Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#26054 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C4×C4⋊C4×C19 ◁ G | |
760 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22)(24,25,27,29)(26,30,31,28)(32,33)(34,41)(35,45)(36,40)(37,39)(38,44)(42,47)(43,46);(20,21,23,22)(32,34)(33,38)(35,43)(36,44)(37,42)(39,46)(40,41)(45,47);(24,26,27,31)(25,28,29,30)(34,42)(35,37)(38,46)(39,45)(41,47)(43,44);(20,22,23,21)(32,35,36,37)(33,39,40,45)(34,43,44,42)(38,46,41,47)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19042);