Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#32871 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2826 |
| 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 | |
492 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)(20,21,26,28,25,31,24,30)(22,32,33,40,36,42,35,27)(23,29,37,43,39,46,38,45)(34,47,48,44,49,51,50,41);(20,22,24,35,25,36,26,33)(21,27,28,32,31,40,30,42)(23,34,37,48,39,49,38,50)(29,44,45,47,46,41,43,51);(21,28)(22,33)(23,37)(24,26)(27,40)(30,31)(34,49)(35,36)(38,39)(41,47)(43,45)(44,51);(20,23)(21,29)(22,34)(24,38)(25,39)(26,37)(27,41)(28,43)(30,45)(31,46)(32,47)(33,48)(35,50)(36,49)(40,44)(42,51)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25859);