Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33539 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33540 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
1078 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(23,39)(24,43)(25,33)(26,32)(27,30)(28,36)(29,41)(31,46)(35,62)(37,68)(38,61)(40,71)(42,58)(44,59)(45,55)(47,57)(48,53)(49,56)(50,77)(51,67)(52,75)(54,74)(60,64)(63,69)(65,82)(66,80)(70,73)(72,78)(76,81)(79,83);(20,22,27,38)(21,28,30,51)(23,35,42,66)(24,44,47,75)(25,37,26,49)(29,50,53,78)(31,56,55,68)(32,52,33,59)(34,57,61,43)(36,45,67,46)(39,69,58,79)(40,72,74,77)(41,64,48,65)(54,80,71,62)(60,81,82,70)(63,76,83,73);(20,23)(21,29)(22,35)(24,40)(25,48)(26,41)(27,42)(28,50)(30,53)(31,54)(32,58)(33,39)(34,60)(36,63)(37,65)(38,66)(43,70)(44,72)(45,76)(46,73)(47,74)(49,64)(51,78)(52,79)(55,71)(56,80)(57,81)(59,69)(61,82)(62,68)(67,83)(75,77);(21,30)(28,51)(29,53)(31,55)(32,33)(34,61)(39,58)(43,57)(50,78)(52,59)(54,71)(56,68)(60,82)(62,80)(69,79)(70,81)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26528);