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G = C24order 24 = 23·3

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C24, also denoted Z24, SmallGroup(24,2)

Series: Derived Chief Lower central Upper central

C1 — C24
C1C2C4C12 — C24
C1 — C24
C1 — C24

Generators and relations for C24
 G = < a | a24=1 >


Character table of C24

 class 123A3B4A4B6A6B8A8B8C8D12A12B12C12D24A24B24C24D24E24F24G24H
 size 111111111111111111111111
ρ1111111111111111111111111    trivial
ρ211111111-1-1-1-11111-1-1-1-1-1-1-1-1    linear of order 2
ρ31-111i-i-1-1ζ8ζ85ζ83ζ87i-ii-iζ87ζ85ζ83ζ87ζ8ζ85ζ83ζ8    linear of order 8
ρ41111-1-111ii-i-i-1-1-1-1-ii-i-iii-ii    linear of order 4
ρ51-111-ii-1-1ζ83ζ87ζ8ζ85-ii-iiζ85ζ87ζ8ζ85ζ83ζ87ζ8ζ83    linear of order 8
ρ61-111i-i-1-1ζ85ζ8ζ87ζ83i-ii-iζ83ζ8ζ87ζ83ζ85ζ8ζ87ζ85    linear of order 8
ρ71111-1-111-i-iii-1-1-1-1i-iii-i-ii-i    linear of order 4
ρ81-111-ii-1-1ζ87ζ83ζ85ζ8-ii-iiζ8ζ83ζ85ζ8ζ87ζ83ζ85ζ87    linear of order 8
ρ911ζ3ζ3211ζ3ζ321111ζ3ζ3ζ32ζ32ζ32ζ3ζ3ζ3ζ32ζ32ζ32ζ3    linear of order 3
ρ101-1ζ186ζ32ζ2ζ2ζ1815ζ6ζ8ζ85ζ83ζ87ζ82ζ3ζ86ζ3ζ82ζ32ζ86ζ32ζ87ζ32ζ85ζ3ζ83ζ3ζ87ζ3ζ8ζ32ζ85ζ32ζ83ζ32ζ8ζ3    linear of order 24 faithful
ρ1111ζ62ζ32-1-1ζ62ζ32ζ2ζ2ζ2ζ2ζ65ζ65ζ6ζ6ζ43ζ32ζ4ζ3ζ43ζ3ζ43ζ3ζ4ζ32ζ4ζ32ζ43ζ32ζ4ζ3    linear of order 12
ρ121-1ζ186ζ32ζ2ζ2ζ1815ζ6ζ83ζ87ζ8ζ85ζ86ζ3ζ82ζ3ζ86ζ32ζ82ζ32ζ85ζ32ζ87ζ3ζ8ζ3ζ85ζ3ζ83ζ32ζ87ζ32ζ8ζ32ζ83ζ3    linear of order 24 faithful
ρ1311ζ3ζ3211ζ3ζ32-1-1-1-1ζ3ζ3ζ32ζ32ζ6ζ65ζ65ζ65ζ6ζ6ζ6ζ65    linear of order 6
ρ141-1ζ186ζ32ζ2ζ2ζ1815ζ6ζ85ζ8ζ87ζ83ζ82ζ3ζ86ζ3ζ82ζ32ζ86ζ32ζ83ζ32ζ8ζ3ζ87ζ3ζ83ζ3ζ85ζ32ζ8ζ32ζ87ζ32ζ85ζ3    linear of order 24 faithful
ρ1511ζ62ζ32-1-1ζ62ζ32ζ2ζ2ζ2ζ2ζ65ζ65ζ6ζ6ζ4ζ32ζ43ζ3ζ4ζ3ζ4ζ3ζ43ζ32ζ43ζ32ζ4ζ32ζ43ζ3    linear of order 12
ρ161-1ζ186ζ32ζ2ζ2ζ1815ζ6ζ87ζ83ζ85ζ8ζ86ζ3ζ82ζ3ζ86ζ32ζ82ζ32ζ8ζ32ζ83ζ3ζ85ζ3ζ8ζ3ζ87ζ32ζ83ζ32ζ85ζ32ζ87ζ3    linear of order 24 faithful
ρ1711ζ32ζ311ζ32ζ31111ζ32ζ32ζ3ζ3ζ3ζ32ζ32ζ32ζ3ζ3ζ3ζ32    linear of order 3
ρ181-1ζ32ζ186ζ2ζ2ζ6ζ1815ζ8ζ85ζ83ζ87ζ82ζ32ζ86ζ32ζ82ζ3ζ86ζ3ζ87ζ3ζ85ζ32ζ83ζ32ζ87ζ32ζ8ζ3ζ85ζ3ζ83ζ3ζ8ζ32    linear of order 24 faithful
ρ1911ζ32ζ62-1-1ζ32ζ62ζ2ζ2ζ2ζ2ζ6ζ6ζ65ζ65ζ43ζ3ζ4ζ32ζ43ζ32ζ43ζ32ζ4ζ3ζ4ζ3ζ43ζ3ζ4ζ32    linear of order 12
ρ201-1ζ32ζ186ζ2ζ2ζ6ζ1815ζ83ζ87ζ8ζ85ζ86ζ32ζ82ζ32ζ86ζ3ζ82ζ3ζ85ζ3ζ87ζ32ζ8ζ32ζ85ζ32ζ83ζ3ζ87ζ3ζ8ζ3ζ83ζ32    linear of order 24 faithful
ρ2111ζ32ζ311ζ32ζ3-1-1-1-1ζ32ζ32ζ3ζ3ζ65ζ6ζ6ζ6ζ65ζ65ζ65ζ6    linear of order 6
ρ221-1ζ32ζ186ζ2ζ2ζ6ζ1815ζ85ζ8ζ87ζ83ζ82ζ32ζ86ζ32ζ82ζ3ζ86ζ3ζ83ζ3ζ8ζ32ζ87ζ32ζ83ζ32ζ85ζ3ζ8ζ3ζ87ζ3ζ85ζ32    linear of order 24 faithful
ρ2311ζ32ζ62-1-1ζ32ζ62ζ2ζ2ζ2ζ2ζ6ζ6ζ65ζ65ζ4ζ3ζ43ζ32ζ4ζ32ζ4ζ32ζ43ζ3ζ43ζ3ζ4ζ3ζ43ζ32    linear of order 12
ρ241-1ζ32ζ186ζ2ζ2ζ6ζ1815ζ87ζ83ζ85ζ8ζ86ζ32ζ82ζ32ζ86ζ3ζ82ζ3ζ8ζ3ζ83ζ32ζ85ζ32ζ8ζ32ζ87ζ3ζ83ζ3ζ85ζ3ζ87ζ32    linear of order 24 faithful

Permutation representations of C24
Regular action on 24 points - transitive group 24T1
Generators in S24
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24)

G:=sub<Sym(24)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24)>;

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) );

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)])

G:=TransitiveGroup(24,1);

Matrix representation of C24 in GL1(𝔽73) generated by

21
G:=sub<GL(1,GF(73))| [21] >;

C24 in GAP, Magma, Sage, TeX

C_{24}
% in TeX

G:=Group("C24");
// GroupNames label

G:=SmallGroup(24,2);
// by ID

G=gap.SmallGroup(24,2);
# by ID

G:=PCGroup([4,-2,-3,-2,-2,24,34]);
// Polycyclic

G:=Group<a|a^24=1>;
// generators/relations

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