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G = Dic11order 44 = 22·11

Dicyclic group

metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: Dic11, C11⋊C4, C22.C2, C2.D11, SmallGroup(44,1)

Series: Derived Chief Lower central Upper central

C1C11 — Dic11
C1C11C22 — Dic11
C11 — Dic11
C1C2

Generators and relations for Dic11
 G = < a,b | a22=1, b2=a11, bab-1=a-1 >

11C4

Character table of Dic11

 class 124A4B11A11B11C11D11E22A22B22C22D22E
 size 1111112222222222
ρ111111111111111    trivial
ρ211-1-11111111111    linear of order 2
ρ31-1-ii11111-1-1-1-1-1    linear of order 4
ρ41-1i-i11111-1-1-1-1-1    linear of order 4
ρ52200ζ116115ζ119112ζ117114ζ118113ζ111011ζ111011ζ116115ζ119112ζ117114ζ118113    orthogonal lifted from D11
ρ62200ζ117114ζ116115ζ111011ζ119112ζ118113ζ118113ζ117114ζ116115ζ111011ζ119112    orthogonal lifted from D11
ρ72200ζ118113ζ111011ζ119112ζ117114ζ116115ζ116115ζ118113ζ111011ζ119112ζ117114    orthogonal lifted from D11
ρ82200ζ119112ζ118113ζ116115ζ111011ζ117114ζ117114ζ119112ζ118113ζ116115ζ111011    orthogonal lifted from D11
ρ92200ζ111011ζ117114ζ118113ζ116115ζ119112ζ119112ζ111011ζ117114ζ118113ζ116115    orthogonal lifted from D11
ρ102-200ζ119112ζ118113ζ116115ζ111011ζ117114117114119112118113116115111011    symplectic faithful, Schur index 2
ρ112-200ζ116115ζ119112ζ117114ζ118113ζ111011111011116115119112117114118113    symplectic faithful, Schur index 2
ρ122-200ζ111011ζ117114ζ118113ζ116115ζ119112119112111011117114118113116115    symplectic faithful, Schur index 2
ρ132-200ζ117114ζ116115ζ111011ζ119112ζ118113118113117114116115111011119112    symplectic faithful, Schur index 2
ρ142-200ζ118113ζ111011ζ119112ζ117114ζ116115116115118113111011119112117114    symplectic faithful, Schur index 2

Smallest permutation representation of Dic11
Regular action on 44 points
Generators in S44
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22)(23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44)
(1 28 12 39)(2 27 13 38)(3 26 14 37)(4 25 15 36)(5 24 16 35)(6 23 17 34)(7 44 18 33)(8 43 19 32)(9 42 20 31)(10 41 21 30)(11 40 22 29)

G:=sub<Sym(44)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44), (1,28,12,39)(2,27,13,38)(3,26,14,37)(4,25,15,36)(5,24,16,35)(6,23,17,34)(7,44,18,33)(8,43,19,32)(9,42,20,31)(10,41,21,30)(11,40,22,29)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44), (1,28,12,39)(2,27,13,38)(3,26,14,37)(4,25,15,36)(5,24,16,35)(6,23,17,34)(7,44,18,33)(8,43,19,32)(9,42,20,31)(10,41,21,30)(11,40,22,29) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22),(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44)], [(1,28,12,39),(2,27,13,38),(3,26,14,37),(4,25,15,36),(5,24,16,35),(6,23,17,34),(7,44,18,33),(8,43,19,32),(9,42,20,31),(10,41,21,30),(11,40,22,29)])

Matrix representation of Dic11 in GL2(𝔽23) generated by

225
520
,
022
10
G:=sub<GL(2,GF(23))| [22,5,5,20],[0,1,22,0] >;

Dic11 in GAP, Magma, Sage, TeX

{\rm Dic}_{11}
% in TeX

G:=Group("Dic11");
// GroupNames label

G:=SmallGroup(44,1);
// by ID

G=gap.SmallGroup(44,1);
# by ID

G:=PCGroup([3,-2,-2,-11,6,362]);
// Polycyclic

G:=Group<a,b|a^22=1,b^2=a^11,b*a*b^-1=a^-1>;
// generators/relations

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