Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#15523 |
| 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 | |
1170 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)(24,25,27,28)(26,30,31,29)(32,33)(34,38)(35,36)(37,39)(40,41)(42,47)(43,46)(44,45);(25,28)(26,31)(33,35)(37,38)(40,42,45,43)(41,46,44,47);(24,25)(26,29)(27,28)(30,31)(32,34)(33,37)(35,38)(36,39)(40,43,45,42)(41,46,44,47);(20,21)(22,23)(24,26,27,31)(25,29,28,30)(32,35,36,33)(34,38,39,37)(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, 8511);