Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #20338 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C23×C42 |
| direct product | C19×#20370 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C22×C42 |
| commutator | C4 | C22×C42×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#376 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ G | |
908 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)(22,30,33,43)(23,27)(24,28)(25,29)(26,32,38,46)(31,42,44,50)(34,39)(35,40)(36,41)(37,45,48,51)(47,49);(20,22)(21,26,29,38)(23,31)(24,32)(25,33)(27,37,39,48)(28,30,41,43)(34,44)(35,45)(36,46)(40,42,49,50)(47,51);(20,23,24,35,25,34,36,47)(21,27,28,40,29,39,41,49)(22,31,32,45,33,44,46,51)(26,37,30,42,38,48,43,50);(23,34)(27,39)(31,44)(35,47)(37,48)(40,49)(42,50)(45,51)1558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13358);