Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C11 · Schur multiplier (H2) = C26×C4 |
| direct product | C4×C11×#381 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C11 | C23 |
| commutator | C22 | C22×C42×C11 |
| Frattini, cosocle | C24 | C24×C11 |
| socle | C24×C11 | C24 |
| prime radical | C25×C11 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C11 ◁ G | |
2606 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)(21,22,23,24,25,26,27,28,29,30,31);(6,8)(9,10,11,12)(14,17)(15,19);(13,14)(15,18)(16,17)(19,20);(5,6)(7,8)(9,10)(11,12)(13,15,16,19)(14,18,17,20)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6758);