,46)(30,45)(34,65)(36,52)(37,54)(38,53)(40,73)(41,74)(43,60)(44,72)(48,59)(49,58)(50,61)(51,70)(55,81)(56,77)(57,78)(62,76)(63,67)(64,71)(66,83)(68,82)(69,80)(75,79);(20,22)(21,27)(23,40)(24,37)(25,48)(26,38)(28,55)(29,53)(30,59)(31,33)(32,54)(34,43)(35,46)(36,50)(39,65)(41,68)(42,75)(44,66)(45,69)(47,64)(49,67)(51,56)(52,62)(57,63)(58,79)(60,83)(61,80)(70,78)(71,76)(72,82)(73,74)(77,81);(20,23,26,44)(21,28,32,57)(22,34)(24,43,46,41)(25,49,50,77)(27,51)(29,58,31,56)(30,60,62,74)(33,63)(35,40)(36,70)(37,66)(38,68)(39,61,72,47)(42,76,78,45)(48,75)(52,65)(53,55)(54,79)(59,82)(64,83)(67,71)(69,81)(73,80)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6394);