Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23601 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×#121 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
994 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)(16,17,20,25,22,26,21,35)(18,27,29,38,31,44,30,23)(19,24,36,41,34,42,33,40)(28,43,46,37,45,39,32,47);(12,13)(14,15)(16,18,21,30,22,31,20,29)(17,23,25,27,26,38,35,44)(19,32,33,45,34,46,36,28)(24,39,41,47,42,43,40,37);(13,15)(16,19)(17,24)(18,28)(20,33)(21,36)(22,34)(23,37)(25,40)(26,42)(27,43)(29,32)(30,46)(31,45)(35,41)(38,47)(39,44);(16,20,22,21)(17,25,26,35)(18,29,31,30)(19,33,34,36)(23,27,38,44)(24,40,42,41)(28,32,45,46)(37,43,47,39)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16589);