Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#34491 |
| 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 | |
1956 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)(17,20)(18,19)(25,29)(27,35)(30,32)(33,39);(16,17,21,20)(18,23,19,22)(24,25)(26,32)(27,31)(28,29)(30,34)(33,38)(35,36)(37,39);(16,18,21,19)(17,22,20,23);(12,14,15,13)(16,19,21,18)(17,23,20,22)(24,26,28,34)(25,30,29,32)(27,33,35,39)(31,37,36,38);(16,20,21,17)(18,23,19,22)(24,27,28,35)(25,31,29,36)(26,33,34,39)(30,37,32,38)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27479);