Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#13184 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#106 |
| 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 | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17)(18,26,28,42)(19,30)(20,23)(21,35)(22,27,37,43)(24,33)(25,34)(29,44,36,40)(31,38,46,41)(32,45)(39,47);(16,18,21,36,20,28,34,29)(17,22,25,41,23,37,35,38)(19,31,33,27,32,46,47,43)(24,40,30,26,39,44,45,42);(12,13,14,15)(17,23)(22,37)(24,39)(25,35)(26,42)(30,45)(38,41)(40,44)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6172);