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## G = C39⋊3C12order 468 = 22·32·13

### 1st semidirect product of C39 and C12 acting via C12/C2=C6

Aliases: C393C12, C78.1C6, Dic39⋊C3, C6.(C13⋊C6), C26.(C3×S3), C3⋊(C26.C6), C2.(D39⋊C3), C13⋊C32Dic3, C132(C3×Dic3), (C3×C13⋊C3)⋊3C4, (C2×C13⋊C3).S3, (C6×C13⋊C3).1C2, SmallGroup(468,21)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C39 — C39⋊3C12
 Chief series C1 — C13 — C39 — C78 — C6×C13⋊C3 — C39⋊3C12
 Lower central C39 — C39⋊3C12
 Upper central C1 — C2

Generators and relations for C393C12
G = < a,b | a39=b12=1, bab-1=a17 >

Character table of C393C12

 class 1 2 3A 3B 3C 3D 3E 4A 4B 6A 6B 6C 6D 6E 12A 12B 12C 12D 13A 13B 26A 26B 39A 39B 39C 39D 78A 78B 78C 78D size 1 1 2 13 13 26 26 39 39 2 13 13 26 26 39 39 39 39 6 6 6 6 6 6 6 6 6 6 6 6 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 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 1 1 1 linear of order 2 ρ3 1 1 1 ζ32 ζ3 ζ32 ζ3 -1 -1 1 ζ3 ζ32 ζ32 ζ3 ζ65 ζ6 ζ65 ζ6 1 1 1 1 1 1 1 1 1 1 1 1 linear of order 6 ρ4 1 1 1 ζ32 ζ3 ζ32 ζ3 1 1 1 ζ3 ζ32 ζ32 ζ3 ζ3 ζ32 ζ3 ζ32 1 1 1 1 1 1 1 1 1 1 1 1 linear of order 3 ρ5 1 1 1 ζ3 ζ32 ζ3 ζ32 -1 -1 1 ζ32 ζ3 ζ3 ζ32 ζ6 ζ65 ζ6 ζ65 1 1 1 1 1 1 1 1 1 1 1 1 linear of order 6 ρ6 1 1 1 ζ3 ζ32 ζ3 ζ32 1 1 1 ζ32 ζ3 ζ3 ζ32 ζ32 ζ3 ζ32 ζ3 1 1 1 1 1 1 1 1 1 1 1 1 linear of order 3 ρ7 1 -1 1 1 1 1 1 i -i -1 -1 -1 -1 -1 i i -i -i 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 linear of order 4 ρ8 1 -1 1 1 1 1 1 -i i -1 -1 -1 -1 -1 -i -i i i 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 linear of order 4 ρ9 1 -1 1 ζ32 ζ3 ζ32 ζ3 -i i -1 ζ65 ζ6 ζ6 ζ65 ζ43ζ3 ζ43ζ32 ζ4ζ3 ζ4ζ32 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 linear of order 12 ρ10 1 -1 1 ζ32 ζ3 ζ32 ζ3 i -i -1 ζ65 ζ6 ζ6 ζ65 ζ4ζ3 ζ4ζ32 ζ43ζ3 ζ43ζ32 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 linear of order 12 ρ11 1 -1 1 ζ3 ζ32 ζ3 ζ32 -i i -1 ζ6 ζ65 ζ65 ζ6 ζ43ζ32 ζ43ζ3 ζ4ζ32 ζ4ζ3 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 linear of order 12 ρ12 1 -1 1 ζ3 ζ32 ζ3 ζ32 i -i -1 ζ6 ζ65 ζ65 ζ6 ζ4ζ32 ζ4ζ3 ζ43ζ32 ζ43ζ3 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 linear of order 12 ρ13 2 2 -1 2 2 -1 -1 0 0 -1 2 2 -1 -1 0 0 0 0 2 2 2 2 -1 -1 -1 -1 -1 -1 -1 -1 orthogonal lifted from S3 ρ14 2 -2 -1 2 2 -1 -1 0 0 1 -2 -2 1 1 0 0 0 0 2 2 -2 -2 -1 -1 -1 -1 1 1 1 1 symplectic lifted from Dic3, Schur index 2 ρ15 2 -2 -1 -1-√-3 -1+√-3 ζ6 ζ65 0 0 1 1-√-3 1+√-3 ζ32 ζ3 0 0 0 0 2 2 -2 -2 -1 -1 -1 -1 1 1 1 1 complex lifted from C3×Dic3 ρ16 2 2 -1 -1+√-3 -1-√-3 ζ65 ζ6 0 0 -1 -1-√-3 -1+√-3 ζ65 ζ6 0 0 0 0 2 2 2 2 -1 -1 -1 -1 -1 -1 -1 -1 complex lifted from C3×S3 ρ17 2 -2 -1 -1+√-3 -1-√-3 ζ65 ζ6 0 0 1 1+√-3 1-√-3 ζ3 ζ32 0 0 0 0 2 2 -2 -2 -1 -1 -1 -1 1 1 1 1 complex lifted from C3×Dic3 ρ18 2 2 -1 -1-√-3 -1+√-3 ζ6 ζ65 0 0 -1 -1+√-3 -1-√-3 ζ6 ζ65 0 0 0 0 2 2 2 2 -1 -1 -1 -1 -1 -1 -1 -1 complex lifted from C3×S3 ρ19 6 6 6 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 -1+√13/2 -1-√13/2 -1+√13/2 -1-√13/2 -1+√13/2 -1-√13/2 -1+√13/2 -1-√13/2 -1+√13/2 -1-√13/2 -1+√13/2 -1-√13/2 