Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#23691 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C19×#376 ◁ G | |
796 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)(20,21,22,23)(24,25)(26,29)(27,28)(30,31)(32,33)(34,37)(35,39)(36,42)(38,40)(41,45)(43,46)(44,47);(25,28)(29,31)(32,34,37,33)(35,43,45,47)(36,42,38,40)(39,44,41,46);(21,23)(32,35,37,45)(33,39,34,41)(36,44,38,46)(40,43,42,47);(24,26,27,30)(25,29,28,31)(32,36,37,38)(33,40,34,42)(35,44,45,46)(39,43,41,47)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16679);