Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33539 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33541 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
1104 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)(22,32)(23,25)(24,35)(28,43)(29,36)(30,41)(31,42)(33,48)(34,39)(37,38)(40,44)(45,51)(46,49);(20,21)(22,28)(23,29)(24,36)(25,30)(26,31)(27,35)(32,44)(33,49)(34,46)(37,42)(38,41)(39,45)(40,47)(43,48)(50,51);(20,22)(21,28)(23,32)(24,33)(25,39)(26,34)(27,40)(29,44)(30,45)(31,46)(35,47)(36,49)(37,50)(38,48)(41,43)(42,51);(20,23,26,25)(21,29,31,30)(22,32,34,39)(24,35,38,37)(27,41,42,36)(28,44,46,45)(33,47,48,50)(40,43,51,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26529);