Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10273 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
542 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)(20,21)(22,23)(24,25,27,30)(26,28,31,29)(32,33,38,35)(34,42,46,43)(36,41,37,40)(39,45,47,44);(21,23)(32,34,38,46)(33,39,35,47)(36,45,37,44)(40,43,41,42);(25,28)(26,31)(29,30)(32,35,38,33)(34,43,46,42)(36,40,37,41)(39,44,47,45)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3261);