Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23472 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#393 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1148 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)(23,35,37,46)(24,29)(25,40)(26,30)(28,38,45,39)(31,44,47,51)(32,42)(33,43)(34,49)(36,41,48,50);(20,22)(21,27)(23,36,37,48)(24,33)(25,34)(26,32)(28,44,45,51)(29,43)(30,42)(31,39,47,38)(35,50,46,41)(40,49);(20,23)(21,28)(22,31)(24,39)(25,38)(26,37)(27,41)(29,46)(30,45)(32,47)(33,36)(34,48)(35,40)(42,50)(43,51)(44,49);(22,32)(27,42)(31,47)(33,34)(36,48)(41,50)(43,49)(44,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16460);