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×#19791 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3303 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
606 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)(36,37,40,44)(38,41,46,50)(39,42,47,43)(45,48,51,49);(20,21)(22,26)(23,27)(24,28)(25,31)(29,33)(30,34)(32,35)(36,38,40,46)(37,41,44,50)(39,45,47,51)(42,48,43,49);(20,22,24,30)(21,26,28,34)(23,29,31,35)(25,32,27,33)(37,42)(39,47)(41,48)(43,44)(45,51)(49,50);(21,27)(23,31)(25,28)(26,33)(29,35)(32,34)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12779);