Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33657 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33659 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#481 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3060 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 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)(22,31)(23,28)(24,37)(25,35)(26,30)(27,34)(29,40)(32,46)(33,48)(36,38)(39,45)(41,51)(42,49)(43,50)(44,47);(20,21)(22,27)(23,35)(24,38)(25,28)(26,30)(29,41)(31,47)(32,45)(33,44)(34,48)(36,37)(39,49)(40,51)(42,43)(46,50);(20,22,25,42,26,33,23,32)(21,27,28,43,30,44,35,45)(24,39,40,47,41,50,36,34)(29,46,37,48,38,49,51,31);(20,23,26,25)(21,28,30,35)(22,32,33,42)(24,36,41,40)(27,43,44,45)(29,37,38,51)(31,46,48,49)(34,50,47,39)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26647);