Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18250 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#1600 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
932 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)(21,26)(23,34)(27,38)(28,37)(29,35)(32,42)(36,44)(39,45)(40,48)(41,49)(46,47)(50,51);(20,21,24,29)(22,27,30,39)(23,35,34,26)(25,28,31,40)(32,45,42,38)(33,41,43,51)(36,48,44,37)(46,49,47,50);(22,30)(23,36)(26,37)(27,39)(32,46)(33,43)(34,44)(35,48)(38,50)(41,51)(42,47)(45,49);(20,22,31,43)(21,27,40,51)(23,32,44,46)(24,30,25,33)(26,38,48,50)(28,41,29,39)(34,42,36,47)(35,45,37,49)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11238);