p-group, cyclic, elementary abelian, simple, monomial
Aliases: C47, also denoted Z47, SmallGroup(47,1)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
| C1 — C47 |
| C1 — C47 |
| C1 — C47 |
| C1 — C47 |
Generators and relations for C47
G = < a | a47=1 >
Smallest permutation representation of C47
►Regular action on 47 points
Generators in S47
(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 41 42 43 44 45 46 47)
G:=sub<Sym(47)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)]])
C47 is a maximal subgroup of
D47
47 conjugacy classes
| class | 1 | 47A | ··· | 47AT |
| order | 1 | 47 | ··· | 47 |
| size | 1 | 1 | ··· | 1 |
47 irreducible representations
| dim | 1 | 1 |
| type | + | |
| image | C1 | C47 |
| kernel | C47 | C1 |
| # reps | 1 | 46 |
Matrix representation of C47 ►in GL1(𝔽283) generated by
| 230 |
G:=sub<GL(1,GF(283))| [230] >;
C47 in GAP, Magma, Sage, TeX
C_{47} % in TeX
G:=Group("C47"); // GroupNames label
G:=SmallGroup(47,1);
// by ID
G=gap.SmallGroup(47,1);
# by ID
G:=PCGroup([1,-47]:ExponentLimit:=1);
// Polycyclic
G:=Group<a|a^47=1>;
// generators/relations
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