Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#10956 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #386 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
918 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)(16,17)(18,27)(19,31,33,40)(20,34)(21,25)(22,26)(23,29)(24,32,41,36)(28,43,46,37)(30,38)(35,39)(42,45,47,44);(12,13,14,15)(16,18)(17,23)(19,28)(20,35)(21,29)(22,30)(24,37)(25,38)(26,39)(27,34)(31,42)(32,45)(33,46)(36,44)(40,47)(41,43);(16,19,21,36,22,33,20,32)(17,24,25,40,26,41,34,31)(18,28,29,44,30,46,35,45)(23,37,38,47,39,43,27,42)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3944);