direct product, cyclic, abelian, monomial
Aliases: C66, also denoted Z66, SmallGroup(66,4)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C66 |
| C1 — C66 |
| C1 — C66 |
Generators and relations for C66
G = < a | a66=1 >
Smallest permutation representation of C66
►Regular action on 66 points
Generators in S66
(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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66)
G:=sub<Sym(66)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66)]])
C66 is a maximal subgroup of
Dic33
66 conjugacy classes
| class | 1 | 2 | 3A | 3B | 6A | 6B | 11A | ··· | 11J | 22A | ··· | 22J | 33A | ··· | 33T | 66A | ··· | 66T |
| order | 1 | 2 | 3 | 3 | 6 | 6 | 11 | ··· | 11 | 22 | ··· | 22 | 33 | ··· | 33 | 66 | ··· | 66 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
66 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | ||||||
| image | C1 | C2 | C3 | C6 | C11 | C22 | C33 | C66 |
| kernel | C66 | C33 | C22 | C11 | C6 | C3 | C2 | C1 |
| # reps | 1 | 1 | 2 | 2 | 10 | 10 | 20 | 20 |
Matrix representation of C66 ►in GL2(𝔽23) generated by
| 0 | 14 |
| 1 | 3 |
G:=sub<GL(2,GF(23))| [0,1,14,3] >;
C66 in GAP, Magma, Sage, TeX
C_{66} % in TeX
G:=Group("C66"); // GroupNames label
G:=SmallGroup(66,4);
// by ID
G=gap.SmallGroup(66,4);
# by ID
G:=PCGroup([3,-2,-3,-11]);
// Polycyclic
G:=Group<a|a^66=1>;
// generators/relations
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