orthogonal lifted from C13⋊C6 ρ20 6 6 -3 0 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 -1+√13/2 -1-√13/2 -1+√13/2 -1-√13/2 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 orthogonal lifted from D39⋊C3 ρ21 6 6 6 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 -1-√13/2 -1+√13/2 -1-√13/2 -1+√13/2 -1-√13/2 -1+√13/2 -1-√13/2 -1+√13/2 -1-√13/2 -1+√13/2 -1-√13/2 -1+√13/2 orthogonal lifted from C13⋊C6 ρ22 6 6 -3 0 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 -1-√13/2 -1+√13/2 -1-√13/2 -1+√13/2 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 orthogonal lifted from D39⋊C3 ρ23 6 6 -3 0 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 -1-√13/2 -1+√13/2 -1-√13/2 -1+√13/2 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 orthogonal lifted from D39⋊C3 ρ24 6 6 -3 0 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 -1+√13/2 -1-√13/2 -1+√13/2 -1-√13/2 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 orthogonal lifted from D39⋊C3 ρ25 6 -6 -3 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 -1+√13/2 -1-√13/2 1-√13/2 1+√13/2 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13+ζ139+ζ133+ζ13 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132+ζ1311+ζ138+ζ137 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13+ζ1312+ζ1310+ζ134 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132+ζ136+ζ135+ζ132 symplectic faithful, Schur index 2 ρ26 6 -6 6 0 0 0 0 0 0 -6 0 0 0 0 0 0 0 0 -1-√13/2 -1+√13/2 1+√13/2 1-√13/2 -1-√13/2 -1+√13/2 -1-√13/2 -1+√13/2 1+√13/2 1-√13/2 1+√13/2 1-√13/2 symplectic lifted from C26.C6, Schur index 2 ρ27 6 -6 6 0 0 0 0 0 0 -6 0 0 0 0 0 0 0 0 -1+√13/2 -1-√13/2 1-√13/2 1+√13/2 -1+√13/2 -1-√13/2 -1+√13/2 -1-√13/2 1-√13/2 1+√13/2 1-√13/2 1+√13/2 symplectic lifted from C26.C6, Schur index 2 ρ28 6 -6 -3 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 -1+√13/2 -1-√13/2 1-√13/2 1+√13/2 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13+ζ1312+ζ1310+ζ134 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132+ζ136+ζ135+ζ132 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13+ζ139+ζ133+ζ13 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132+ζ1311+ζ138+ζ137 symplectic faithful, Schur index 2 ρ29 6 -6 -3 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 -1-√13/2 -1+√13/2 1+√13/2 1-√13/2 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132+ζ136+ζ135+ζ132 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13+ζ139+ζ133+ζ13 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132+ζ1311+ζ138+ζ137 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13+ζ1312+ζ1310+ζ134 symplectic faithful, Schur index 2 ρ30 6 -6 -3 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 -1-√13/2 -1+√13/2 1+√13/2 1-√13/2 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132+ζ1311+ζ138+ζ137 ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13+ζ1312+ζ1310+ζ134 -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132+ζ136+ζ135+ζ132 -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13+ζ139+ζ133+ζ13 symplectic faithful, Schur index 2

