C3xAGammaL(1,9) - GroupNames

G = C₃xAΓL₁(F₉) order 432 = 2⁴·3³

Direct product of C₃ and AΓL₁(F₉)

direct product, non-abelian, soluble, monomial

Aliases: C₃xAΓL₁(F₉), F₉:C₆, C₃³:₁SD₁₆, PSU₃(F₂):₂C₆, S₃wrC₂.C₆, (C₃xF₉):₃C₂, C₃²:(C₃xSD₁₆), (C₃xPSU₃(F₂)):₃C₂, C₃:S₃.(C₃xD₄), C₃²:C₄.(C₂xC₆), (C₃xC₃:S₃).₁D₄, (C₃xS₃wrC₂).₂C₂, (C₃xC₃²:C₄).₆C₂², SmallGroup(432,737)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₃² — C₃²:C₄ — C₃xAΓL₁(F₉)

Chief series

C₁ — C₃² — C₃:S₃ — C₃²:C₄ — C₃xC₃²:C₄ — C₃xF₉ — C₃xAΓL₁(F₉)

Lower central

C₃² — C₃:S₃ — C₃²:C₄ — C₃xAΓL₁(F₉)

Upper central

C₁ — C₃

Generators and relations for C₃xAΓL₁(F₉)
G = < a,b,c,d,e | a³=b³=c³=d⁸=e²=1, ab=ba, ac=ca, ad=da, ae=ea, dbd^-1=bc=cb, ebe=b^-1c, dcd^-1=b, ce=ec, ede=d³ >

Subgroups: 372 in 54 conjugacy classes, 16 normal (all characteristic)
Quotients: C₁, C₂, C₃, C₂², C₆, D₄, C₂xC₆, SD₁₆, C₃xD₄, C₃xSD₁₆, AΓL₁(F₉), C₃xAΓL₁(F₉)

C₁

₉C₂

₁₂C₂

C₃

₄C₃

₈C₃

₉C₄

₁₈C₄

₁₈C₂²

₄S₃

₉C₆

₁₂C₆

₁₂S₃

₂₄C₆

C₃²

₄C₃²

₈C₃²

₉C₈

₉Q₈

₉D₄

₉C₁₂

₁₂D₆

₁₈C₁₂

₁₈C₂xC₆

C₃:S₃

₄C₃xS₃

₈C₃xS₃

₁₂C₃xS₃

₁₂C₃xC₆

C₃³

₉SD₁₆

₉C₃xQ₈

₉C₃xD₄

₉C₂₄

C₃²:C₄

₂C₃²:C₄

₂S₃²

₁₂S₃xC₆

C₃xC₃:S₃

₄S₃xC₃²

₉C₃xSD₁₆

PSU₃(F₂)

S₃wrC₂

F₉

C₃xC₃²:C₄

₂C₃xS₃²

₂C₃xC₃²:C₄

AΓL₁(F₉)

C₃xPSU₃(F₂)

C₃xS₃wrC₂

C₃xF₉

C₃xAΓL₁(F₉)

Character table of C₃xAΓL₁(F₉)

