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G = AGL2(𝔽3)  order 432 = 24·33

Affine linear group on 𝔽32

non-abelian, soluble

Aliases: AGL2(𝔽3), PSU3(𝔽2)⋊S3, ASL2(𝔽3)⋊C2, C32⋊GL2(𝔽3), C3⋊S3.S4, Aut(C3⋊S3), Hol(C32), SmallGroup(432,734)

Series: Derived Chief Lower central Upper central

C1C32C3⋊S3PSU3(𝔽2)ASL2(𝔽3) — AGL2(𝔽3)
C1C32C3⋊S3PSU3(𝔽2)ASL2(𝔽3) — AGL2(𝔽3)
ASL2(𝔽3) — AGL2(𝔽3)
C1

Generators and relations for AGL2(𝔽3)
 G = < a,b,c,d,e,f | a3=b3=c4=e3=f2=1, d2=c2, dbd-1=ebe-1=ab=ba, cac-1=b-1, dad-1=a-1b, ae=ea, af=fa, cbc-1=a, fbf=a-1b-1, dcd-1=ede-1=c-1, ece-1=c-1d, fcf=cd, fdf=c2d, fef=e-1 >

9C2
36C2
4C3
12C3
24C3
27C4
54C22
12S3
12S3
12S3
24S3
36S3
36C6
36C6
4C32
8C32
9Q8
27C8
27D4
36D6
36D6
4C3⋊S3
12C3×S3
12C3×S3
12C3×S3
24C3×S3
4He3
27SD16
9SL2(𝔽3)
3C32⋊C4
6S32
12S32
4C32⋊C6
4He3⋊C2
4C32⋊C6
9GL2(𝔽3)
3S3≀C2
3F9
4C32⋊D6
3AΓL1(𝔽9)

Character table of AGL2(𝔽3)

 class 12A2B3A3B3C46A6B8A8B
 size 1936824485472725454
ρ111111111111    trivial
ρ211-111111-1-1-1    linear of order 2
ρ32202-1-12-1000    orthogonal lifted from S3
ρ42-202-1-1010--2-2    complex lifted from GL2(𝔽3)
ρ52-202-1-1010-2--2    complex lifted from GL2(𝔽3)
ρ6331300-101-1-1    orthogonal lifted from S4
ρ733-1300-10-111    orthogonal lifted from S4
ρ84-404110-1000    orthogonal lifted from GL2(𝔽3)
ρ9802-12-100-100    orthogonal faithful
ρ1080-2-12-100100    orthogonal faithful
ρ111600-2-2100000    orthogonal faithful

Permutation representations of AGL2(𝔽3)
On 9 points: primitive, doubly transitive - transitive group 9T26
Generators in S9
(1 9 7)(2 6 5)(3 8 4)
(1 6 8)(2 3 7)(4 9 5)
(2 3 4 5)(6 7 8 9)
(2 9 4 7)(3 8 5 6)
(2 5 6)(3 8 4)
(2 4)(3 6)(5 8)

G:=sub<Sym(9)| (1,9,7)(2,6,5)(3,8,4), (1,6,8)(2,3,7)(4,9,5), (2,3,4,5)(6,7,8,9), (2,9,4,7)(3,8,5,6), (2,5,6)(3,8,4), (2,4)(3,6)(5,8)>;

G:=Group( (1,9,7)(2,6,5)(3,8,4), (1,6,8)(2,3,7)(4,9,5), (2,3,4,5)(6,7,8,9), (2,9,4,7)(3,8,5,6), (2,5,6)(3,8,4), (2,4)(3,6)(5,8) );

G=PermutationGroup([(1,9,7),(2,6,5),(3,8,4)], [(1,6,8),(2,3,7),(4,9,5)], [(2,3,4,5),(6,7,8,9)], [(2,9,4,7),(3,8,5,6)], [(2,5,6),(3,8,4)], [(2,4),(3,6),(5,8)])

G:=TransitiveGroup(9,26);

On 12 points - transitive group 12T157
Generators in S12
(1 10 12)(2 11 9)(4 8 6)
(1 12 10)(2 11 9)(3 5 7)
(1 2)(3 4)(5 6 7 8)(9 10 11 12)
(1 4)(2 3)(5 11 7 9)(6 10 8 12)
(1 4 2)(6 9 12)(8 11 10)
(1 4)(5 7)(6 12)(8 10)

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

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

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

G:=TransitiveGroup(12,157);

On 18 points - transitive group 18T157
Generators in S18
(1 17 15)(2 8 10)(3 6 7)(4 5 9)(11 12 18)(13 16 14)
(1 18 16)(2 9 7)(3 8 4)(5 6 10)(11 14 17)(12 13 15)
(3 4 5 6)(7 8 9 10)(11 12 13 14)(15 16 17 18)
(3 10 5 8)(4 9 6 7)(11 18 13 16)(12 17 14 15)
(3 6 7)(4 9 5)(11 18 12)(13 16 14)
(1 2)(3 12)(4 16)(5 14)(6 18)(7 11)(8 17)(9 13)(10 15)

