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×#19831 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3332 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
614 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)(38,42)(39,46)(40,48)(41,44)(43,45)(47,50)(49,51);(20,21)(22,26)(23,30)(24,32)(25,28)(27,29)(31,34)(33,35)(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)(36,39,41,47)(37,43,44,51)(38,45,40,49)(42,50,48,46);(20,23,25,31)(21,27,28,35)(22,29,24,33)(26,34,32,30)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12819);