Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34394 |
| 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 | |
1998 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)(26,27)(33,37)(34,40)(39,44)(41,46);(24,25,29,28)(26,31,27,30)(33,37)(38,43)(39,44)(45,47);(24,26,29,27)(25,30,28,31)(32,33,36,37)(34,38,40,43)(35,39,42,44)(41,45,46,47);(24,27,29,26)(25,31,28,30)(32,34)(33,38)(35,41)(36,40)(37,43)(39,45)(42,46)(44,47);(24,28,29,25)(26,31,27,30)(32,35,36,42)(33,39,37,44)(34,41,40,46)(38,45,43,47)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27382);