Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33531 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33533 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
1102 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)(27,33)(29,40)(32,48)(34,49)(36,39)(38,43)(41,50)(42,46)(44,47)(45,51);(20,22)(21,27)(23,32)(24,38)(25,42)(26,34)(28,43)(29,46)(30,44)(31,37)(33,40)(35,45)(36,47)(39,48)(41,51)(49,50);(20,21)(22,27)(23,35)(24,39)(25,28)(26,30)(29,41)(31,47)(32,45)(33,49)(34,44)(36,37)(38,48)(40,50)(42,43)(46,51);(20,23,26,25)(21,28,30,35)(22,32,34,42)(24,36,41,40)(27,43,44,45)(29,37,39,50)(31,48,49,46)(33,38,47,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26521);