Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18354 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1022 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)(21,27)(22,31)(23,33)(24,36)(28,41)(29,37)(30,43)(32,46)(34,50)(35,38)(39,48)(42,44)(45,51)(47,49);(20,21)(22,28)(23,34)(24,37)(25,30)(26,29)(27,36)(31,44)(32,47)(33,49)(35,42)(38,50)(39,51)(40,45)(41,46)(43,48);(20,22,26,23)(21,28,29,34)(24,38,36,46)(25,31,40,33)(27,41,37,50)(30,44,45,49)(32,48,35,39)(42,51,47,43);(20,23,26,22)(21,28,29,34)(24,35,36,32)(25,33,40,31)(27,42,37,47)(30,44,45,49)(38,39,46,48)(41,51,50,43)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11342);