Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#21476 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×2−1+4 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
1322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17,21,25)(18,26,29,40)(19,23,30,38)(20,32,35,24)(22,33,37,28)(27,43,44,42)(31,41,34,39)(36,46,47,45);(16,18)(17,22)(19,27)(20,33)(21,29)(23,36)(24,40)(25,37)(26,32)(28,35)(30,44)(31,46)(34,45)(38,47)(39,42)(41,43);(16,19,21,30)(17,23,25,38)(18,27,29,44)(20,34,35,31)(22,36,37,47)(24,41,32,39)(26,42,40,43)(28,46,33,45);(12,14,15,13)(19,30)(23,38)(27,44)(31,34)(36,47)(39,41)(42,43)(45,46)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14464);