Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#25961 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C4×C22⋊C4×C19 ◁ G | |
958 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)(34,41)(35,37)(36,38)(39,42)(40,44)(43,47)(45,46);(20,21)(22,23)(33,37)(35,44)(38,40)(39,41)(42,45)(46,47);(21,23)(24,26,27,31)(25,28,29,30)(33,38)(37,40)(39,46)(41,47);(32,34,36,43)(33,39,38,46)(35,45,44,42)(37,41,40,47)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 18949);