Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24775 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
850 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,14)(16,17,21,26,20,25,22,27)(18,28,31,43,30,23,37,39)(19,32,35,41,34,42,36,24)(29,45,33,38,46,40,47,44);(12,13,15,14)(16,18,20,30)(17,23,25,28)(19,33,34,47)(21,31,22,37)(24,40,41,45)(26,39,27,43)(29,35,46,36)(32,44,42,38);(16,19,20,34)(17,24,25,41)(18,29,30,46)(21,36,22,35)(23,38,28,44)(26,42,27,32)(31,47,37,33)(39,45,43,40);(12,14,15,13)(17,25)(23,28)(24,41)(26,27)(32,42)(38,44)(39,43)(40,45)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17763);