Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23913 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1898 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(26,32)(27,34)(29,37)(31,35)(33,36)(38,39);(20,21)(22,23)(24,25,28,30)(26,29,33,38)(27,35,34,31)(32,39,36,37);(21,23)(24,26)(25,29)(27,36)(28,33)(30,38)(31,39)(32,34)(35,37);(25,30)(27,34)(29,38)(32,36)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16901);