direct product, cyclic, abelian, monomial
Aliases: C39, also denoted Z39, SmallGroup(39,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C39 |
| C1 — C39 |
| C1 — C39 |
Generators and relations for C39
G = < a | a39=1 >
Smallest permutation representation of C39
►Regular action on 39 points
Generators in S39
(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)
G:=sub<Sym(39)| (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)>;
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) );
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)]])
C39 is a maximal subgroup of
D39 C13⋊C9
39 conjugacy classes
| class | 1 | 3A | 3B | 13A | ··· | 13L | 39A | ··· | 39X |
| order | 1 | 3 | 3 | 13 | ··· | 13 | 39 | ··· | 39 |
| size | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
39 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | |||
| image | C1 | C3 | C13 | C39 |
| kernel | C39 | C13 | C3 | C1 |
| # reps | 1 | 2 | 12 | 24 |
Matrix representation of C39 ►in GL1(𝔽79) generated by
| 25 |
G:=sub<GL(1,GF(79))| [25] >;
C39 in GAP, Magma, Sage, TeX
C_{39} % in TeX
G:=Group("C39"); // GroupNames label
G:=SmallGroup(39,2);
// by ID
G=gap.SmallGroup(39,2);
# by ID
G:=PCGroup([2,-3,-13]);
// Polycyclic
G:=Group<a|a^39=1>;
// generators/relations
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