class	1	2A	2B	3A	3B	3C	3D	3E	4A	4B	6A	6B	6C	6D	6E	6F	6G	8A	8B	12A	12B	12C	12D	24A	24B	24C	24D
size	1	9	12	1	1	8	8	8	18	36	9	9	12	12	24	24	24	18	18	18	18	36	36	18	18	18	18
ρ₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	trivial
ρ₂	1	1	-1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	linear of order 2
ρ₃	1	1	1	1	1	1	1	1	1	-1	1	1	1	1	1	1	1	-1	-1	1	1	-1	-1	-1	-1	-1	-1	linear of order 2
ρ₄	1	1	-1	1	1	1	1	1	1	-1	1	1	-1	-1	-1	-1	-1	1	1	1	1	-1	-1	1	1	1	1	linear of order 2
ρ₅	1	1	1	ζ₃	ζ₃²	1	ζ₃²	ζ₃	1	-1	ζ₃²	ζ₃	ζ₃²	ζ₃	1	ζ₃	ζ₃²	-1	-1	ζ₃	ζ₃²	ζ₆⁵	ζ₆	ζ₆⁵	ζ₆	ζ₆	ζ₆⁵	linear of order 6
ρ₆	1	1	1	ζ₃	ζ₃²	1	ζ₃²	ζ₃	1	1	ζ₃²	ζ₃	ζ₃²	ζ₃	1	ζ₃	ζ₃²	1	1	ζ₃	ζ₃²	ζ₃	ζ₃²	ζ₃	ζ₃²	ζ₃²	ζ₃	linear of order 3
ρ₇	1	1	1	ζ₃²	ζ₃	1	ζ₃	ζ₃²	1	1	ζ₃	ζ₃²	ζ₃	ζ₃²	1	ζ₃²	ζ₃	1	1	ζ₃²	ζ₃	ζ₃²	ζ₃	ζ₃²	ζ₃	ζ₃	ζ₃²	linear of order 3
ρ₈	1	1	-1	ζ₃²	ζ₃	1	ζ₃	ζ₃²	1	-1	ζ₃	ζ₃²	ζ₆⁵	ζ₆	-1	ζ₆	ζ₆⁵	1	1	ζ₃²	ζ₃	ζ₆	ζ₆⁵	ζ₃²	ζ₃	ζ₃	ζ₃²	linear of order 6
ρ₉	1	1	-1	ζ₃	ζ₃²	1	ζ₃²	ζ₃	1	1	ζ₃²	ζ₃	ζ₆	ζ₆⁵	-1	ζ₆⁵	ζ₆	-1	-1	ζ₃	ζ₃²	ζ₃	ζ₃²	ζ₆⁵	ζ₆	ζ₆	ζ₆⁵	linear of order 6
ρ₁₀	1	1	-1	ζ₃²	ζ₃	1	ζ₃	ζ₃²	1	1	ζ₃	ζ₃²	ζ₆⁵	ζ₆	-1	ζ₆	ζ₆⁵	-1	-1	ζ₃²	ζ₃	ζ₃²	ζ₃	ζ₆	ζ₆⁵	ζ₆⁵	ζ₆	linear of order 6
ρ₁₁	1	1	1	ζ₃²	ζ₃	1	ζ₃	ζ₃²	1	-1	ζ₃	ζ₃²	ζ₃	ζ₃²	1	ζ₃²	ζ₃	-1	-1	ζ₃²	ζ₃	ζ₆	ζ₆⁵	ζ₆	ζ₆⁵	ζ₆⁵	ζ₆	linear of order 6
ρ₁₂	1	1	-1	ζ₃	ζ₃²	1	ζ₃²	ζ₃	1	-1	ζ₃²	ζ₃	ζ₆	ζ₆⁵	-1	ζ₆⁵	ζ₆	1	1	ζ₃	ζ₃²	ζ₆⁵	ζ₆	ζ₃	ζ₃²	ζ₃²	ζ₃	linear of order 6
ρ₁₃	2	2	0	2	2	2	2	2	-2	0	2	2	0	0	0	0	0	0	0	-2	-2	0	0	0	0	0	0	orthogonal lifted from D₄
ρ₁₄	2	2	0	-1-√-3	-1+√-3	2	-1+√-3	-1-√-3	-2	0	-1+√-3	-1-√-3	0	0	0	0	0	0	0	1+√-3	1-√-3	0	0	0	0	0	0	complex lifted from C₃xD₄
