Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C11 · Schur multiplier (H2) = C213 |
| direct product | C22×C11×#551 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C11 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C11 |
| prime radical | C22×C11×#120 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
9526 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 6 generators on 31 points:
(1,2)(21,22,23,24,25,26,27,28,29,30,31);(3,4);(5,6,8,12)(7,13,14,10)(9,11,16,18)(15,19,20,17);(5,7,9,15)(6,10,11,17)(8,14,16,20)(12,13,18,19);(6,11)(10,17)(12,18)(13,19);(7,14)(10,13)(15,20)(17,19)1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 55691);