Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#20675 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#121 |
| 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 ◁ C23×C4×C19 ◁ G | |
1308 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)(22,31)(23,36,38,43)(24,39)(25,29)(26,30)(27,34)(28,37,44,40)(32,41,47,51)(33,46)(35,42)(45,48,50,49);(20,22,24,34,26,33,25,35)(21,27,29,31,30,42,39,46)(23,32,37,48,38,47,40,49)(28,41,43,45,44,51,36,50);(20,23)(21,28)(22,32)(24,37)(25,40)(26,38)(27,41)(29,43)(30,44)(31,45)(33,47)(34,48)(35,49)(36,39)(42,51)(46,50);(22,33)(27,42)(31,46)(32,47)(34,35)(41,51)(45,50)(48,49)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13663);