direct product, cyclic, abelian, monomial
Aliases: C35, also denoted Z35, SmallGroup(35,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C35 |
| C1 — C35 |
| C1 — C35 |
Generators and relations for C35
G = < a | a35=1 >
Smallest permutation representation of C35
►Regular action on 35 points
Generators in S35
(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)
G:=sub<Sym(35)| (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)>;
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) );
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)]])
C35 is a maximal subgroup of
D35
35 conjugacy classes
| class | 1 | 5A | 5B | 5C | 5D | 7A | ··· | 7F | 35A | ··· | 35X |
| order | 1 | 5 | 5 | 5 | 5 | 7 | ··· | 7 | 35 | ··· | 35 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
35 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | |||
| image | C1 | C5 | C7 | C35 |
| kernel | C35 | C7 | C5 | C1 |
| # reps | 1 | 4 | 6 | 24 |
Matrix representation of C35 ►in GL1(𝔽71) generated by
| 58 |
G:=sub<GL(1,GF(71))| [58] >;
C35 in GAP, Magma, Sage, TeX
C_{35} % in TeX
G:=Group("C35"); // GroupNames label
G:=SmallGroup(35,1);
// by ID
G=gap.SmallGroup(35,1);
# by ID
G:=PCGroup([2,-5,-7]);
// Polycyclic
G:=Group<a|a^35=1>;
// generators/relations
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