Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#11030 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #392 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C22×C19×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1422 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)(20,21)(22,23)(24,25,28,32)(26,33)(27,29,37,31)(30,36)(34,38)(35,39);(21,23)(25,29)(26,34)(27,37)(31,32)(35,36)(38,39);(24,26)(25,30)(27,35)(28,36)(29,38)(31,39)(32,33)(34,37)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4018);