Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13310 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13311 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1999 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
520 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)(22,34)(23,40)(24,44)(25,33)(26,31)(27,32)(28,36)(29,42)(30,47)(35,64)(37,57)(38,62)(39,63)(41,73)(43,60)(45,51)(46,59)(48,58)(49,56)(50,74)(52,69)(53,68)(54,79)(55,76)(61,66)(65,71)(67,81)(70,80)(72,75)(77,82)(78,83);(20,22,27,39)(21,28,32,52)(23,35,43,67)(24,45,48,68)(25,38,26,37)(29,54,56,50)(30,57,59,62)(31,53,33,51)(34,58,63,44)(36,46,69,47)(40,71,60,78)(41,74,76,79)(42,70,49,66)(55,81,73,64)(61,72,80,82)(65,77,83,75);(20,23)(21,29)(22,35)(24,41)(25,49)(26,42)(27,43)(28,50)(30,55)(31,60)(32,56)(33,40)(34,61)(36,65)(37,70)(38,66)(39,67)(44,72)(45,74)(46,77)(47,75)(48,76)(51,78)(52,54)(53,71)(57,64)(58,82)(59,73)(62,81)(63,80)(68,79)(69,83)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6299);