Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33690 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#2190 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C4×M16×C19 ◁ G | |
526 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)(22,27)(23,33)(24,37)(25,41)(26,30)(28,36)(29,38)(31,48)(32,47)(34,46)(35,50)(39,42)(40,45)(43,49)(44,51);(20,22,26,25)(21,27,30,41)(23,31,35,34)(24,38,40,32)(28,42,43,44)(29,45,47,37)(33,46,50,48)(36,51,49,39);(20,23)(21,28)(22,31)(24,39)(25,34)(26,35)(27,42)(29,46)(30,43)(32,49)(33,37)(36,38)(40,51)(41,44)(45,50)(47,48);(23,34,35,31)(24,40)(28,42,43,44)(29,47)(32,38)(33,46,50,48)(36,39,49,51)(37,45)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26678);