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×#34378 |
| 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 | |
2010 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)(17,20)(18,22)(24,25)(26,33)(27,30)(28,36)(29,32)(31,37)(34,38)(35,39);(17,20)(21,23)(24,26,29,27)(25,30,32,33)(28,34,37,35)(31,38,36,39);(16,17)(18,21)(19,20)(22,23)(24,27,29,26)(25,30,32,33)(28,35,37,34)(31,38,36,39);(16,18,19,22)(17,21,20,23)(24,25)(26,33)(27,30)(28,31)(29,32)(34,39)(35,38)(36,37);(24,28)(25,31)(26,34)(27,35)(29,37)(30,38)(32,36)(33,39)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27366);