Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13010 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #481 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#469 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C22×M16×C19 ◁ G | |
548 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,29,32,39,36,27,37,28,33,38,35,30,26,34,31);(20,21,22,23)(24,26,30,25,28,36,39,33)(27,37,29,35,34,31,38,32);(27,34)(29,38)(31,37)(32,35)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5998);