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G = C3×D11order 66 = 2·3·11

Direct product of C3 and D11

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

Aliases: C3×D11, C11⋊C6, C332C2, SmallGroup(66,2)

Series: Derived Chief Lower central Upper central

C1C11 — C3×D11
C1C11C33 — C3×D11
C11 — C3×D11
C1C3

Generators and relations for C3×D11
 G = < a,b,c | a3=b11=c2=1, ab=ba, ac=ca, cbc=b-1 >

11C2
11C6

Character table of C3×D11

 class 123A3B6A6B11A11B11C11D11E33A33B33C33D33E33F33G33H33I33J
 size 111111111222222222222222
ρ1111111111111111111111    trivial
ρ21-111-1-1111111111111111    linear of order 2
ρ31-1ζ3ζ32ζ65ζ611111ζ32ζ32ζ3ζ3ζ3ζ3ζ3ζ32ζ32ζ32    linear of order 6
ρ41-1ζ32ζ3ζ6ζ6511111ζ3ζ3ζ32ζ32ζ32ζ32ζ32ζ3ζ3ζ3    linear of order 6
ρ511ζ32ζ3ζ32ζ311111ζ3ζ3ζ32ζ32ζ32ζ32ζ32ζ3ζ3ζ3    linear of order 3
ρ611ζ3ζ32ζ3ζ3211111ζ32ζ32ζ3ζ3ζ3ζ3ζ3ζ32ζ32ζ32    linear of order 3
ρ7202200ζ111011ζ119112ζ118113ζ117114ζ116115ζ116115ζ111011ζ111011ζ119112ζ118113ζ117114ζ116115ζ119112ζ118113ζ117114    orthogonal lifted from D11
ρ8202200ζ119112ζ117114ζ116115ζ118113ζ111011ζ111011ζ119112ζ119112ζ117114ζ116115ζ118113ζ111011ζ117114ζ116115ζ118113    orthogonal lifted from D11
ρ9202200ζ117114ζ118113ζ111011ζ116115ζ119112ζ119112ζ117114ζ117114ζ118113ζ111011ζ116115ζ119112ζ118113ζ111011ζ116115    orthogonal lifted from D11
ρ10202200ζ116115ζ111011ζ117114ζ119112ζ118113ζ118113ζ116115ζ116115ζ111011ζ117114ζ119112ζ118113ζ111011ζ117114ζ119112    orthogonal lifted from D11
ρ11202200ζ118113ζ116115ζ119112ζ111011ζ117114ζ117114ζ118113ζ118113ζ116115ζ119112ζ111011ζ117114ζ116115ζ119112ζ111011    orthogonal lifted from D11
ρ1220-1+-3-1--300ζ111011ζ119112ζ118113ζ117114ζ116115ζ32ζ11632ζ115ζ32ζ111032ζ11ζ3ζ11103ζ11ζ3ζ1193ζ112ζ3ζ1183ζ113ζ3ζ1173ζ114ζ3ζ1163ζ115ζ32ζ11932ζ112ζ32ζ11832ζ113ζ32ζ11732ζ114    complex faithful
ρ1320-1--3-1+-300ζ117114ζ118113ζ111011ζ116115ζ119112ζ3ζ1193ζ112ζ3ζ1173ζ114ζ32ζ11732ζ114ζ32ζ11832ζ113ζ32ζ111032ζ11ζ32ζ11632ζ115ζ32ζ11932ζ112ζ3ζ1183ζ113ζ3ζ11103ζ11ζ3ζ1163ζ115    complex faithful
ρ1420-1+-3-1--300ζ118113ζ116115ζ119112ζ111011ζ117114ζ32ζ11732ζ114ζ32ζ11832ζ113ζ3ζ1183ζ113ζ3ζ1163ζ115ζ3ζ1193ζ112ζ3ζ11103ζ11ζ3ζ1173ζ114ζ32ζ11632ζ115ζ32ζ11932ζ112ζ32ζ111032ζ11    complex faithful
ρ1520-1--3-1+-300ζ119112ζ117114ζ116115ζ118113ζ111011ζ3ζ11103ζ11ζ3ζ1193ζ112ζ32ζ11932ζ112ζ32ζ11732ζ114ζ32ζ11632ζ115ζ32ζ11832ζ113ζ32ζ111032ζ11ζ3ζ1173ζ114ζ3ζ1163ζ115ζ3ζ1183ζ113    complex faithful
ρ1620-1--3-1+-300ζ116115ζ111011ζ117114ζ119112ζ118113ζ3ζ1183ζ113ζ3ζ1163ζ115ζ32ζ11632ζ115ζ32ζ111032ζ11ζ32ζ11732ζ114ζ32ζ11932ζ112ζ32ζ11832ζ113ζ3ζ11103ζ11ζ3ζ1173ζ114ζ3ζ1193ζ112    complex faithful
ρ1720-1--3-1+-300ζ111011ζ119112ζ118113ζ117114ζ116115ζ3ζ1163ζ115ζ3ζ11103ζ11ζ32ζ111032ζ11ζ32ζ11932ζ112ζ32ζ11832ζ113ζ32ζ11732ζ114ζ32ζ11632ζ115ζ3ζ1193ζ112ζ3ζ1183ζ113ζ3ζ1173ζ114    complex faithful
ρ1820-1+-3-1--300ζ119112ζ117114ζ116115ζ118113ζ111011ζ32ζ111032ζ11ζ32ζ11932ζ112ζ3ζ1193ζ112ζ3ζ1173ζ114ζ3ζ1163ζ115ζ3ζ1183ζ113ζ3ζ11103ζ11ζ32ζ11732ζ114ζ32ζ11632ζ115ζ32ζ11832ζ113    complex faithful
ρ1920-1+-3-1--300ζ116115ζ111011ζ117114ζ119112ζ118113ζ32ζ11832ζ113ζ32ζ11632ζ115ζ3ζ1163ζ115ζ3ζ11103ζ11ζ3ζ1173ζ114ζ3ζ1193ζ112ζ3ζ1183ζ113ζ32ζ111032ζ11ζ32ζ11732ζ114ζ32ζ11932ζ112    complex faithful
ρ2020-1+-3-1--300ζ117114ζ118113ζ111011ζ116115ζ119112ζ32ζ11932ζ112ζ32ζ11732ζ114ζ3ζ1173ζ114ζ3ζ1183ζ113ζ3ζ11103ζ11ζ3ζ1163ζ115ζ3ζ1193ζ112ζ32ζ11832ζ113ζ32ζ111032ζ11ζ32ζ11632ζ115    complex faithful
ρ2120-1--3-1+-300ζ118113ζ116115ζ119112ζ111011ζ117114ζ3ζ1173ζ114ζ3ζ1183ζ113ζ32ζ11832ζ113ζ32ζ11632ζ115ζ32ζ11932ζ112ζ32ζ111032ζ11ζ32ζ11732ζ114ζ3ζ1163ζ115ζ3ζ1193ζ112ζ3ζ11103ζ11    complex faithful