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

G:=Group( (1,17,15)(2,8,10)(3,6,7)(4,5,9)(11,12,18)(13,16,14), (1,18,16)(2,9,7)(3,8,4)(5,6,10)(11,14,17)(12,13,15), (3,4,5,6)(7,8,9,10)(11,12,13,14)(15,16,17,18), (3,10,5,8)(4,9,6,7)(11,18,13,16)(12,17,14,15), (3,6,7)(4,9,5)(11,18,12)(13,16,14), (1,2)(3,12)(4,16)(5,14)(6,18)(7,11)(8,17)(9,13)(10,15) );

G=PermutationGroup([(1,17,15),(2,8,10),(3,6,7),(4,5,9),(11,12,18),(13,16,14)], [(1,18,16),(2,9,7),(3,8,4),(5,6,10),(11,14,17),(12,13,15)], [(3,4,5,6),(7,8,9,10),(11,12,13,14),(15,16,17,18)], [(3,10,5,8),(4,9,6,7),(11,18,13,16),(12,17,14,15)], [(3,6,7),(4,9,5),(11,18,12),(13,16,14)], [(1,2),(3,12),(4,16),(5,14),(6,18),(7,11),(8,17),(9,13),(10,15)])

G:=TransitiveGroup(18,157);

On 24 points - transitive group 24T1325
Generators in S24
(1 14 16)(2 13 15)(3 24 22)(4 21 23)(6 11 9)(8 20 18)
(1 14 16)(2 15 13)(3 22 24)(4 21 23)(5 12 10)(7 17 19)
(1 2)(3 4)(5 6)(7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)
(1 5)(2 6)(3 8)(4 7)(9 13 11 15)(10 16 12 14)(17 21 19 23)(18 24 20 22)
(1 2 6)(3 8 4)(9 16 15)(11 14 13)(18 23 22)(20 21 24)
(1 4)(2 8)(3 6)(5 7)(9 22)(10 17)(11 24)(12 19)(13 20)(14 21)(15 18)(16 23)

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

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

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

G:=TransitiveGroup(24,1325);

On 24 points - transitive group 24T1326
Generators in S24
(2 15 20)(4 18 13)(5 21 10)(6 22 11)(7 12 23)(8 9 24)
(1 19 14)(3 16 17)(5 10 21)(6 22 11)(7 23 12)(8 9 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)
(1 24 3 22)(2 23 4 21)(5 20 7 18)(6 19 8 17)(9 16 11 14)(10 15 12 13)
(2 22 21)(4 24 23)(5 20 6)(7 18 8)(9 12 13)(10 15 11)
(1 3)(2 21)(4 23)(5 20)(7 18)(10 15)(12 13)(14 16)(17 19)

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

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

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

G:=TransitiveGroup(24,1326);

On 24 points - transitive group 24T1327
Generators in S24
(2 15 20)(4 18 13)(5 21 10)(6 22 11)(7 12 23)(8 9 24)
(1 19 14)(3 16 17)(5 10 21)(6 22 11)(7 23 12)(8 9 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)
(1 24 3 22)(2 23 4 21)(5 20 7 18)(6 19 8 17)(9 16 11 14)(10 15 12 13)
(2 22 21)(4 24 23)(5 20 6)(7 18 8)(9 12 13)(10 15 11)
(2 23)(4 21)(5 13)(6 9)(7 15)(8 11)(10 18)(12 20)(14 19)(16 17)(22 24)

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

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

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

G:=TransitiveGroup(24,1327);

On 24 points - transitive group 24T1334
Generators in S24
(2 15 20)(4 18 13)(5 21 10)(6 22 11)(7 12 23)(8 9 24)
(1 19 14)(3 16 17)(5 10 21)(6 22 11)(7 23 12)(8 9 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)
(1 24 3 22)(2 23 4 21)(5 20 7 18)(6 19 8 17)(9 16 11 14)(10 15 12 13)
(1 14 19)(2 11 5)(3 16 17)(4 9 7)(6 21 15)(8 23 13)(10 20 22)(12 18 24)
(2 23)(4 21)(5 13)(6 9)(7 15)(8 11)(10 18)(12 20)(14 19)(16 17)(22 24)

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

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

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

G:=TransitiveGroup(24,1334);

