Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33538 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C2×C19 | C2×#447 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
1088 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)(22,34)(23,39)(24,30)(25,45)(26,32)(27,33)(28,37)(29,42)(31,47)(35,63)(36,61)(38,62)(40,55)(41,72)(43,59)(44,58)(46,51)(48,57)(49,56)(50,77)(52,76)(53,68)(54,75)(60,66)(64,82)(65,69)(67,80)(70,74)(71,81)(73,79)(78,83);(20,22)(21,28)(23,35)(24,36)(25,46)(26,49)(27,38)(29,50)(30,51)(31,56)(32,52)(33,53)(34,45)(37,47)(39,69)(40,64)(41,73)(42,66)(43,67)(44,68)(48,76)(54,80)(55,79)(57,62)(58,61)(59,78)(60,70)(63,72)(65,74)(71,83)(75,77)(81,82);(20,23)(21,29)(22,35)(24,40)(25,41)(26,42)(27,43)(28,50)(30,39)(31,54)(32,59)(33,55)(34,60)(36,64)(37,65)(38,67)(44,71)(45,70)(46,73)(47,74)(48,75)(49,66)(51,69)(52,78)(53,79)(56,80)(57,81)(58,72)(61,63)(62,82)(68,83)(76,77);(20,24,27,26)(21,30,33,32)(22,36,38,49)(23,40,43,42)(25,44,48,47)(28,51,53,52)(29,39,55,59)(31,45,58,57)(34,61,62,56)(35,64,67,66)(37,46,68,76)(41,71,75,74)(50,69,79,78)(54,70,72,81)(60,63,82,80)(65,73,83,77)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26526);