ρ₁₅	2	2	0	-1+√-3	-1-√-3	2	-1-√-3	-1+√-3	-2	0	-1-√-3	-1+√-3	0	0	0	0	0	0	0	1-√-3	1+√-3	0	0	0	0	0	0	complex lifted from C₃xD₄
ρ₁₆	2	-2	0	2	2	2	2	2	0	0	-2	-2	0	0	0	0	0	-√-2	√-2	0	0	0	0	√-2	-√-2	√-2	-√-2	complex lifted from SD₁₆
ρ₁₇	2	-2	0	2	2	2	2	2	0	0	-2	-2	0	0	0	0	0	√-2	-√-2	0	0	0	0	-√-2	√-2	-√-2	√-2	complex lifted from SD₁₆
ρ₁₈	2	-2	0	-1+√-3	-1-√-3	2	-1-√-3	-1+√-3	0	0	1+√-3	1-√-3	0	0	0	0	0	√-2	-√-2	0	0	0	0	ζ₈⁷ζ₃+ζ₈⁵ζ₃	ζ₈³ζ₃²+ζ₈ζ₃²	ζ₈⁷ζ₃²+ζ₈⁵ζ₃²	ζ₈³ζ₃+ζ₈ζ₃	complex lifted from C₃xSD₁₆
ρ₁₉	2	-2	0	-1-√-3	-1+√-3	2	-1+√-3	-1-√-3	0	0	1-√-3	1+√-3	0	0	0	0	0	-√-2	√-2	0	0	0	0	ζ₈³ζ₃²+ζ₈ζ₃²	ζ₈⁷ζ₃+ζ₈⁵ζ₃	ζ₈³ζ₃+ζ₈ζ₃	ζ₈⁷ζ₃²+ζ₈⁵ζ₃²	complex lifted from C₃xSD₁₆
ρ₂₀	2	-2	0	-1+√-3	-1-√-3	2	-1-√-3	-1+√-3	0	0	1+√-3	1-√-3	0	0	0	0	0	-√-2	√-2	0	0	0	0	ζ₈³ζ₃+ζ₈ζ₃	ζ₈⁷ζ₃²+ζ₈⁵ζ₃²	ζ₈³ζ₃²+ζ₈ζ₃²	ζ₈⁷ζ₃+ζ₈⁵ζ₃	complex lifted from C₃xSD₁₆
ρ₂₁	2	-2	0	-1-√-3	-1+√-3	2	-1+√-3	-1-√-3	0	0	1-√-3	1+√-3	0	0	0	0	0	√-2	-√-2	0	0	0	0	ζ₈⁷ζ₃²+ζ₈⁵ζ₃²	ζ₈³ζ₃+ζ₈ζ₃	ζ₈⁷ζ₃+ζ₈⁵ζ₃	ζ₈³ζ₃²+ζ₈ζ₃²	complex lifted from C₃xSD₁₆
ρ₂₂	8	0	-2	8	8	-1	-1	-1	0	0	0	0	-2	-2	1	1	1	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from AΓL₁(F₉)
ρ₂₃	8	0	2	8	8	-1	-1	-1	0	0	0	0	2	2	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from AΓL₁(F₉)
ρ₂₄	8	0	-2	-4+4√-3	-4-4√-3	-1	ζ₆	ζ₆⁵	0	0	0	0	1+√-3	1-√-3	1	ζ₃	ζ₃²	0	0	0	0	0	0	0	0	0	0	complex faithful
ρ₂₅	8	0	-2	-4-4√-3	-4+4√-3	-1	ζ₆⁵	ζ₆	0	0	0	0	1-√-3	1+√-3	1	ζ₃²	ζ₃	0	0	0	0	0	0	0	0	0	0	complex faithful
ρ₂₆	8	0	2	-4+4√-3	-4-4√-3	-1	ζ₆	ζ₆⁵	0	0	0	0	-1-√-3	-1+√-3	-1	ζ₆⁵	ζ₆	0	0	0	0	0	0	0	0	0	0	complex faithful
ρ₂₇	8	0	2	-4-4√-3	-4+4√-3	-1	ζ₆⁵	ζ₆	0	0	0	0	-1+√-3	-1-√-3	-1	ζ₆	ζ₆⁵	0	0	0	0	0	0	0	0	0	0	complex faithful

