Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#21294 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C11×#97 ◁ G | |
722 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21,25,29,26,30,24,39)(22,27,34,42,32,41,33,48)(23,35,37,43,38,49,36,28)(31,44,47,50,45,51,46,40);(13,16)(17,19)(20,22,25,34,26,32,24,33)(21,27,29,42,30,41,39,48)(23,31,37,47,38,45,36,46)(28,40,35,44,43,50,49,51);(20,23,24,36,26,38,25,37)(21,28,29,35,30,43,39,49)(22,31,33,46,32,45,34,47)(27,40,42,44,41,50,48,51);(12,14,15,18)(13,17,16,19)(22,32)(27,41)(31,45)(33,34)(40,50)(42,48)(44,51)(46,47)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14282);