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×#34369 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C2×C19×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2410 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)(20,21,22,23)(25,28)(26,30)(32,33,36,37)(34,40,41,38)(35,43,44,39)(42,45,47,46);(25,28)(29,31)(33,37)(34,41)(39,43)(42,47);(24,25,27,28)(26,29,30,31)(32,33)(34,38)(35,39)(36,37)(40,41)(42,45)(43,44)(46,47);(24,26)(25,29)(27,30)(28,31)(32,34,36,41)(33,38,37,40)(35,42,44,47)(39,45,43,46);(32,35,36,44)(33,39,37,43)(34,42,41,47)(38,45,40,46)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27357);