p-group, cyclic, elementary abelian, simple, monomial
Aliases: C31, also denoted Z31, SmallGroup(31,1)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
| C1 — C31 |
| C1 — C31 |
| C1 — C31 |
| C1 — C31 |
Generators and relations for C31
G = < a | a31=1 >
Permutation representations of C31
►Regular action on 31 points - transitive group 31T1
Generators in S31
(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)
G:=sub<Sym(31)| (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)>;
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) );
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)]])
G:=TransitiveGroup(31,1);
C31 is a maximal subgroup of
D31 C31⋊C3 C31⋊C5
31 conjugacy classes
| class | 1 | 31A | ··· | 31AD |
| order | 1 | 31 | ··· | 31 |
| size | 1 | 1 | ··· | 1 |
31 irreducible representations
| dim | 1 | 1 |
| type | + | |
| image | C1 | C31 |
| kernel | C31 | C1 |
| # reps | 1 | 30 |
Matrix representation of C31 ►in GL1(𝔽311) generated by
| 113 |
G:=sub<GL(1,GF(311))| [113] >;
C31 in GAP, Magma, Sage, TeX
C_{31} % in TeX
G:=Group("C31"); // GroupNames label
G:=SmallGroup(31,1);
// by ID
G=gap.SmallGroup(31,1);
# by ID
G:=PCGroup([1,-31]:ExponentLimit:=1);
// Polycyclic
G:=Group<a|a^31=1>;
// generators/relations
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