Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #20671 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#20671 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#117 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#380 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×M16×C19 ◁ G | |
1324 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)(22,30)(23,34,36,27)(24,37)(25,29)(26,33)(28,38)(31,44,45,42)(32,43)(35,41,50,49)(39,46,48,51)(40,47);(20,22,24,33,25,32,38,47)(21,26,28,30,29,40,37,43)(23,31,35,46,36,45,50,51)(27,39,41,42,34,48,49,44);(20,23)(21,27)(22,31)(24,35)(25,36)(26,39)(28,41)(29,34)(30,42)(32,45)(33,46)(37,49)(38,50)(40,48)(43,44)(47,51);(22,32)(26,40)(30,43)(31,45)(33,47)(39,48)(42,44)(46,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13659);