Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#32699 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
538 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)(20,21,26,31,25,30,38,46)(22,23,28,35,33,27,39,42)(24,29,37,45,36,44,40,47)(32,41,48,51,49,34,43,50);(20,22)(21,27)(23,30)(24,32)(25,33)(26,39)(28,38)(29,34)(31,35)(36,49)(37,43)(40,48)(41,44)(42,46)(45,51)(47,50);(20,23)(21,28,30,39)(22,31,33,46)(24,34)(25,27)(26,35)(29,43,44,48)(32,47,49,45)(36,41)(37,50)(38,42)(40,51);(20,24,25,36)(21,29,30,44)(22,32,33,49)(23,34,27,41)(26,40,38,37)(28,43,39,48)(31,47,46,45)(35,51,42,50)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25687);