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) = C27 |
| direct product | C11×#20991 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C11×#41 ◁ G | |
1674 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)(14,15)(16,17,20,25,21,24,26,38)(18,22,29,34,28,35,32,39)(19,23,31,37,30,36,40,46)(27,33,42,45,41,44,43,47);(16,18,26,29,21,28,20,32)(17,22,25,39,24,35,38,34)(19,27,40,42,30,41,31,43)(23,33,37,47,36,44,46,45);(13,15)(16,19)(17,23)(18,27)(20,31)(21,30)(22,33)(24,36)(25,37)(26,40)(28,41)(29,42)(32,43)(34,45)(35,44)(38,46)(39,47);(19,30)(23,36)(27,41)(31,40)(33,44)(37,46)(42,43)(45,47)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13979);