Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13068 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13070 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1893 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C11×#3067 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,22,19,15,18,30)(14,23,27,39,28,40,26,38)(16,31,32,29,34,43,33,21)(20,35,37,42,24,41,36,25);(12,14,16,25,17,27,32,35,19,28,34,42,18,26,33,41)(13,20,29,40,30,36,31,39,15,24,21,23,22,37,43,38);(12,15)(13,19)(14,24)(16,21)(17,22)(18,30)(20,28)(23,25)(26,36)(27,37)(29,34)(31,33)(32,43)(35,38)(39,41)(40,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6058);