Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1913 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#10941 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #386 |
| commutator | C23 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1437 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
904 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,21,17,20,28,34)(14,18,24,31,23,30,27,35)(15,19,26,32,25,33,39,43)(22,36,38,42,37,29,40,41);(12,14)(13,18,20,30)(15,22)(16,27)(17,23)(19,29,33,36)(21,35,34,31)(24,28)(25,37)(26,40)(32,42,43,41)(38,39);(12,15,16,26,17,25,28,39)(13,19,21,32,20,33,34,43)(14,22,27,40,23,37,24,38)(18,29,35,42,30,36,31,41)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3929);