Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#10589 |
| 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 | |
370 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,26,31,28,27,29,30)(33,38)(34,39)(35,36);(20,21)(22,23)(24,26,28,29)(25,30,27,31)(32,33,35,38,37,39,36,34);(21,23)(24,27,28,25)(26,31,29,30)(32,34,37,38)(33,35,39,36)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3577);