Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#34328 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2036 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17,20,19)(18,22,23,21)(25,26)(28,36)(30,32)(34,39);(24,25,29,26)(27,32,35,30)(28,31,36,33)(34,38,39,37);(16,18,20,23)(17,21,19,22)(24,26,29,25)(27,32,35,30)(28,33,36,31)(34,38,39,37);(16,17,20,19)(18,21,23,22)(24,27)(25,30)(26,32)(28,34)(29,35)(31,37)(33,38)(36,39);(12,14,15,13)(16,19,20,17)(18,22,23,21)(24,28)(25,31)(26,33)(27,34)(29,36)(30,37)(32,38)(35,39)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27316);