On 27 points - transitive group 27T139
Generators in S27
(1 16 18)(2 23 21)(3 9 11)(4 8 5)(6 7 10)(12 13 17)(14 19 15)(20 25 26)(22 24 27)
(1 17 19)(2 20 22)(3 10 8)(4 11 7)(5 9 6)(12 15 16)(13 14 18)(21 26 27)(23 25 24)
(4 5 6 7)(8 9 10 11)(12 13 14 15)(16 17 18 19)(20 21 22 23)(24 25 26 27)
(4 8 6 10)(5 11 7 9)(12 17 14 19)(13 16 15 18)(20 27 22 25)(21 26 23 24)
(1 2 3)(4 19 24)(5 14 22)(6 17 26)(7 12 20)(8 15 27)(9 16 23)(10 13 25)(11 18 21)
(1 2)(4 10)(5 7)(6 8)(12 22)(13 24)(14 20)(15 26)(16 23)(17 27)(18 21)(19 25)

G:=sub<Sym(27)| (1,16,18)(2,23,21)(3,9,11)(4,8,5)(6,7,10)(12,13,17)(14,19,15)(20,25,26)(22,24,27), (1,17,19)(2,20,22)(3,10,8)(4,11,7)(5,9,6)(12,15,16)(13,14,18)(21,26,27)(23,25,24), (4,5,6,7)(8,9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27), (4,8,6,10)(5,11,7,9)(12,17,14,19)(13,16,15,18)(20,27,22,25)(21,26,23,24), (1,2,3)(4,19,24)(5,14,22)(6,17,26)(7,12,20)(8,15,27)(9,16,23)(10,13,25)(11,18,21), (1,2)(4,10)(5,7)(6,8)(12,22)(13,24)(14,20)(15,26)(16,23)(17,27)(18,21)(19,25)>;

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

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

G:=TransitiveGroup(27,139);

Polynomial with Galois group AGL2(𝔽3) over ℚ
actionf(x)Disc(f)
9T26x9-60x7-30x6+441x5+90x4-1116x3+180x2+972x-480220·315·54·114·134·7092
12T157x12-x11-53x10+53x9+847x8-482x7-5571x6+1485x5+16143x4-1208x3-17855x2-864x+2389212·116·1392·27774·629212·108496732

Matrix representation of AGL2(𝔽3) in GL8(ℤ)

-1-1-1-1-1-1-1-1
00000010
00000001
00100000
10000000
01000000
00000100
00010000
,
00000001
-1-1-1-1-1-1-1-1
00000010
01000000
00100000
10000000
00001000
00000100
,
10000000
00000010
00010000
01000000
00000001
00001000
00100000
-1-1-1-1-1-1-1-1
,
10000000
-1-1-1-1-1-1-1-1
00001000
00000100
01000000
00000010
00000001
00010000
,
10000000
00000100
00000001
00100000
00001000
00000010
01000000
00010000
,
10000000
00100000
01000000
00000100
00001000
00010000
00000001
00000010

G:=sub<GL(8,Integers())| [-1,0,0,0,1,0,0,0,-1,0,0,0,0,1,0,0,-1,0,0,1,0,0,0,0,-1,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,1,0,-1,1,0,0,0,0,0,0,-1,0,1,0,0,0,0,0],[0,-1,0,0,0,1,0,0,0,-1,0,1,0,0,0,0,0,-1,0,0,1,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,1,0,0,-1,0,0,0,0,0,1,0,-1,1,0,0,0,0,0,1,-1,0,0,0,0,0,0],[1,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,-1,0,0,0,0,0,0,1,-1,0,0,1,0,0,0,0,-1,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,-1,0,0,0,0,1,0,0,-1],[1,-1,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,1,0,-1,1,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,-1,0,0,0,1,0,0,0,-1,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;

AGL2(𝔽3) in GAP, Magma, Sage, TeX

{\rm AGL}_2({\mathbb F}_3)
% in TeX

G:=Group("AGL(2,3)");
// GroupNames label

G:=SmallGroup(432,734);
// by ID

G=gap.SmallGroup(432,734);
# by ID

G:=PCGroup([7,-2,-3,-2,2,-2,-3,3,57,632,387,100,1179,262,185,80,14117,6060,1699,1034,201,14118,8245,1588,223,622]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^3=b^3=c^4=e^3=f^2=1,d^2=c^2,d*b*d^-1=e*b*e^-1=a*b=b*a,c*a*c^-1=b^-1,d*a*d^-1=a^-1*b,a*e=e*a,a*f=f*a,c*b*c^-1=a,f*b*f=a^-1*b^-1,d*c*d^-1=e*d*e^-1=c^-1,e*c*e^-1=c^-1*d,f*c*f=c*d,f*d*f=c^2*d,f*e*f=e^-1>;
// generators/relations

Export

Subgroup lattice of AGL2(𝔽3) in TeX
Character table of AGL2(𝔽3) in TeX

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