Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25×C4 |
| direct product | C11×#21250 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1434 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)(13,15)(16,17,21,26,22,25,20,34)(18,23,29,38,28,39,35,37)(19,30,33,40,31,44,32,24)(27,41,43,36,42,47,45,46);(12,13,14,15)(16,18,20,29,22,28,21,35)(17,23,26,37,25,39,34,38)(19,27,32,43,31,42,33,45)(24,36,30,41,40,46,44,47);(16,19,20,32,22,31,21,33)(17,24,26,30,25,40,34,44)(18,27,29,43,28,42,35,45)(23,36,37,41,39,46,38,47);(19,31)(24,40)(27,42)(30,44)(32,33)(36,46)(41,47)(43,45)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14238);