Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10013 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | #392 |
| prime radical | C11×#3100 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(17,19)(20,21)(22,28)(23,31)(24,27)(25,29)(26,33)(30,35)(32,34);(12,13,15,17)(14,19,18,16)(20,22,24,30)(21,25,27,34)(23,32,33,29)(26,35,31,28);(12,13)(14,19)(15,17)(16,18)(25,34)(28,35)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3001);