Smallest permutation representation of C393C12
On 156 points
Generators in S156
```(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 32 33 34 35 36 37 38 39)(40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78)(79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117)(118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156)
(1 133 52 96)(2 156 74 95 17 150 53 80 23 132 68 113)(3 140 57 94 33 128 54 103 6 131 45 91)(4 124 40 93 10 145 55 87 28 130 61 108)(5 147 62 92 26 123 56 110 11 129 77 86)(7 154 67 90 19 118 58 117 16 127 70 81)(8 138 50 89 35 135 59 101 38 126 47 98)(9 122 72 88 12 152 60 85 21 125 63 115)(13 136 43 84 37 142 64 99 31 121 49 105)(14 120 65 83)(15 143 48 82 30 137 66 106 36 119 42 100)(18 134 75 79 39 149 69 97 24 155 51 112)(20 141 41 116 32 144 71 104 29 153 44 107)(22 148 46 114 25 139 73 111 34 151 76 102)(27 146 78 109)```

`G:=sub<Sym(156)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39)(40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117)(118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156), (1,133,52,96)(2,156,74,95,17,150,53,80,23,132,68,113)(3,140,57,94,33,128,54,103,6,131,45,91)(4,124,40,93,10,145,55,87,28,130,61,108)(5,147,62,92,26,123,56,110,11,129,77,86)(7,154,67,90,19,118,58,117,16,127,70,81)(8,138,50,89,35,135,59,101,38,126,47,98)(9,122,72,88,12,152,60,85,21,125,63,115)(13,136,43,84,37,142,64,99,31,121,49,105)(14,120,65,83)(15,143,48,82,30,137,66,106,36,119,42,100)(18,134,75,79,39,149,69,97,24,155,51,112)(20,141,41,116,32,144,71,104,29,153,44,107)(22,148,46,114,25,139,73,111,34,151,76,102)(27,146,78,109)>;`

`G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39)(40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117)(118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156), (1,133,52,96)(2,156,74,95,17,150,53,80,23,132,68,113)(3,140,57,94,33,128,54,103,6,131,45,91)(4,124,40,93,10,145,55,87,28,130,61,108)(5,147,62,92,26,123,56,110,11,129,77,86)(7,154,67,90,19,118,58,117,16,127,70,81)(8,138,50,89,35,135,59,101,38,126,47,98)(9,122,72,88,12,152,60,85,21,125,63,115)(13,136,43,84,37,142,64,99,31,121,49,105)(14,120,65,83)(15,143,48,82,30,137,66,106,36,119,42,100)(18,134,75,79,39,149,69,97,24,155,51,112)(20,141,41,116,32,144,71,104,29,153,44,107)(22,148,46,114,25,139,73,111,34,151,76,102)(27,146,78,109) );`

`G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39),(40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78),(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117),(118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156)], [(1,133,52,96),(2,156,74,95,17,150,53,80,23,132,68,113),(3,140,57,94,33,128,54,103,6,131,45,91),(4,124,40,93,10,145,55,87,28,130,61,108),(5,147,62,92,26,123,56,110,11,129,77,86),(7,154,67,90,19,118,58,117,16,127,70,81),(8,138,50,89,35,135,59,101,38,126,47,98),(9,122,72,88,12,152,60,85,21,125,63,115),(13,136,43,84,37,142,64,99,31,121,49,105),(14,120,65,83),(15,143,48,82,30,137,66,106,36,119,42,100),(18,134,75,79,39,149,69,97,24,155,51,112),(20,141,41,116,32,144,71,104,29,153,44,107),(22,148,46,114,25,139,73,111,34,151,76,102),(27,146,78,109)])`

Matrix representation of C393C12 in GL8(𝔽157)

 130 52 0 0 0 0 0 0 68 26 0 0 0 0 0 0 0 0 70 138 69 69 138 70 0 0 87 20 155 89 86 88 0 0 69 69 1 68 70 68 0 0 89 155 90 155 89 156 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
,
 50 99 0 0 0 0 0 0 0 107 0 0 0 0 0 0 0 0 10 148 113 35 69 35 0 0 113 35 34 79 88 35 0 0 146 73 8 40 154 92 0 0 96 93 150 49 140 147 0 0 44 122 44 19 44 44 0 0 36 30 149 19 55 11

`G:=sub<GL(8,GF(157))| [130,68,0,0,0,0,0,0,52,26,0,0,0,0,0,0,0,0,70,87,69,89,1,0,0,0,138,20,69,155,0,1,0,0,69,155,1,90,0,0,0,0,69,89,68,155,0,0,0,0,138,86,70,89,0,0,0,0,70,88,68,156,0,0],[50,0,0,0,0,0,0,0,99,107,0,0,0,0,0,0,0,0,10,113,146,96,44,36,0,0,148,35,73,93,122,30,0,0,113,34,8,150,44,149,0,0,35,79,40,49,19,19,0,0,69,88,154,140,44,55,0,0,35,35,92,147,44,11] >;`

C393C12 in GAP, Magma, Sage, TeX

`C_{39}\rtimes_3C_{12}`
`% in TeX`

`G:=Group("C39:3C12");`
`// GroupNames label`

`G:=SmallGroup(468,21);`
`// by ID`

`G=gap.SmallGroup(468,21);`
`# by ID`

`G:=PCGroup([5,-2,-3,-2,-3,-13,30,483,10804,1359]);`
`// Polycyclic`

`G:=Group<a,b|a^39=b^12=1,b*a*b^-1=a^17>;`
`// generators/relations`

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