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×#34357 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C23×D4×C11 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2502 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)(12,13,14,15)(17,20)(18,22)(24,25)(26,29)(27,32)(28,33)(30,34)(31,36)(35,37)(38,39);(17,20)(21,23)(25,26)(27,34)(31,33)(35,39);(16,17)(18,21)(19,20)(22,23)(24,26,29,25)(27,32,34,30)(28,33,36,31)(35,38,39,37);(16,18)(17,21)(19,22)(20,23)(24,27)(25,30)(26,32)(28,35)(29,34)(31,37)(33,38)(36,39);(24,28)(25,31)(26,33)(27,35)(29,36)(30,37)(32,38)(34,39)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27345);