Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#8912 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | #120 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
412 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)(20,21,23,22)(25,28)(26,30)(29,31)(32,33,38,43)(34,44,35,46)(36,42,37,41)(39,47,40,45);(20,22,23,21)(26,30)(28,31)(32,34,38,35)(33,39,43,40)(36,47,37,45)(41,46,42,44);(24,25)(26,31)(27,29)(28,30)(32,35,38,34)(33,40,43,39)(36,47,37,45)(41,46,42,44)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1900);