Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24411 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1294 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)(22,32,36,27)(23,37)(24,42,44,29)(25,30)(26,31)(28,40)(33,58,61,48)(34,49)(35,56,46,50)(38,65,64,51)(39,66,68,52)(41,57)(43,70,73,54)(45,55)(47,53)(59,62)(60,80)(63,75)(67,83)(69,79,72,77)(71,78)(74,81)(76,82);(20,22,25,36)(21,27,30,32)(23,38,40,64)(24,34,44,62)(26,46,45,35)(28,51,37,65)(29,49,42,59)(31,56,55,50)(33,47,61,41)(39,67,68,82)(43,71,73,63)(48,57,58,53)(52,76,66,83)(54,78,70,75)(60,72,81,69)(74,79,80,77);(20,23)(21,28)(22,33)(24,39)(25,40)(26,47)(27,48)(29,52)(30,37)(31,57)(32,58)(34,60)(35,64)(36,61)(38,46)(41,45)(42,66)(43,72)(44,68)(49,74)(50,65)(51,56)(53,55)(54,79)(59,80)(62,81)(63,82)(67,71)(69,73)(70,77)(75,83)(76,78);(20,24)(21,29)(22,34)(23,39)(25,44)(26,43)(27,49)(28,52)(30,42)(31,54)(32,59)(33,60)(35,63)(36,62)(37,66)(38,67)(40,68)(41,69)(45,73)(46,71)(47,72)(48,74)(50,75)(51,76)(53,77)(55,70)(56,78)(57,79)(58,80)(61,81)(64,82)(65,83)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17399);