Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23730 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C22×D4 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C22×C42×C19 ◁ G | |
1126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,27,29)(26,30,31,28)(32,33,36,41,37,42,35,40)(34,43,44,39,46,47,45,38);(20,21)(22,23)(24,26,27,31)(25,28,29,30)(32,34)(33,38)(35,44)(36,45)(37,46)(39,42)(40,43)(41,47);(21,23)(32,34)(33,39)(35,44)(36,45)(37,46)(38,42)(40,47)(41,43);(32,35,37,36)(33,40,42,41)(34,44,46,45)(38,43,39,47)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16718);