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G = C2×C8order 16 = 24

Abelian group of type [2,8]

direct product, p-group, abelian, monomial

Aliases: C2×C8, SmallGroup(16,5)

Series: Derived Chief Lower central Upper central Jennings

C1 — C2×C8
C1C2C4C2×C4 — C2×C8
C1 — C2×C8
C1 — C2×C8
C1C2C2C4 — C2×C8

Generators and relations for C2×C8
 G = < a,b | a2=b8=1, ab=ba >


Character table of C2×C8

 class 12A2B2C4A4B4C4D8A8B8C8D8E8F8G8H
 size 1111111111111111
ρ11111111111111111    trivial
ρ211-1-11-11-1-1-11-11-111    linear of order 2
ρ311111111-1-1-1-1-1-1-1-1    linear of order 2
ρ411-1-11-11-111-11-11-1-1    linear of order 2
ρ51-11-1ii-i-iζ87ζ8ζ85ζ85ζ83ζ83ζ87ζ8    linear of order 8
ρ61-1-11i-i-iiζ83ζ85ζ85ζ8ζ83ζ87ζ87ζ8    linear of order 8
ρ71-11-1-i-iiiζ85ζ83ζ87ζ87ζ8ζ8ζ85ζ83    linear of order 8
ρ81-1-11-iii-iζ8ζ87ζ87ζ83ζ8ζ85ζ85ζ83    linear of order 8
ρ91111-1-1-1-1-iiii-i-i-ii    linear of order 4
ρ1011-1-1-11-11i-ii-i-ii-ii    linear of order 4
ρ111-11-1ii-i-iζ83ζ85ζ8ζ8ζ87ζ87ζ83ζ85    linear of order 8
ρ121-1-11i-i-iiζ87ζ8ζ8ζ85ζ87ζ83ζ83ζ85    linear of order 8
ρ131111-1-1-1-1i-i-i-iiii-i    linear of order 4
ρ1411-1-1-11-11-ii-iii-ii-i    linear of order 4
ρ151-11-1-i-iiiζ8ζ87ζ83ζ83ζ85ζ85ζ8ζ87    linear of order 8
ρ161-1-11-iii-iζ85ζ83ζ83ζ87ζ85ζ8ζ8ζ87    linear of order 8

Permutation representations of C2×C8
Regular action on 16 points - transitive group 16T5
Generators in S16
(1 11)(2 12)(3 13)(4 14)(5 15)(6 16)(7 9)(8 10)
(1 2 3 4 5 6 7 8)(9 10 11 12 13 14 15 16)

G:=sub<Sym(16)| (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,9)(8,10), (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16)>;

G:=Group( (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,9)(8,10), (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16) );

G=PermutationGroup([(1,11),(2,12),(3,13),(4,14),(5,15),(6,16),(7,9),(8,10)], [(1,2,3,4,5,6,7,8),(9,10,11,12,13,14,15,16)])

G:=TransitiveGroup(16,5);

Polynomial with Galois group C2×C8 over ℚ
actionf(x)Disc(f)
16T5x16+1264

Matrix representation of C2×C8 in GL2(𝔽17) generated by

160
016
,
10
09
G:=sub<GL(2,GF(17))| [16,0,0,16],[1,0,0,9] >;

C2×C8 in GAP, Magma, Sage, TeX

C_2\times C_8
% in TeX

G:=Group("C2xC8");
// GroupNames label

G:=SmallGroup(16,5);
// by ID

G=gap.SmallGroup(16,5);
# by ID

G:=PCGroup([4,-2,2,-2,-2,16,34]);
// Polycyclic

G:=Group<a,b|a^2=b^8=1,a*b=b*a>;
// generators/relations

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