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## G = C11×D11order 242 = 2·112

### Direct product of C11 and D11

Aliases: C11×D11, C11C2, AΣL1(𝔽121), C11⋊C22, C1121C2, SmallGroup(242,3)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C11 — C11×D11
 Chief series C1 — C11 — C112 — C11×D11
 Lower central C11 — C11×D11
 Upper central C1 — C11

Generators and relations for C11×D11
G = < a,b,c | a11=b11=c2=1, ab=ba, ac=ca, cbc=b-1 >

Permutation representations of C11×D11
On 22 points - transitive group 22T7
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)
(1 11 10 9 8 7 6 5 4 3 2)(12 13 14 15 16 17 18 19 20 21 22)
(1 22)(2 12)(3 13)(4 14)(5 15)(6 16)(7 17)(8 18)(9 19)(10 20)(11 21)

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), (1,11,10,9,8,7,6,5,4,3,2)(12,13,14,15,16,17,18,19,20,21,22), (1,22)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(11,21)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22), (1,11,10,9,8,7,6,5,4,3,2)(12,13,14,15,16,17,18,19,20,21,22), (1,22)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(11,21) );

G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11),(12,13,14,15,16,17,18,19,20,21,22)], [(1,11,10,9,8,7,6,5,4,3,2),(12,13,14,15,16,17,18,19,20,21,22)], [(1,22),(2,12),(3,13),(4,14),(5,15),(6,16),(7,17),(8,18),(9,19),(10,20),(11,21)]])

G:=TransitiveGroup(22,7);

77 conjugacy classes

 class 1 2 11A ··· 11J 11K ··· 11BM 22A ··· 22J order 1 2 11 ··· 11 11 ··· 11 22 ··· 22 size 1 11 1 ··· 1 2 ··· 2 11 ··· 11

77 irreducible representations

 dim 1 1 1 1 2 2 type + + + image C1 C2 C11 C22 D11 C11×D11 kernel C11×D11 C112 D11 C11 C11 C1 # reps 1 1 10 10 5 50

Matrix representation of C11×D11 in GL2(𝔽23) generated by

 9 0 0 9
,
 4 0 0 6
,
 0 6 4 0
G:=sub<GL(2,GF(23))| [9,0,0,9],[4,0,0,6],[0,4,6,0] >;

C11×D11 in GAP, Magma, Sage, TeX

C_{11}\times D_{11}
% in TeX

G:=Group("C11xD11");
// GroupNames label

G:=SmallGroup(242,3);
// by ID

G=gap.SmallGroup(242,3);
# by ID

G:=PCGroup([3,-2,-11,-11,1982]);
// Polycyclic

G:=Group<a,b,c|a^11=b^11=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

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