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×#10057 |
| 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 | |
614 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)(25,28)(26,30)(29,31)(32,33,37,40)(34,41,43,46)(35,39,36,44)(38,45,47,42);(20,21)(22,23)(26,30)(28,31)(32,34,37,43)(33,38,40,47)(35,42,36,45)(39,46,44,41);(21,23)(24,25)(26,31)(27,29)(28,30)(32,35,37,36)(33,39,40,44)(34,42,43,45)(38,46,47,41)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3045);