Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10059 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,28,31)(26,30,27,29)(32,33,38,42)(34,43,35,46)(36,41,37,40)(39,45,47,44);(20,21)(22,23)(25,29)(26,27)(30,31)(32,34,38,35)(33,39,42,47)(36,45,37,44)(40,46,41,43);(21,23)(24,26,28,27)(25,30,31,29)(32,35,38,34)(33,39,42,47)(36,44,37,45)(40,46,41,43)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3047);