Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33687 |
| 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 | |
520 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)(28,29,32,37)(30,40,42,35)(31,45,46,81)(33,51,49,80)(34,54,50,39)(36,59,60,47)(38,63,62,53)(41,69,70,79)(43,75,73,84)(44,58,74,68)(48,82,55,64)(52,65,83,61)(56,71,66,88)(57,77,67,89)(72,86,78,90)(76,85,91,87);(21,24)(25,27)(28,30)(29,35)(31,41)(32,42)(33,43)(34,44)(36,56)(37,40)(38,57)(39,58)(45,79)(46,70)(47,71)(48,72)(49,73)(50,74)(51,84)(52,76)(53,77)(54,68)(55,78)(59,88)(60,66)(61,85)(62,67)(63,89)(64,86)(65,87)(69,81)(75,80)(82,90)(83,91);(28,31,32,46)(29,36,37,60)(30,41,42,70)(33,52,49,83)(34,55,50,48)(35,56,40,66)(38,64,62,82)(39,65,54,61)(43,76,73,91)(44,78,74,72)(45,80,81,51)(47,63,59,53)(57,86,67,90)(58,87,68,85)(69,84,79,75)(71,89,88,77);(20,22,23,26)(21,25,24,27)(30,42)(35,40)(41,70)(43,73)(44,74)(56,66)(57,67)(58,68)(69,79)(71,88)(72,78)(75,84)(76,91)(77,89)(85,87)(86,90)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26675);