direct product, cyclic, abelian, monomial
Aliases: C34, also denoted Z34, SmallGroup(34,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C34 |
| C1 — C34 |
| C1 — C34 |
Generators and relations for C34
G = < a | a34=1 >
Smallest permutation representation of C34
►Regular action on 34 points
Generators in S34
(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)
G:=sub<Sym(34)| (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)>;
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) );
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)]])
C34 is a maximal subgroup of
Dic17
34 conjugacy classes
| class | 1 | 2 | 17A | ··· | 17P | 34A | ··· | 34P |
| order | 1 | 2 | 17 | ··· | 17 | 34 | ··· | 34 |
| size | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
34 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C17 | C34 |
| kernel | C34 | C17 | C2 | C1 |
| # reps | 1 | 1 | 16 | 16 |
Matrix representation of C34 ►in GL1(𝔽103) generated by
| 90 |
G:=sub<GL(1,GF(103))| [90] >;
C34 in GAP, Magma, Sage, TeX
C_{34} % in TeX
G:=Group("C34"); // GroupNames label
G:=SmallGroup(34,2);
// by ID
G=gap.SmallGroup(34,2);
# by ID
G:=PCGroup([2,-2,-17]);
// Polycyclic
G:=Group<a|a^34=1>;
// generators/relations
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