Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#15524 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C19 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
1126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
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)(21,23)(24,25)(26,30)(27,28)(29,31)(32,33,35,37)(34,36,38,39)(40,41,45,44)(42,47,43,46);(25,27)(26,31)(34,38)(36,39)(40,42,45,43)(41,46,44,47);(24,26)(25,29)(27,30)(28,31)(32,34)(33,36)(35,38)(37,39)(40,43,45,42)(41,46,44,47);(20,21)(22,23)(24,27,28,25)(26,30,31,29)(32,33)(34,36)(35,37)(38,39)(40,44,45,41)(42,46,43,47)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 8512);