Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2010 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11112 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #127 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #399 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
874 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,21,25,22,26,20,36)(18,27,30,39,31,38,29,23)(19,32,34,24,35,41,33,42)(28,40,45,47,46,37,44,43);(12,13,14,15)(16,18,20,29,22,31,21,30)(17,23,25,27,26,39,36,38)(19,28,33,44,35,46,34,45)(24,40,41,47,42,37,32,43);(16,19)(17,24)(18,28)(20,33)(21,34)(22,35)(23,37)(25,41)(26,42)(27,43)(29,44)(30,45)(31,46)(32,36)(38,47)(39,40)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4100);