Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12077 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13038 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #442 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G | |
474 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)(16,17,21,26,22,27,20,38,23,28,19,35,37,42,36,24)(18,29,32,25,33,41,31,43,34,46,30,44,40,47,39,45);(12,13,14,15)(17,24,28,38)(19,36)(20,21)(22,37)(25,41,44,47)(26,27,35,42)(29,45,46,43)(30,39)(31,32)(33,40);(16,18,23,34)(17,25,28,44)(19,31,21,39)(20,30,36,32)(22,40,37,33)(24,41,38,47)(26,29,35,46)(27,45,42,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6026);