Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11320 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #124 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #397 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
546 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)(13,14)(16,17)(18,26,29,39)(19,23)(20,24)(21,25)(22,28,36,33)(27,42,30,41)(31,37)(32,38)(34,40)(35,45,46,44)(43,47);(12,13)(14,15)(16,18,20,33,21,29,34,28)(17,22,24,39,25,36,40,26)(19,30,31,44,32,27,43,45)(23,35,37,42,38,46,47,41);(12,14,15,13)(16,19,20,31,21,32,34,43)(17,23,24,37,25,38,40,47)(18,27,28,44,29,30,33,45)(22,35,26,41,36,46,39,42)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4308);