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×#34371 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C24×C11 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17,20,18)(19,22,23,21)(25,30)(26,27)(28,36)(38,39);(17,18)(21,22)(24,25,29,30)(26,32,27,31)(28,33,36,37)(34,39,35,38);(24,26,29,27)(25,31,30,32)(28,34,36,35)(33,38,37,39);(16,18,20,17)(19,22,23,21)(24,27,29,26)(25,32,30,31)(28,35,36,34)(33,39,37,38);(16,19)(17,21)(18,22)(20,23)(24,28)(25,33)(26,34)(27,35)(29,36)(30,37)(31,38)(32,39)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27359);