Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34631 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| socle | C23×C19 | C25 |
| prime radical | C2×C19×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
2138 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)(21,23)(24,25)(26,29)(27,28)(30,31)(32,33,36,39)(34,37,40,44)(35,42,43,38)(41,47,46,45);(25,28)(29,31)(32,34)(33,37)(35,41)(36,40)(38,45)(39,44)(42,47)(43,46);(20,21,22,23)(34,40)(37,44)(41,46)(45,47);(32,35,36,43)(33,38,39,42)(34,41,40,46)(37,45,44,47);(24,26,27,30)(25,29,28,31)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27619);