Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10078 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#10426 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C22×D4×C19 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22)(26,31)(28,30)(32,33)(34,38)(35,39)(36,40)(37,41)(42,45)(43,46)(44,47);(20,21)(22,23)(24,25)(26,28)(27,29)(30,31)(32,34,37,44)(33,38,41,47)(35,43,36,42)(39,46,40,45);(20,22,23,21)(25,28)(26,31)(29,30)(33,39)(34,42)(35,36)(40,41)(43,44)(45,46)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3414);