Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33608 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×#41×C19 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 87 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,30,35)(26,36,41,61)(27,32,42,53)(28,45,47,73)(29,48,46,34)(31,49,52,39)(33,56,57,37)(38,58,64,80)(40,68,67,60)(43,71,69,86)(44,72,70,55)(50,74,76,65)(51,62,59,75)(54,79,78,63)(66,85,84,82)(77,83,81,87);(24,26,37,62,29,40,47,49,30,41,56,75,46,67,28,39)(25,31,45,60,34,51,57,61,35,52,73,68,48,59,33,36)(27,38,63,83,44,66,69,74,42,64,79,87,70,84,43,65)(32,50,71,82,55,77,78,80,53,76,86,85,72,81,54,58);(21,23)(24,27)(25,32)(26,38)(28,43)(29,44)(30,42)(31,50)(33,54)(34,55)(35,53)(36,58)(37,63)(39,65)(40,66)(41,64)(45,71)(46,70)(47,69)(48,72)(49,74)(51,77)(52,76)(56,79)(57,78)(59,81)(60,82)(61,80)(62,83)(67,84)(68,85)(73,86)(75,87);(27,42)(32,53)(38,64)(43,69)(44,70)(50,76)(54,78)(55,72)(58,80)(63,79)(65,74)(66,84)(71,86)(77,81)(82,85)(83,87)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26596);