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×#24824 |
| 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 | |
824 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)(16,17,20,23)(18,22,19,21)(24,25,28,32)(26,33,36,30)(27,37,29,31)(34,39,35,38);(16,18,20,19)(17,21,23,22)(24,26)(25,30)(27,35)(28,36)(29,34)(31,38)(32,33)(37,39);(13,15)(26,34)(27,29)(30,38)(31,37)(33,39)(35,36);(16,19,20,18)(17,22,23,21)(24,27,28,29)(25,31,32,37)(26,35,36,34)(30,38,33,39)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17812);