Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#13104 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C19 | C23 |
| commutator | C22 | C22×C16×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle, prime radical | C23×C19 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C19 ◁ G | |
326 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)(26,29)(27,28)(30,31)(32,33,37,42,38,34,43,44,36,41,45,47,35,40,39,46);(25,28)(29,31)(32,34,37,44,38,41,43,47,36,40,45,46,35,33,39,42);(21,23)(24,26,27,30)(25,29,28,31)(32,35,36,38)(33,40,41,34)(37,39,45,43)(42,46,47,44)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6092);