Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#13289 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#102 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C23×C11 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,16)(17,19)(20,21,25,32,27,33,26,31)(22,34,39,51,40,50,38,46)(23,41,35,29,42,30,24,43)(28,45,47,37,49,36,48,44);(13,16)(17,18)(20,22,35,37,26,39,23,36,27,40,24,44,25,38,42,45)(21,28,30,50,32,48,43,51,33,49,41,34,31,47,29,46);(12,14,15,19)(13,17,16,18)(20,23,25,35,27,42,26,24)(21,29,31,41,33,43,32,30)(22,36,38,37,40,45,39,44)(28,46,47,34,49,51,48,50)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6277);