Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32947 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#32947 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3027 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1306 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)(24,35)(27,36)(28,37)(29,38)(30,42)(31,44)(33,45)(39,49)(40,47)(41,48)(46,50);(20,21,24,26,25,29,35,38)(22,27,31,36,32,40,44,47)(23,28,33,37,34,41,45,48)(30,39,43,46,42,50,51,49);(20,22)(21,27)(23,30)(24,31)(25,32)(26,36)(28,39)(29,40)(33,43)(34,42)(35,44)(37,46)(38,47)(41,50)(45,51)(48,49);(20,23)(21,28)(22,30)(24,33)(25,34)(26,37)(27,39)(29,41)(31,43)(32,42)(35,45)(36,46)(38,48)(40,50)(44,51)(47,49)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25935);