direct product, cyclic, abelian, monomial
Aliases: C40, also denoted Z40, SmallGroup(40,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C40 |
| C1 — C40 |
| C1 — C40 |
Generators and relations for C40
G = < a | a40=1 >
Smallest permutation representation of C40
►Regular action on 40 points
Generators in S40
(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)
G:=sub<Sym(40)| (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)>;
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) );
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)]])
C40 is a maximal subgroup of
C5⋊2C16 C8⋊D5 C40⋊C2 D40 Dic20 C11⋊C40
C40 is a maximal quotient of C11⋊C40
40 conjugacy classes
| class | 1 | 2 | 4A | 4B | 5A | 5B | 5C | 5D | 8A | 8B | 8C | 8D | 10A | 10B | 10C | 10D | 20A | ··· | 20H | 40A | ··· | 40P |
| order | 1 | 2 | 4 | 4 | 5 | 5 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
40 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | ||||||
| image | C1 | C2 | C4 | C5 | C8 | C10 | C20 | C40 |
| kernel | C40 | C20 | C10 | C8 | C5 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 4 | 4 | 8 | 16 |
Matrix representation of C40 ►in GL1(𝔽41) generated by
| 34 |
G:=sub<GL(1,GF(41))| [34] >;
C40 in GAP, Magma, Sage, TeX
C_{40} % in TeX
G:=Group("C40"); // GroupNames label
G:=SmallGroup(40,2);
// by ID
G=gap.SmallGroup(40,2);
# by ID
G:=PCGroup([4,-2,-5,-2,-2,40,34]);
// Polycyclic
G:=Group<a|a^40=1>;
// generators/relations
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