Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33768 |
| 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 | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,25)(24,27)(28,29,34,39)(30,35,41,56)(31,44,47,78)(32,48,52,77)(33,53,50,38)(36,59,61,45)(37,62,64,51)(40,66,67,89)(42,72,70,88)(43,75,71,58)(46,79,54,63)(49,65,80,60)(55,81,82,68)(57,85,84,74)(69,90,76,86)(73,87,91,83);(20,22)(21,24)(23,27)(25,26)(28,30,34,41)(29,35,39,56)(31,40,47,67)(32,42,52,70)(33,43,50,71)(36,55,61,82)(37,57,64,84)(38,58,53,75)(44,66,78,89)(45,68,59,81)(46,69,54,76)(48,72,77,88)(49,73,80,91)(51,74,62,85)(60,83,65,87)(63,86,79,90);(22,27)(24,26)(28,31,34,47)(29,36,39,61)(30,40,41,67)(32,49,52,80)(33,54,50,46)(35,55,56,82)(37,63,64,79)(38,65,53,60)(42,73,70,91)(43,76,71,69)(44,77,78,48)(45,62,59,51)(57,86,84,90)(58,87,75,83)(66,88,89,72)(68,85,81,74);(21,25)(24,26)(30,41)(35,56)(40,67)(42,70)(43,71)(55,82)(57,84)(58,75)(66,89)(68,81)(69,76)(72,88)(73,91)(74,85)(83,87)(86,90)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26756);