Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#36711 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C23×D4×C11 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(18,22)(21,23)(24,25,30,33)(26,28,27,31)(29,37,38,32)(34,39,35,36);(17,20)(21,23)(24,26,30,27)(25,31,33,28)(29,34,38,35)(32,39,37,36);(12,13)(14,15)(16,17)(18,21)(19,20)(22,23)(24,27,30,26)(25,31,33,28)(29,35,38,34)(32,39,37,36);(16,17)(18,21)(19,20)(22,23)(24,28,30,31)(25,26,33,27)(29,36,38,39)(32,34,37,35);(16,18)(17,21)(19,22)(20,23)(24,29)(25,32)(26,34)(27,35)(28,36)(30,38)(31,39)(33,37)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29699);