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 | C11×#412 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C11 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C11 |
| socle | C22×C11 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C11 ◁ G | |
7812 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 6 generators on 27 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19);(13,16)(17,19);(12,14,15,18)(13,17,16,19);(20,21)(22,25)(23,24)(26,27);(21,24)(25,27);(20,22,23,26)(21,25,24,27)1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 55705);