Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23047 |
| 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 | |
840 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)(18,28,31,23,32,39,30,40)(19,33,36,42,37,24,35,43)(29,44,45,47,46,41,34,38);(12,14,15,13)(16,18)(17,23)(19,34)(20,31)(21,30)(22,32)(24,41)(25,39)(26,28)(27,40)(29,35)(33,44)(36,46)(37,45)(38,42)(43,47);(16,18)(17,23)(19,29)(20,30)(21,31)(22,32)(24,38)(25,28)(26,39)(27,40)(33,47)(34,35)(36,45)(37,46)(41,42)(43,44);(16,19,20,35,22,37,21,36)(17,24,25,42,27,33,26,43)(18,29,30,34,32,46,31,45)(23,38,28,41,40,47,39,44)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16035);