direct product, cyclic, abelian, monomial
Aliases: C22, also denoted Z22, SmallGroup(22,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C22 |
| C1 — C22 |
| C1 — C22 |
Generators and relations for C22
G = < a | a22=1 >
Character table of C22
| class | 1 | 2 | 11A | 11B | 11C | 11D | 11E | 11F | 11G | 11H | 11I | 11J | 22A | 22B | 22C | 22D | 22E | 22F | 22G | 22H | 22I | 22J | |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 2 |
| ρ3 | 1 | 1 | ζ112 | ζ113 | ζ114 | ζ115 | ζ116 | ζ117 | ζ118 | ζ119 | ζ1110 | ζ11 | ζ1110 | ζ112 | ζ113 | ζ114 | ζ115 | ζ116 | ζ117 | ζ118 | ζ119 | ζ11 | linear of order 11 |
| ρ4 | 1 | -1 | ζ112 | ζ113 | ζ114 | ζ115 | ζ116 | ζ117 | ζ118 | ζ119 | ζ1110 | ζ11 | -ζ1110 | -ζ112 | -ζ113 | -ζ114 | -ζ115 | -ζ116 | -ζ117 | -ζ118 | -ζ119 | -ζ11 | linear of order 22 faithful |
| ρ5 | 1 | 1 | ζ114 | ζ116 | ζ118 | ζ1110 | ζ11 | ζ113 | ζ115 | ζ117 | ζ119 | ζ112 | ζ119 | ζ114 | ζ116 | ζ118 | ζ1110 | ζ11 | ζ113 | ζ115 | ζ117 | ζ112 | linear of order 11 |
| ρ6 | 1 | -1 | ζ114 | ζ116 | ζ118 | ζ1110 | ζ11 | ζ113 | ζ115 | ζ117 | ζ119 | ζ112 | -ζ119 | -ζ114 | -ζ116 | -ζ118 | -ζ1110 | -ζ11 | -ζ113 | -ζ115 | -ζ117 | -ζ112 | linear of order 22 faithful |
| ρ7 | 1 | 1 | ζ116 | ζ119 | ζ11 | ζ114 | ζ117 | ζ1110 | ζ112 | ζ115 | ζ118 | ζ113 | ζ118 | ζ116 | ζ119 | ζ11 | ζ114 | ζ117 | ζ1110 | ζ112 | ζ115 | ζ113 | linear of order 11 |
| ρ8 | 1 | -1 | ζ116 | ζ119 | ζ11 | ζ114 | ζ117 | ζ1110 | ζ112 | ζ115 | ζ118 | ζ113 | -ζ118 | -ζ116 | -ζ119 | -ζ11 | -ζ114 | -ζ117 | -ζ1110 | -ζ112 | -ζ115 | -ζ113 | linear of order 22 faithful |
| ρ9 | 1 | 1 | ζ118 | ζ11 | ζ115 | ζ119 | ζ112 | ζ116 | ζ1110 | ζ113 | ζ117 | ζ114 | ζ117 | ζ118 | ζ11 | ζ115 | ζ119 | ζ112 | ζ116 | ζ1110 | ζ113 | ζ114 | linear of order 11 |
| ρ10 | 1 | -1 | ζ118 | ζ11 | ζ115 | ζ119 | ζ112 | ζ116 | ζ1110 | ζ113 | ζ117 | ζ114 | -ζ117 | -ζ118 | -ζ11 | -ζ115 | -ζ119 | -ζ112 | -ζ116 | -ζ1110 | -ζ113 | -ζ114 | linear of order 22 faithful |
| ρ11 | 1 | 1 | ζ1110 | ζ114 | ζ119 | ζ113 | ζ118 | ζ112 | ζ117 | ζ11 | ζ116 | ζ115 | ζ116 | ζ1110 | ζ114 | ζ119 | ζ113 | ζ118 | ζ112 | ζ117 | ζ11 | ζ115 | linear of order 11 |
| ρ12 | 1 | -1 | ζ1110 | ζ114 | ζ119 | ζ113 | ζ118 | ζ112 | ζ117 | ζ11 | ζ116 | ζ115 | -ζ116 | -ζ1110 | -ζ114 | -ζ119 | -ζ113 | -ζ118 | -ζ112 | -ζ117 | -ζ11 | -ζ115 | linear of order 22 faithful |
| ρ13 | 1 | 1 | ζ11 | ζ117 | ζ112 | ζ118 | ζ113 | ζ119 | ζ114 | ζ1110 | ζ115 | ζ116 | ζ115 | ζ11 | ζ117 | ζ112 | ζ118 | ζ113 | ζ119 | ζ114 | ζ1110 | ζ116 | linear of order 11 |
