Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#34153 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| socle | C23×C11 | C25 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
2542 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(17,21)(22,23)(25,28)(26,30);(12,14,15,13)(16,17)(18,22)(19,23)(20,21)(24,25)(26,29)(27,28)(30,31);(16,18,20,19)(17,22,21,23)(24,26,27,30)(25,29,28,31);(17,21)(22,23)(25,28)(29,31);(16,19,20,18)(17,23,21,22)1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27141);