Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#10377 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #393 |
| commutator, Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,27)(22,30,32,45)(24,38,36,28)(25,29,37,44)(26,41,42,49)(31,39,43,33)(34,47,35,48)(40,51,50,46);(20,21)(22,31,34,26)(23,27)(24,28)(25,29)(30,33,47,49)(32,43,35,42)(36,38)(37,44)(39,48,41,45)(40,46)(50,51);(20,22,23,35)(21,26,27,43)(24,39,36,49)(25,34,37,32)(28,45,38,47)(29,31,44,42)(30,46,48,51)(33,40,41,50)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3365);