Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#24695 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G | |
780 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17,19,20)(18,22,23,21)(24,25,29,33)(26,30,36,39)(27,31,28,32)(34,37,35,38);(17,20)(21,22)(24,26,29,36)(25,30,33,39)(27,35,28,34)(31,38,32,37);(13,15)(26,34)(27,28)(30,37)(31,32)(35,36)(38,39);(16,18,19,23)(17,21,20,22)(24,27,29,28)(25,31,33,32)(26,35,36,34)(30,38,39,37)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17683);