Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#21429 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G | |
1010 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)(20,21,24,29,25,28,30,42)(22,26,33,38,32,39,36,43)(23,27,35,41,34,40,44,50)(31,37,46,49,45,48,47,51);(20,22,30,33,25,32,24,36)(21,26,29,43,28,39,42,38)(23,31,44,46,34,45,35,47)(27,37,41,51,40,48,50,49);(13,16)(17,19)(20,23,25,34)(21,27,28,40)(22,31,32,45)(24,35,30,44)(26,37,39,48)(29,41,42,50)(33,46,36,47)(38,49,43,51);(12,14,15,18)(13,17,16,19)(23,34)(27,40)(31,45)(35,44)(37,48)(41,50)(46,47)(49,51)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14417);