Permutation representations of C₃xAΓL₁(F₉)
►On 24 points - transitive group 24T1330

Generators in S₂₄

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

(1 9 21)(3 11 23)(4 12 24)(5 17 13)(7 19 15)(8 20 16)

(1 21 9)(2 10 22)(4 12 24)(5 13 17)(6 18 14)(8 20 16)

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

(2 4)(3 7)(6 8)(10 12)(11 15)(14 16)(18 20)(19 23)(22 24)

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

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

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

G:=TransitiveGroup(24,1330);

►On 27 points - transitive group 27T142

Generators in S₂₇

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

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

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

(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 6)(5 9)(8 10)(12 16)(13 19)(15 17)(20 22)(21 25)(24 26)

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

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

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

G:=TransitiveGroup(27,142);

Matrix representation of C₃xAΓL₁(F₉) ►in GL₈(F₇₃)

64	0	0	0	0	0	0	0
0	64	0	0	0	0	0	0
0	0	64	0	0	0	0	0
0	0	0	64	0	0	0	0
0	0	0	0	64	0	0	0
0	0	0	0	0	64	0	0
0	0	0	0	0	0	64	0
0	0	0	0	0	0	0	64

64	0	0	0	0	0	0	0
0	8	0	0	0	0	0	0
0	0	8	0	0	0	0	0
0	0	0	64	0	0	0	0
0	0	0	0	8	0	0	0
0	0	0	0	0	64	0	0
0	0	0	0	0	0	1	0
0	0	0	0	0	0	0	1

8	0	0	0	0	0	0	0
0	64	0	0	0	0	0	0
0	0	1	0	0	0	0	0
0	0	0	1	0	0	0	0
0	0	0	0	8	0	0	0
0	0	0	0	0	64	0	0
0	0	0	0	0	0	8	0
0	0	0	0	0	0	0	64

0	0	0	0	1	0	0	0
0	0	0	0	0	1	0	0
0	0	0	0	0	0	1	0
0	0	0	0	0	0	0	1
0	0	1	0	0	0	0	0
0	0	0	1	0	0	0	0
0	1	0	0	0	0	0	0
1	0	0	0	0	0	0	0

1	0	0	0	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	0	0	1
0	0	0	0	1	0	0	0
0	0	0	0	0	1	0	0

G:=sub<GL(8,GF(73))| [64,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,64],[64,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[8,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,64],[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0] >;

C₃xAΓL₁(F₉) in GAP, Magma, Sage, TeX

C_3\times {\rm AGammaL}_1({\mathbb F}_9)

% in TeX

G:=Group("C3xAGammaL(1,9)");

// GroupNames label

G:=SmallGroup(432,737);

// by ID

G=gap.SmallGroup(432,737);

# by ID

G:=PCGroup([7,-2,-2,-3,-2,-2,-3,3,84,533,514,80,6053,7068,1202,201,16470,7069,1595,622]);

// Polycyclic

G:=Group<a,b,c,d,e|a^3=b^3=c^3=d^8=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,d*b*d^-1=b*c=c*b,e*b*e=b^-1*c,d*c*d^-1=b,c*e=e*c,e*d*e=d^3>;

// generators/relations

Export

Subgroup lattice of C₃xAΓL₁(F₉) in TeX
Character table of C₃xAΓL₁(F₉) in TeX

64	0	0	0	0	0	0	0
0	64	0	0	0	0	0	0
0	0	64	0	0	0	0	0
0	0	0	64	0	0	0	0
0	0	0	0	64	0	0	0
0	0	0	0	0	64	0	0
0	0	0	0	0	0	64	0
0	0	0	0	0	0	0	64

64	0	0	0	0	0	0	0
0	8	0	0	0	0	0	0
0	0	8	0	0	0	0	0
0	0	0	64	0	0	0	0
0	0	0	0	8	0	0	0
0	0	0	0	0	64	0	0
0	0	0	0	0	0	1	0
0	0	0	0	0	0	0	1

