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G = C26order 26 = 2·13

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C26, also denoted Z26, SmallGroup(26,2)

Series: Derived Chief Lower central Upper central

C1 — C26
C1C13 — C26
C1 — C26
C1 — C26

Generators and relations for C26
 G = < a | a26=1 >


Character table of C26

 class 1213A13B13C13D13E13F13G13H13I13J13K13L26A26B26C26D26E26F26G26H26I26J26K26L
 size 11111111111111111111111111
ρ111111111111111111111111111    trivial
ρ21-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1    linear of order 2
ρ311ζ132ζ133ζ134ζ135ζ136ζ137ζ138ζ139ζ1310ζ1311ζ1312ζ13ζ1312ζ132ζ133ζ134ζ135ζ136ζ137ζ138ζ139ζ1310ζ1311ζ13    linear of order 13
ρ41-1ζ132ζ133ζ134ζ135ζ136ζ137ζ138ζ139ζ1310ζ1311ζ1312ζ1313121321331341351361371381391310131113    linear of order 26 faithful
ρ511ζ134ζ136ζ138ζ1310ζ1312ζ13ζ133ζ135ζ137ζ139ζ1311ζ132ζ1311ζ134ζ136ζ138ζ1310ζ1312ζ13ζ133ζ135ζ137ζ139ζ132    linear of order 13
ρ61-1ζ134ζ136ζ138ζ1310ζ1312ζ13ζ133ζ135ζ137ζ139ζ1311ζ13213111341361381310131213133135137139132    linear of order 26 faithful
ρ711ζ136ζ139ζ1312ζ132ζ135ζ138ζ1311ζ13ζ134ζ137ζ1310ζ133ζ1310ζ136ζ139ζ1312ζ132ζ135ζ138ζ1311ζ13ζ134ζ137ζ133    linear of order 13
ρ81-1ζ136ζ139ζ1312ζ132ζ135ζ138ζ1311ζ13ζ134ζ137ζ1310ζ13313101361391312132135138131113134137133    linear of order 26 faithful
ρ911ζ138ζ1312ζ133ζ137ζ1311ζ132ζ136ζ1310ζ13ζ135ζ139ζ134ζ139ζ138ζ1312ζ133ζ137ζ1311ζ132ζ136ζ1310ζ13ζ135ζ134    linear of order 13
ρ101-1ζ138ζ1312ζ133ζ137ζ1311ζ132ζ136ζ1310ζ13ζ135ζ139ζ13413913813121331371311132136131013135134    linear of order 26 faithful
ρ1111ζ1310ζ132ζ137ζ1312ζ134ζ139ζ13ζ136ζ1311ζ133ζ138ζ135ζ138ζ1310ζ132ζ137ζ1312ζ134ζ139ζ13ζ136ζ1311ζ133ζ135    linear of order 13
ρ121-1ζ1310ζ132ζ137ζ1312ζ134ζ139ζ13ζ136ζ1311ζ133ζ138ζ13513813101321371312134139131361311133135    linear of order 26 faithful
ρ1311ζ1312ζ135ζ1311ζ134ζ1310ζ133ζ139ζ132ζ138ζ13ζ137ζ136ζ137ζ1312ζ135ζ1311ζ134ζ1310ζ133ζ139ζ132ζ138ζ13ζ136    linear of order 13
ρ141-1ζ1312ζ135ζ1311ζ134ζ1310ζ133ζ139ζ132ζ138ζ13ζ137ζ13613713121351311134131013313913213813136    linear of order 26 faithful
ρ1511ζ13ζ138ζ132ζ139ζ133ζ1310ζ134ζ1311ζ135ζ1312ζ136ζ137ζ136ζ13ζ138ζ132ζ139ζ133ζ1310ζ134ζ1311ζ135ζ1312ζ137    linear of order 13
ρ161-1ζ13ζ138ζ132ζ139ζ133ζ1310ζ134ζ1311ζ135ζ1312ζ136ζ13713613138132139133131013413111351312137    linear of order 26 faithful
ρ1711ζ133ζ1311ζ136ζ13ζ139ζ134ζ1312ζ137ζ132ζ1310ζ135ζ138ζ135ζ133ζ1311ζ136ζ13ζ139ζ134ζ1312ζ137ζ132ζ1310ζ138    linear of order 13
ρ181-1ζ133ζ1311ζ136ζ13ζ139ζ134ζ1312ζ137ζ132ζ1310ζ135ζ13813513313111361313913413121371321310138    linear of order 26 faithful
ρ1911ζ135ζ13ζ1310ζ136ζ132ζ1311ζ137ζ133ζ1312ζ138ζ134ζ139ζ134ζ135ζ13ζ1310ζ136ζ132ζ1311ζ137ζ133ζ1312ζ138ζ139    linear of order 13
ρ201-1ζ135ζ13ζ1310ζ136ζ132ζ1311ζ137ζ133ζ1312ζ138ζ134ζ13913413513131013613213111371331312138139    linear of order 26 faithful
ρ2111ζ137ζ134ζ13ζ1311ζ138ζ135ζ132ζ1312ζ139ζ136ζ133ζ1310ζ133ζ137ζ134ζ13ζ1311ζ138ζ135ζ132ζ1312ζ139ζ136ζ1310    linear of order 13
ρ221-1ζ137ζ134ζ13ζ1311ζ138ζ135ζ132ζ1312ζ139ζ136ζ133ζ131013313713413131113813513213121391361310    linear of order 26 faithful
ρ2311ζ139ζ137ζ135ζ133ζ13ζ1312ζ1310ζ138ζ136ζ134ζ132ζ1311ζ132ζ139ζ137ζ135ζ133ζ13ζ1312ζ1310ζ138ζ136ζ134ζ1311    linear of order 13
ρ241-1ζ139ζ137ζ135ζ133ζ13ζ1312ζ1310ζ138ζ136ζ134ζ132ζ131113213913713513313131213101381361341311    linear of order 26 faithful
ρ2511ζ1311ζ1310ζ139ζ138ζ137ζ136ζ135ζ134ζ133ζ132ζ13ζ1312ζ13ζ1311ζ1310ζ139ζ138ζ137ζ136ζ135ζ134ζ133ζ132ζ1312    linear of order 13
ρ261-1ζ1311ζ1310ζ139ζ138ζ137ζ136ζ135ζ134ζ133ζ132ζ13ζ131213131113101391381371361351341331321312    linear of order 26 faithful

Permutation representations of C26
Regular action on 26 points - transitive group 26T1
Generators in S26
(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)

G:=sub<Sym(26)| (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)>;

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) );

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)])

G:=TransitiveGroup(26,1);

Matrix representation of C26 in GL1(𝔽53) generated by

4
G:=sub<GL(1,GF(53))| [4] >;

C26 in GAP, Magma, Sage, TeX

C_{26}
% in TeX

G:=Group("C26");
// GroupNames label

G:=SmallGroup(26,2);
// by ID

G=gap.SmallGroup(26,2);
# by ID

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

G:=Group<a|a^26=1>;
// generators/relations

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