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G = C42order 16 = 24

Abelian group of type [4,4]

direct product, p-group, abelian, monomial

Aliases: C42, SmallGroup(16,2)

Series: Derived Chief Lower central Upper central Jennings

C1 — C42
C1C2C22C2×C4 — C42
C1 — C42
C1 — C42
C1C22 — C42

Generators and relations for C42
 G = < a,b | a4=b4=1, ab=ba >


Character table of C42

 class 12A2B2C4A4B4C4D4E4F4G4H4I4J4K4L
 size 1111111111111111
ρ11111111111111111    trivial
ρ21111-1-1-1111-1-1-1-1-11    linear of order 2
ρ31111-11-1-1-1-1111-1-1-1    linear of order 2
ρ411111-11-1-1-1-1-1-111-1    linear of order 2
ρ511-1-1-iii1-1-1i-i-ii-i1    linear of order 4
ρ611-1-1i-i-i1-1-1-iii-ii1    linear of order 4
ρ71-1-11-1i-1-i-ii-i-ii11i    linear of order 4
ρ81-1-111-i1-i-iiii-i-1-1i    linear of order 4
ρ91-11-1-i1i-ii-i-11-1-iii    linear of order 4
ρ1011-1-1ii-i-111i-i-i-ii-1    linear of order 4
ρ111-11-1i-1-i-ii-i1-11i-ii    linear of order 4
ρ1211-1-1-i-ii-111-iiii-i-1    linear of order 4
ρ131-11-1i1-ii-ii-11-1i-i-i    linear of order 4
ρ141-1-111i1ii-i-i-ii-1-1-i    linear of order 4
ρ151-11-1-i-1ii-ii1-11-ii-i    linear of order 4
ρ161-1-11-1-i-1ii-iii-i11-i    linear of order 4

Permutation representations of C42
Regular action on 16 points - transitive group 16T4
Generators in S16
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)
(1 10 15 7)(2 11 16 8)(3 12 13 5)(4 9 14 6)

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

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

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

G:=TransitiveGroup(16,4);

Matrix representation of C42 in GL2(𝔽5) generated by

40
03
,
30
02
G:=sub<GL(2,GF(5))| [4,0,0,3],[3,0,0,2] >;

C42 in GAP, Magma, Sage, TeX

C_4^2
% in TeX

G:=Group("C4^2");
// GroupNames label

G:=SmallGroup(16,2);
// by ID

G=gap.SmallGroup(16,2);
# by ID

G:=PCGroup([4,-2,2,-2,2,16,37]);
// Polycyclic

G:=Group<a,b|a^4=b^4=1,a*b=b*a>;
// generators/relations

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