Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23045 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#41 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G | |
844 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)(12,13,15,14)(16,17,21,26,22,27,20,25)(18,28,31,23,32,38,30,39)(19,24,35,42,36,43,34,41)(29,40,44,37,45,47,33,46);(12,14,15,13)(16,18)(17,23)(19,33)(20,31)(21,30)(22,32)(24,40)(25,38)(26,28)(27,39)(29,34)(35,45)(36,44)(37,41)(42,46)(43,47);(16,18)(17,23)(19,29)(20,30)(21,31)(22,32)(24,37)(25,28)(26,38)(27,39)(33,34)(35,44)(36,45)(40,41)(42,47)(43,46);(16,19,21,35,22,36,20,34)(17,24,26,42,27,43,25,41)(18,29,31,44,32,45,30,33)(23,37,38,47,39,46,28,40)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16033);