Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C27×C4 |
| direct product | C19×#34262 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C24×C19 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2198 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 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)(29,31)(32,33,38,36)(34,41,35,39)(37,44,45,40)(42,46,43,47);(32,34,38,35)(33,39,36,41)(37,42,45,43)(40,46,44,47);(20,22,23,21)(24,25)(26,29)(27,28)(30,31)(32,35,38,34)(33,39,36,41)(37,43,45,42)(40,46,44,47);(32,36,38,33)(34,39,35,41)(37,44,45,40)(42,46,43,47);(24,26,27,30)(25,29,28,31)(32,37)(33,40)(34,42)(35,43)(36,44)(38,45)(39,46)(41,47)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27250);