8	0	0	0	0	0	0	0
0	64	0	0	0	0	0	0
0	0	1	0	0	0	0	0
0	0	0	1	0	0	0	0
0	0	0	0	8	0	0	0
0	0	0	0	0	64	0	0
0	0	0	0	0	0	8	0
0	0	0	0	0	0	0	64

0	0	0	0	1	0	0	0
0	0	0	0	0	1	0	0
0	0	0	0	0	0	1	0
0	0	0	0	0	0	0	1
0	0	1	0	0	0	0	0
0	0	0	1	0	0	0	0
0	1	0	0	0	0	0	0
1	0	0	0	0	0	0	0

1	0	0	0	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	0	0	1
0	0	0	0	1	0	0	0
0	0	0	0	0	1	0	0

64	0	0	0	0	0	0	0
0	64	0	0	0	0	0	0
0	0	64	0	0	0	0	0
0	0	0	64	0	0	0	0
0	0	0	0	64	0	0	0
0	0	0	0	0	64	0	0
0	0	0	0	0	0	64	0
0	0	0	0	0	0	0	64

64	0	0	0	0	0	0	0
0	8	0	0	0	0	0	0
0	0	8	0	0	0	0	0
0	0	0	64	0	0	0	0
0	0	0	0	8	0	0	0
0	0	0	0	0	64	0	0
0	0	0	0	0	0	1	0
0	0	0	0	0	0	0	1

8	0	0	0	0	0	0	0
0	64	0	0	0	0	0	0
0	0	1	0	0	0	0	0
0	0	0	1	0	0	0	0
0	0	0	0	8	0	0	0
0	0	0	0	0	64	0	0
0	0	0	0	0	0	8	0
0	0	0	0	0	0	0	64

0	0	0	0	1	0	0	0
0	0	0	0	0	1	0	0
0	0	0	0	0	0	1	0
0	0	0	0	0	0	0	1
0	0	1	0	0	0	0	0
0	0	0	1	0	0	0	0
0	1	0	0	0	0	0	0
1	0	0	0	0	0	0	0

1	0	0	0	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	0	0	1
0	0	0	0	1	0	0	0
0	0	0	0	0	1	0	0

G = C3xAΓL1(F9) order 432 = 24·33

Direct product of C3 and AΓL1(F9)

G = C₃xAΓL₁(F₉) order 432 = 2⁴·3³

Direct product of C₃ and AΓL₁(F₉)

64	0	0	0	0	0	0	0
0	64	0	0	0	0	0	0
0	0	64	0	0	0	0	0
0	0	0	64	0	0	0	0
0	0	0	0	64	0	0	0
0	0	0	0	0	64	0	0
0	0	0	0	0	0	64	0
0	0	0	0	0	0	0	64

64	0	0	0	0	0	0	0
0	8	0	0	0	0	0	0
0	0	8	0	0	0	0	0
0	0	0	64	0	0	0	0
0	0	0	0	8	0	0	0
0	0	0	0	0	64	0	0
0	0	0	0	0	0	1	0
0	0	0	0	0	0	0	1

8	0	0	0	0	0	0	0
0	64	0	0	0	0	0	0
0	0	1	0	0	0	0	0
0	0	0	1	0	0	0	0
0	0	0	0	8	0	0	0
0	0	0	0	0	64	0	0
0	0	0	0	0	0	8	0
0	0	0	0	0	0	0	64

0	0	0	0	1	0	0	0
0	0	0	0	0	1	0	0
0	0	0	0	0	0	1	0
0	0	0	0	0	0	0	1
0	0	1	0	0	0	0	0
0	0	0	1	0	0	0	0
0	1	0	0	0	0	0	0
1	0	0	0	0	0	0	0

1	0	0	0	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	0	0	1
0	0	0	0	1	0	0	0
0	0	0	0	0	1	0	0