Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19862 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
602 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25)(23,31)(26,32)(27,28)(29,35)(33,34)(36,37,41,44)(38,42,40,48)(39,46,47,50)(43,49,51,45);(20,21)(22,26)(23,27)(24,28)(25,31)(29,33)(30,34)(32,35)(36,38,41,40)(37,42,44,48)(39,45,47,49)(43,50,51,46);(20,22,24,30)(21,26,28,34)(23,29,31,35)(25,32,27,33)(36,39)(37,43)(38,45)(40,49)(41,47)(42,50)(44,51)(46,48);(21,27)(23,31)(25,28)(26,33)(29,35)(32,34)(36,38,41,40)(37,42,44,48)(39,45,47,49)(43,50,51,46)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12850);