Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23196 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | #2366 |
| prime radical | C11×#3147 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
884 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,25,29,38)(15,30)(16,22)(17,23)(18,35)(19,24)(20,28,39,34)(21,31)(26,36,27,40)(32,41)(33,43,42,37);(12,14,17,34,19,29,18,28)(13,20,23,38,24,39,35,25)(15,26,16,33,32,27,31,42)(21,36,30,43,22,40,41,37);(12,15,18,31,19,32,17,16)(13,21,23,30,24,22,35,41)(14,26,28,42,29,27,34,33)(20,36,38,43,39,40,25,37);(12,16,17,32,19,31,18,15)(13,22,23,41,24,21,35,30)(14,27,28,33,29,26,34,42)(20,37,25,40,39,43,38,36)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16184);