Copied to
clipboard

G = C2×C26order 52 = 22·13

Abelian group of type [2,26]

direct product, abelian, monomial, 2-elementary

Aliases: C2×C26, SmallGroup(52,5)

Series: Derived Chief Lower central Upper central

C1 — C2×C26
C1C13C26 — C2×C26
C1 — C2×C26
C1 — C2×C26

Generators and relations for C2×C26
 G = < a,b | a2=b26=1, ab=ba >


Smallest permutation representation of C2×C26
Regular action on 52 points
Generators in S52
(1 27)(2 28)(3 29)(4 30)(5 31)(6 32)(7 33)(8 34)(9 35)(10 36)(11 37)(12 38)(13 39)(14 40)(15 41)(16 42)(17 43)(18 44)(19 45)(20 46)(21 47)(22 48)(23 49)(24 50)(25 51)(26 52)
(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 48 49 50 51 52)

G:=sub<Sym(52)| (1,27)(2,28)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52), (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)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)>;

G:=Group( (1,27)(2,28)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52), (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)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52) );

G=PermutationGroup([(1,27),(2,28),(3,29),(4,30),(5,31),(6,32),(7,33),(8,34),(9,35),(10,36),(11,37),(12,38),(13,39),(14,40),(15,41),(16,42),(17,43),(18,44),(19,45),(20,46),(21,47),(22,48),(23,49),(24,50),(25,51),(26,52)], [(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),(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)])

52 conjugacy classes

class 1 2A2B2C13A···13L26A···26AJ
order122213···1326···26
size11111···11···1

52 irreducible representations

dim1111
type++
imageC1C2C13C26
kernelC2×C26C26C22C2
# reps131236

Matrix representation of C2×C26 in GL2(𝔽53) generated by

520
052
,
100
038
G:=sub<GL(2,GF(53))| [52,0,0,52],[10,0,0,38] >;

C2×C26 in GAP, Magma, Sage, TeX

C_2\times C_{26}
% in TeX

G:=Group("C2xC26");
// GroupNames label

G:=SmallGroup(52,5);
// by ID

G=gap.SmallGroup(52,5);
# by ID

G:=PCGroup([3,-2,-2,-13]);
// Polycyclic

G:=Group<a,b|a^2=b^26=1,a*b=b*a>;
// generators/relations

׿
×
𝔽