Smallest permutation representation of C3×D11
On 33 points
Generators in S33
(1 32 21)(2 33 22)(3 23 12)(4 24 13)(5 25 14)(6 26 15)(7 27 16)(8 28 17)(9 29 18)(10 30 19)(11 31 20)
(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)
(1 11)(2 10)(3 9)(4 8)(5 7)(12 18)(13 17)(14 16)(19 22)(20 21)(23 29)(24 28)(25 27)(30 33)(31 32)

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

G:=Group( (1,32,21)(2,33,22)(3,23,12)(4,24,13)(5,25,14)(6,26,15)(7,27,16)(8,28,17)(9,29,18)(10,30,19)(11,31,20), (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), (1,11)(2,10)(3,9)(4,8)(5,7)(12,18)(13,17)(14,16)(19,22)(20,21)(23,29)(24,28)(25,27)(30,33)(31,32) );

G=PermutationGroup([(1,32,21),(2,33,22),(3,23,12),(4,24,13),(5,25,14),(6,26,15),(7,27,16),(8,28,17),(9,29,18),(10,30,19),(11,31,20)], [(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)], [(1,11),(2,10),(3,9),(4,8),(5,7),(12,18),(13,17),(14,16),(19,22),(20,21),(23,29),(24,28),(25,27),(30,33),(31,32)])

C3×D11 is a maximal subgroup of   C11⋊F7
C3×D11 is a maximal quotient of   C11⋊F7

Matrix representation of C3×D11 in GL2(𝔽43) generated by

360
036
,
07
69
,
942
3734
G:=sub<GL(2,GF(43))| [36,0,0,36],[0,6,7,9],[9,37,42,34] >;

C3×D11 in GAP, Magma, Sage, TeX

C_3\times D_{11}
% in TeX

G:=Group("C3xD11");
// GroupNames label

G:=SmallGroup(66,2);
// by ID

G=gap.SmallGroup(66,2);
# by ID

G:=PCGroup([3,-2,-3,-11,542]);
// Polycyclic

G:=Group<a,b,c|a^3=b^11=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C3×D11 in TeX
Character table of C3×D11 in TeX

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