Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#9752 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | #390 |
| prime radical | C23×C11 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
394 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)(12,13,15,17,16,19,14,18)(20,21,24,28,25,29,23,26)(22,30,33,35,31,34,32,27);(13,17)(14,15)(18,19)(21,26,29,28)(22,31)(27,30,35,34)(32,33);(20,22,23,32,25,31,24,33)(21,27,28,30,29,35,26,34)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2740);