Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33741 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C23×C19 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
484 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)(22,25)(23,24)(26,27)(28,29,34,39)(30,35,41,54)(31,44,48,73)(32,49,51,77)(33,52,50,38)(36,57,59,46)(37,60,61,45)(40,62,64,84)(42,69,67,90)(43,70,68,56)(47,76,75,72)(53,78,79,65)(55,82,81,63)(58,74,71,83)(66,89,88,86)(80,87,85,91);(21,24)(25,27)(28,30,34,41)(29,35,39,54)(31,40,48,64)(32,42,51,67)(33,43,50,68)(36,53,59,79)(37,55,61,81)(38,56,52,70)(44,62,73,84)(45,63,60,82)(46,65,57,78)(47,66,75,88)(49,69,77,90)(58,80,71,85)(72,86,76,89)(74,87,83,91);(28,31,45,74,33,47,51,57,34,48,60,83,50,75,32,46)(29,36,49,72,38,58,61,73,39,59,77,76,52,71,37,44)(30,40,63,87,43,66,67,78,41,64,82,91,68,88,42,65)(35,53,69,86,56,80,81,84,54,79,90,89,70,85,55,62);(20,22,23,26)(21,25,24,27)(30,41)(35,54)(40,64)(42,67)(43,68)(53,79)(55,81)(56,70)(62,84)(63,82)(65,78)(66,88)(69,90)(80,85)(86,89)(87,91)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26729);