direct product, cyclic, abelian, monomial
Aliases: C38, also denoted Z38, SmallGroup(38,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C38 |
| C1 — C38 |
| C1 — C38 |
Generators and relations for C38
G = < a | a38=1 >
Smallest permutation representation of C38
►Regular action on 38 points
Generators in S38
(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)
G:=sub<Sym(38)| (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)>;
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) );
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)]])
C38 is a maximal subgroup of
Dic19
38 conjugacy classes
| class | 1 | 2 | 19A | ··· | 19R | 38A | ··· | 38R |
| order | 1 | 2 | 19 | ··· | 19 | 38 | ··· | 38 |
| size | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
38 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C19 | C38 |
| kernel | C38 | C19 | C2 | C1 |
| # reps | 1 | 1 | 18 | 18 |
Matrix representation of C38 ►in GL1(𝔽191) generated by
| 122 |
G:=sub<GL(1,GF(191))| [122] >;
C38 in GAP, Magma, Sage, TeX
C_{38} % in TeX
G:=Group("C38"); // GroupNames label
G:=SmallGroup(38,2);
// by ID
G=gap.SmallGroup(38,2);
# by ID
G:=PCGroup([2,-2,-19]);
// Polycyclic
G:=Group<a|a^38=1>;
// generators/relations
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