| ρ14 | 1 | -1 | ζ11 | ζ117 | ζ112 | ζ118 | ζ113 | ζ119 | ζ114 | ζ1110 | ζ115 | ζ116 | -ζ115 | -ζ11 | -ζ117 | -ζ112 | -ζ118 | -ζ113 | -ζ119 | -ζ114 | -ζ1110 | -ζ116 | linear of order 22 faithful |
| ρ15 | 1 | 1 | ζ113 | ζ1110 | ζ116 | ζ112 | ζ119 | ζ115 | ζ11 | ζ118 | ζ114 | ζ117 | ζ114 | ζ113 | ζ1110 | ζ116 | ζ112 | ζ119 | ζ115 | ζ11 | ζ118 | ζ117 | linear of order 11 |
| ρ16 | 1 | -1 | ζ113 | ζ1110 | ζ116 | ζ112 | ζ119 | ζ115 | ζ11 | ζ118 | ζ114 | ζ117 | -ζ114 | -ζ113 | -ζ1110 | -ζ116 | -ζ112 | -ζ119 | -ζ115 | -ζ11 | -ζ118 | -ζ117 | linear of order 22 faithful |
| ρ17 | 1 | 1 | ζ115 | ζ112 | ζ1110 | ζ117 | ζ114 | ζ11 | ζ119 | ζ116 | ζ113 | ζ118 | ζ113 | ζ115 | ζ112 | ζ1110 | ζ117 | ζ114 | ζ11 | ζ119 | ζ116 | ζ118 | linear of order 11 |
| ρ18 | 1 | -1 | ζ115 | ζ112 | ζ1110 | ζ117 | ζ114 | ζ11 | ζ119 | ζ116 | ζ113 | ζ118 | -ζ113 | -ζ115 | -ζ112 | -ζ1110 | -ζ117 | -ζ114 | -ζ11 | -ζ119 | -ζ116 | -ζ118 | linear of order 22 faithful |
| ρ19 | 1 | 1 | ζ117 | ζ115 | ζ113 | ζ11 | ζ1110 | ζ118 | ζ116 | ζ114 | ζ112 | ζ119 | ζ112 | ζ117 | ζ115 | ζ113 | ζ11 | ζ1110 | ζ118 | ζ116 | ζ114 | ζ119 | linear of order 11 |
| ρ20 | 1 | -1 | ζ117 | ζ115 | ζ113 | ζ11 | ζ1110 | ζ118 | ζ116 | ζ114 | ζ112 | ζ119 | -ζ112 | -ζ117 | -ζ115 | -ζ113 | -ζ11 | -ζ1110 | -ζ118 | -ζ116 | -ζ114 | -ζ119 | linear of order 22 faithful |
| ρ21 | 1 | 1 | ζ119 | ζ118 | ζ117 | ζ116 | ζ115 | ζ114 | ζ113 | ζ112 | ζ11 | ζ1110 | ζ11 | ζ119 | ζ118 | ζ117 | ζ116 | ζ115 | ζ114 | ζ113 | ζ112 | ζ1110 | linear of order 11 |
| ρ22 | 1 | -1 | ζ119 | ζ118 | ζ117 | ζ116 | ζ115 | ζ114 | ζ113 | ζ112 | ζ11 | ζ1110 | -ζ11 | -ζ119 | -ζ118 | -ζ117 | -ζ116 | -ζ115 | -ζ114 | -ζ113 | -ζ112 | -ζ1110 | linear of order 22 faithful |
►Regular action on 22 points - transitive group 22T1
Generators in S22
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22)
G:=sub<Sym(22)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)]])
G:=TransitiveGroup(22,1);
C22 is a maximal subgroup of
Dic11
| action | f(x) | Disc(f) |
|---|---|---|
| 22T1 | x22+x21+x20+x19+x18+x17+x16+x15+x14+x13+x12+x11+x10+x9+x8+x7+x6+x5+x4+x3+x2+x+1 | -2321 |
Matrix representation of C22 ►in GL1(𝔽23) generated by
| 15 |
G:=sub<GL(1,GF(23))| [15] >;
C22 in GAP, Magma, Sage, TeX
C_{22} % in TeX
G:=Group("C22"); // GroupNames label
G:=SmallGroup(22,2);
// by ID
G=gap.SmallGroup(22,2);
# by ID
G:=PCGroup([2,-2,-11]);
// Polycyclic
G:=Group<a|a^22=1>;
// generators/relations
Export
Subgroup lattice of C22 in TeX
Character table of C22 in TeX