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G = C31⋊C5order 155 = 5·31

The semidirect product of C31 and C5 acting faithfully

metacyclic, supersoluble, monomial, Z-group, 5-hyperelementary

Aliases: C31⋊C5, SmallGroup(155,1)

Series: Derived Chief Lower central Upper central

C1C31 — C31⋊C5
C1C31 — C31⋊C5
C31 — C31⋊C5
C1

Generators and relations for C31⋊C5
 G = < a,b | a31=b5=1, bab-1=a2 >

31C5

Character table of C31⋊C5

 class 15A5B5C5D31A31B31C31D31E31F
 size 131313131555555
ρ111111111111    trivial
ρ21ζ53ζ54ζ5ζ52111111    linear of order 5
ρ31ζ5ζ53ζ52ζ54111111    linear of order 5
ρ41ζ52ζ5ζ54ζ53111111    linear of order 5
ρ51ζ54ζ52ζ53ζ5111111    linear of order 5
ρ650000ζ31263122312131133111ζ31303129312731233115ζ311631831431231ζ312431173112316313ζ312031183110319315ζ3128312531193114317    complex faithful
ρ750000ζ31303129312731233115ζ312431173112316313ζ3128312531193114317ζ31263122312131133111ζ311631831431231ζ312031183110319315    complex faithful
ρ850000ζ3128312531193114317ζ312031183110319315ζ31263122312131133111ζ311631831431231ζ312431173112316313ζ31303129312731233115    complex faithful
ρ950000ζ312031183110319315ζ311631831431231ζ31303129312731233115ζ3128312531193114317ζ31263122312131133111ζ312431173112316313    complex faithful
ρ1050000ζ311631831431231ζ3128312531193114317ζ312431173112316313ζ312031183110319315ζ31303129312731233115ζ31263122312131133111    complex faithful
ρ1150000ζ312431173112316313ζ31263122312131133111ζ312031183110319315ζ31303129312731233115ζ3128312531193114317ζ311631831431231    complex faithful

Permutation representations of C31⋊C5
On 31 points: primitive - transitive group 31T4
Generators in S31
(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)
(2 17 9 5 3)(4 18 25 13 7)(6 19 10 21 11)(8 20 26 29 15)(12 22 27 14 23)(16 24 28 30 31)

G:=sub<Sym(31)| (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), (2,17,9,5,3)(4,18,25,13,7)(6,19,10,21,11)(8,20,26,29,15)(12,22,27,14,23)(16,24,28,30,31)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31), (2,17,9,5,3)(4,18,25,13,7)(6,19,10,21,11)(8,20,26,29,15)(12,22,27,14,23)(16,24,28,30,31) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)], [(2,17,9,5,3),(4,18,25,13,7),(6,19,10,21,11),(8,20,26,29,15),(12,22,27,14,23),(16,24,28,30,31)])

G:=TransitiveGroup(31,4);

C31⋊C5 is a maximal subgroup of   C31⋊C10  C31⋊C15

Matrix representation of C31⋊C5 in GL5(𝔽2)

00100
00111
00001
11000
01000
,
10010
00100
00010
01001
00011

G:=sub<GL(5,GF(2))| [0,0,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,0,0,0,1,1,0,0],[1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,1] >;

C31⋊C5 in GAP, Magma, Sage, TeX

C_{31}\rtimes C_5
% in TeX

G:=Group("C31:C5");
// GroupNames label

G:=SmallGroup(155,1);
// by ID

G=gap.SmallGroup(155,1);
# by ID

G:=PCGroup([2,-5,-31,321]);
// Polycyclic

G:=Group<a,b|a^31=b^5=1,b*a*b^-1=a^2>;
// generators/relations

Export

Subgroup lattice of C31⋊C5 in TeX
Character table of C31⋊C5 in TeX

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