Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23801 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle, prime radical | C23×C11 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C43×C11 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17,19,20)(18,21,22,23)(24,25,28,32,29,33,38,39)(26,34,35,31,27,36,37,30);(12,13)(14,15)(17,20)(21,23)(24,26,29,27)(25,30,33,31)(28,37,38,35)(32,36,39,34);(13,15)(24,27,29,26)(25,31,33,30)(28,35,38,37)(32,34,39,36);(16,18,19,22)(17,21,20,23)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16789);