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×#20673 |
| 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 | |
1292 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)(20,21,25,29,26,30,24,39)(22,31,35,42,33,46,34,27)(23,36,37,43,38,28,40,44)(32,47,49,51,48,45,50,41);(20,22,24,34,26,33,25,35)(21,27,29,31,30,42,39,46)(23,32,37,49,38,48,40,50)(28,41,43,45,36,51,44,47);(20,23)(21,28)(22,32)(24,37)(25,40)(26,38)(27,41)(29,43)(30,36)(31,45)(33,48)(34,49)(35,50)(39,44)(42,51)(46,47);(22,33)(27,42)(31,46)(32,48)(34,35)(41,51)(45,47)(49,50)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13661);