Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33530 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C2×C19 | C2×#447 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C22×M16×C19 ◁ G | |
1132 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)(22,31)(23,28)(24,36)(25,40)(26,30)(27,33)(29,39)(32,48)(34,47)(35,46)(37,42)(38,50)(41,45)(43,49)(44,51);(20,22)(21,27)(23,32)(24,37)(25,41)(26,34)(28,42)(29,45)(30,43)(31,36)(33,39)(35,49)(38,51)(40,44)(46,48)(47,50);(24,38)(29,46)(31,47)(33,49)(35,39)(36,50)(37,51)(45,48);(20,23,26,25)(21,28,30,40)(22,32,34,41)(24,35,38,39)(27,42,43,44)(29,36,46,50)(31,48,47,45)(33,37,49,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26518);