Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33380 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×D8 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C22×D8 |
| prime radical | C22×C11×#135 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
1170 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)(12,13,14,15)(16,17)(18,27)(19,25)(20,32)(21,36)(22,24)(23,29)(26,34)(28,44)(30,43)(31,41)(33,39)(35,46)(37,42)(38,45)(40,47);(16,18)(17,23)(19,28)(20,33)(21,37)(22,30)(24,38)(25,39)(26,42)(27,32)(29,34)(31,45)(35,47)(36,40)(41,44)(43,46);(17,24)(23,38)(25,36)(26,41)(27,43)(32,46)(39,40)(42,44);(16,19,22,21)(17,25,24,36)(18,28,30,37)(20,31,35,34)(23,39,38,40)(26,32,41,46)(27,44,43,42)(29,33,45,47)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26368);