Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34237 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C2×C19×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2186 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)(34,39)(35,40)(36,44)(37,38)(41,45)(42,43)(46,47);(20,22,23,21)(33,38)(35,39)(41,44)(43,46);(24,25)(26,29)(27,28)(30,31)(32,34,37,40)(33,39,38,35)(36,42,45,47)(41,46,44,43);(32,35,37,39)(33,40,38,34)(36,43,45,46)(41,47,44,42);(24,26,27,30)(25,29,28,31)(32,36,37,45)(33,41,38,44)(34,42,40,47)(35,43,39,46)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27225);