Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C2×C42 |
| direct product | C19×#15572 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C19 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| prime radical | C25×C19 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
1278 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)(21,23)(24,25)(26,28)(27,30)(29,31)(32,33,35,36)(34,38,39,37)(40,41,43,45)(42,46,47,44);(25,26)(27,31)(33,36)(37,38)(40,41,43,45)(42,44,47,46);(24,26,28,25)(27,30,31,29)(32,34,35,39)(33,37,36,38)(40,41)(42,44)(43,45)(46,47);(20,21)(22,23)(24,27)(25,29)(26,30)(28,31)(32,33)(34,37)(35,36)(38,39)(40,42,43,47)(41,44,45,46)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 8560);