Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23723 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#399 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
972 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)(20,21,24,28,25,29,31,39)(22,30,33,41,34,45,38,26)(23,35,37,49,36,27,42,44)(32,46,48,43,47,51,50,40);(20,22,31,33,25,34,24,38)(21,26,39,30,29,41,28,45)(23,32,42,48,36,47,37,50)(27,43,49,51,35,40,44,46);(20,23)(21,27)(22,32)(24,37)(25,36)(26,40)(28,44)(29,35)(30,46)(31,42)(33,48)(34,47)(38,50)(39,49)(41,43)(45,51);(23,36)(27,35)(32,47)(37,42)(40,43)(44,49)(46,51)(48,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16711);