Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19503 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3106 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
612 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)(20,21,25,28)(22,29,31,34)(23,27,24,33)(26,32,35,30)(36,37,41,46)(38,47,39,43)(40,45,42,50)(44,48,51,49);(20,22,23,32,25,31,24,30)(21,26,33,34,28,35,27,29)(36,38,41,39)(37,43,46,47)(40,49,42,48)(44,45,51,50);(36,39,41,38)(37,44,46,51)(40,49,42,48)(43,45,47,50);(20,23,25,24)(21,27,28,33)(22,30,31,32)(26,34,35,29)(36,40,41,42)(37,45,46,50)(38,48,39,49)(43,44,47,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12491);