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×#19866 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C2×D8×C19 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
570 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)(21,26)(22,24)(27,34)(28,32)(29,33)(30,35)(36,37,41,44)(38,42,40,48)(39,46,47,50)(43,49,51,45);(20,21,25,28)(22,26,24,32)(23,30,31,34)(27,33,35,29)(36,38,41,40)(37,42,44,48)(39,45,47,49)(43,50,51,46);(20,22,25,24)(21,26,28,32)(23,29,31,33)(27,34,35,30)(36,39)(37,43)(38,45)(40,49)(41,47)(42,50)(44,51)(46,48);(20,23,25,31)(21,27,28,35)(22,29,24,33)(26,34,32,30)(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, 12854);