Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#19717 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C2×C19×#127 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
720 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(23,30)(26,31)(27,32)(29,34)(33,35)(36,37)(38,43)(39,48)(40,50)(41,45)(42,47)(44,49)(46,51);(20,21,23,25,24,27,30,32)(22,26,29,31,28,33,34,35)(36,38,40,47,41,46,49,39)(37,42,44,43,45,48,50,51);(20,22,24,28)(21,26,27,33)(23,29,30,34)(25,31,32,35)(36,39,49,46,41,47,40,38)(37,43,50,42,45,51,44,48);(22,28)(26,33)(29,34)(31,35)(38,46)(39,47)(42,48)(43,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12705);