Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12503 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C2×C8 |
| direct product | C11×#12516 |
| 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 | |
310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,17)(18,19)(20,21,25,29)(22,30,34,46)(23,35,37,50)(24,38,36,28)(26,39,41,32)(27,42,43,31)(33,49,48,45)(40,47,44,51);(20,22,31,47,24,33,37,39,25,34,42,51,36,48,23,32)(21,26,35,45,28,40,43,46,29,41,50,49,38,44,27,30);(12,13,17,19,15,18,14,16)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5504);