Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C11 · Schur multiplier (H2) = C24×C42 |
| direct product | C11×#13801 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C11 | C24 |
| commutator | C22 | C22×C42×C11 |
| Frattini, cosocle | C24 | C24×C11 |
| prime radical | C25×C11 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
2182 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,18,19)(24,25,28,27)(26,29,31,30);(20,21,22,23)(25,27)(29,30);(12,13)(14,15)(16,17)(18,19)(24,26,28,31)(25,29,27,30);(24,27,28,25)(26,30,31,29)1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6789);