Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12506 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C8 |
| direct product | C11×#12514 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C11 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C11 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C42×C11 ◁ C82×C11 ◁ G | |
246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20)(15,23)(16,18)(17,21)(19,24)(22,26)(25,27)(28,29,36,43)(30,44,49,38)(31,50,45,37)(32,40,51,59)(33,39,53,57)(34,42,35,41)(46,56,52,55)(47,58,48,54);(12,14,15,21,16,22,24,27)(13,17,19,20,18,25,23,26)(28,30,33,46,34,47,51,31,36,49,53,52,35,48,32,45)(29,37,40,54,41,55,57,38,43,50,59,58,42,56,39,44);(13,18)(17,25)(19,23)(20,26)(28,31,51,48,35,46,33,49,36,45,32,47,34,52,53,30)(29,38,57,56,42,54,40,50,43,44,39,55,41,58,59,37)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5502);