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G = C31⋊C3order 93 = 3·31

The semidirect product of C31 and C3 acting faithfully

metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary

Aliases: C31⋊C3, SmallGroup(93,1)

Series: Derived Chief Lower central Upper central

C1C31 — C31⋊C3
C1C31 — C31⋊C3
C31 — C31⋊C3
C1

Generators and relations for C31⋊C3
 G = < a,b | a31=b3=1, bab-1=a5 >

31C3

Character table of C31⋊C3

 class 13A3B31A31B31C31D31E31F31G31H31I31J
 size 131313333333333
ρ11111111111111    trivial
ρ21ζ32ζ31111111111    linear of order 3
ρ31ζ3ζ321111111111    linear of order 3
ρ4300ζ312931213112ζ312831183116ζ312731243111ζ312531531ζ31153113313ζ312331223117ζ31193110312ζ31303126316ζ3120317314ζ3114319318    complex faithful
ρ5300ζ31303126316ζ3114319318ζ312931213112ζ312831183116ζ312331223117ζ312731243111ζ312531531ζ31153113313ζ31193110312ζ3120317314    complex faithful
ρ6300ζ3114319318ζ312931213112ζ312831183116ζ312731243111ζ31193110312ζ312531531ζ312331223117ζ3120317314ζ31153113313ζ31303126316    complex faithful
ρ7300ζ3120317314ζ31303126316ζ3114319318ζ312931213112ζ312531531ζ312831183116ζ312731243111ζ31193110312ζ312331223117ζ31153113313    complex faithful
ρ8300ζ312531531ζ312331223117ζ31193110312ζ31153113313ζ3114319318ζ3120317314ζ31303126316ζ312831183116ζ312931213112ζ312731243111    complex faithful
ρ9300ζ312331223117ζ31193110312ζ31153113313ζ3120317314ζ312931213112ζ31303126316ζ3114319318ζ312731243111ζ312831183116ζ312531531    complex faithful
ρ10300ζ31193110312ζ31153113313ζ3120317314ζ31303126316ζ312831183116ζ3114319318ζ312931213112ζ312531531ζ312731243111ζ312331223117    complex faithful
ρ11300ζ31153113313ζ3120317314ζ31303126316ζ3114319318ζ312731243111ζ312931213112ζ312831183116ζ312331223117ζ312531531ζ31193110312    complex faithful
ρ12300ζ312831183116ζ312731243111ζ312531531ζ312331223117ζ3120317314ζ31193110312ζ31153113313ζ3114319318ζ31303126316ζ312931213112    complex faithful
ρ13300ζ312731243111ζ312531531ζ312331223117ζ31193110312ζ31303126316ζ31153113313ζ3120317314ζ312931213112ζ3114319318ζ312831183116    complex faithful

Permutation representations of C31⋊C3
On 31 points: primitive - transitive group 31T3
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 26 6)(3 20 11)(4 14 16)(5 8 21)(7 27 31)(9 15 10)(12 28 25)(13 22 30)(17 29 19)(18 23 24)

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

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

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

G:=TransitiveGroup(31,3);

C31⋊C3 is a maximal subgroup of   C31⋊C6  C31⋊A4  C31⋊C15
C31⋊C3 is a maximal quotient of   C31⋊C9  C31⋊A4

Matrix representation of C31⋊C3 in GL3(𝔽5) generated by

302
404
311
,
100
004
014
G:=sub<GL(3,GF(5))| [3,4,3,0,0,1,2,4,1],[1,0,0,0,0,1,0,4,4] >;

C31⋊C3 in GAP, Magma, Sage, TeX

C_{31}\rtimes C_3
% in TeX

G:=Group("C31:C3");
// GroupNames label

G:=SmallGroup(93,1);
// by ID

G=gap.SmallGroup(93,1);
# by ID

G:=PCGroup([2,-3,-31,301]);
// Polycyclic

G:=Group<a,b|a^31=b^3=1,b*a*b^-1=a^5>;
// generators/relations

Export

Subgroup lattice of C31⋊C3 in TeX
Character table of C31⋊C3 in TeX

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