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×#19828 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3305 | 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)(20,21,24,28)(22,26,30,34)(23,25,31,27)(29,35,32,33)(36,37)(38,42)(39,46)(40,48)(41,44)(43,45)(47,50)(49,51);(21,25)(22,29)(23,31)(26,34)(27,28)(30,32)(36,38,41,40)(37,42,44,48)(39,45,47,49)(43,50,51,46);(36,39,41,47)(37,43,44,51)(38,45,40,49)(42,50,48,46);(20,22,24,30)(21,26,28,34)(23,32,31,29)(25,33,27,35)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12816);