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×#33531 |
| 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 | |
1122 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)(21,26)(23,33)(24,36)(27,41)(28,40)(29,44)(31,46)(32,45)(34,38)(35,49)(37,50)(39,42)(43,51)(47,48);(20,21)(22,27)(23,34)(24,38)(25,28)(26,33)(29,36)(30,42)(31,47)(32,48)(35,51)(37,44)(39,49)(40,50)(41,46)(43,45);(20,22)(21,27)(23,35)(24,32)(25,30)(26,39)(28,42)(29,43)(31,37)(33,49)(34,51)(36,45)(38,48)(40,41)(44,47)(46,50);(22,30)(27,42)(31,35)(32,45)(39,41)(43,48)(46,49)(47,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26519);