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×#34525 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2008 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)(12,13,15,14)(16,17)(18,19)(20,21)(22,23)(24,25,28,31)(26,32,34,29)(27,30,35,37)(33,38,39,36);(17,21)(18,22)(24,25,28,31)(26,29,34,32)(27,30,35,37)(33,36,39,38);(12,13,15,14)(24,25)(26,29)(27,30)(28,31)(32,34)(33,36)(35,37)(38,39);(16,18,20,22)(17,19,21,23)(24,26)(25,29)(27,33)(28,34)(30,36)(31,32)(35,39)(37,38);(12,14,15,13)(16,19)(17,22)(18,21)(20,23)(24,27,28,35)(25,30,31,37)(26,33,34,39)(29,36,32,38)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27513);