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G = D5×C13⋊C3  order 390 = 2·3·5·13

Direct product of D5 and C13⋊C3

direct product, metacyclic, supersoluble, monomial, Z-group

Aliases: D5×C13⋊C3, C65⋊3C6, (D5×C13)⋊C3, C13⋊2(C3×D5), C5⋊(C2×C13⋊C3), (C5×C13⋊C3)⋊3C2, SmallGroup(390,2)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C65 — D5×C13⋊C3
Chief series
C1 — C13 — C65 — C5×C13⋊C3 — D5×C13⋊C3
Lower central
C65 — D5×C13⋊C3
Upper central
C1

Generators and relations for D5×C13⋊C3
 G = < a,b,c,d | a5=b2=c13=d3=1, bab=a-1, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c9 >

C1
5C2
13C3
C5
C13
65C6
D5
13C15
5C26
C13⋊C3
C65
13C3×D5
5C2×C13⋊C3
D5×C13
C5×C13⋊C3
D5×C13⋊C3

Character table of D5×C13⋊C3

 class 123A3B5A5B6A6B13A13B13C13D15A15B15C15D26A26B26C26D65A65B65C65D65E65F65G65H
 size 1513132265653333262626261515151566666666
ρ11111111111111111111111111111    trivial
ρ21-11111-1-111111111-1-1-1-111111111    linear of order 2
ρ311ζ32ζ311ζ3ζ321111ζ3ζ32ζ3ζ32111111111111    linear of order 3
ρ411ζ3ζ3211ζ32ζ31111ζ32ζ3ζ32ζ3111111111111    linear of order 3
ρ51-1ζ32ζ311ζ65ζ61111ζ3ζ32ζ3ζ32-1-1-1-111111111    linear of order 6
ρ61-1ζ3ζ3211ζ6ζ651111ζ32ζ3ζ32ζ3-1-1-1-111111111    linear of order 6
ρ72022-1-√5/2-1+√5/2002222-1-√5/2-1+√5/2-1+√5/2-1-√5/20000-1+√5/2-1-√5/2-1-√5/2-1-√5/2-1-√5/2-1+√5/2-1+√5/2-1+√5/2    orthogonal lifted from D5
ρ82022-1+√5/2-1-√5/2002222-1+√5/2-1-√5/2-1-√5/2-1+√5/20000-1-√5/2-1+√5/2-1+√5/2-1+√5/2-1+√5/2-1-√5/2-1-√5/2-1-√5/2    orthogonal lifted from D5
ρ920-1+√-3-1-√-3-1-√5/2-1+√5/2002222ζ32ζ53+ζ32ζ52ζ3ζ54+ζ3ζ5ζ32ζ54+ζ32ζ5ζ3ζ53+ζ3ζ520000-1+√5/2-1-√5/2-1-√5/2-1-√5/2-1-√5/2-1+√5/2-1+√5/2-1+√5/2    complex lifted from C3×D5
ρ1020-1-√-3-1+√-3-1+√5/2-1-√5/2002222ζ3ζ54+ζ3ζ5ζ32ζ53+ζ32ζ52ζ3ζ53+ζ3ζ52ζ32ζ54+ζ32ζ50000-1-√5/2-1+√5/2-1+√5/2-1+√5/2-1+√5/2-1-√5/2-1-√5/2-1-√5/2    complex lifted from C3×D5
ρ1120-1+√-3-1-√-3-1+√5/2-1-√5/2002222ζ32ζ54+ζ32ζ5ζ3ζ53+ζ3ζ52ζ32ζ53+ζ32ζ52ζ3ζ54+ζ3ζ50000-1-√5/2-1+√5/2-1+√5/2-1+√5/2-1+√5/2-1-√5/2-1-√5/2-1-√5/2    complex lifted from C3×D5
ρ1220-1-√-3-1+√-3-1-√5/2-1+√5/2002222ζ3ζ53+ζ3ζ52ζ32ζ54+ζ32ζ5ζ3ζ54+ζ3ζ5ζ32ζ53+ζ32ζ520000-1+√5/2-1-√5/2-1-√5/2-1-√5/2-1-√5/2-1+√5/2-1+√5/2-1+√5/2    complex lifted from C3×D5
ρ1333003300ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ1370000ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1312+ζ1310+ζ134ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ136+ζ135+ζ132    complex lifted from C13⋊C3
ρ1433003300ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ136+ζ135+ζ1320000ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ139+ζ133+ζ13ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137    complex lifted from C13⋊C3
ρ153-3003300ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ139+ζ133+ζ130000-ζ139-ζ133-ζ13-ζ136-ζ135-ζ132-ζ1312-ζ1310-ζ134-ζ1311-ζ138-ζ137ζ1311+ζ138+ζ137ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134    complex lifted from C2×C13⋊C3
ρ163-3003300ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ1370000-ζ1311-ζ138-ζ137-ζ139-ζ133-ζ13-ζ136-ζ135-ζ132-ζ1312-ζ1310-ζ134ζ1312+ζ1310+ζ134ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ136+ζ135+ζ132    complex lifted from C2×C13⋊C3
ρ1733003300ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ1312+ζ1310+ζ1340000ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ136+ζ135+ζ132ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ139+ζ133+ζ13    complex lifted from C13⋊C3
ρ183-3003300ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ1312+ζ1310+ζ1340000-ζ1312-ζ1310-ζ134-ζ1311-ζ138-ζ137-ζ139-ζ133-ζ13-ζ136-ζ135-ζ132ζ136+ζ135+ζ132ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ139+ζ133+ζ13    complex lifted from C2×C13⋊C3
ρ1933003300ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ139+ζ133+ζ130000ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ1311+ζ138+ζ137ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134    complex lifted from C13⋊C3
ρ203-3003300ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ136+ζ135+ζ1320000-ζ136-ζ135-ζ132-ζ1312-ζ1310-ζ134-ζ1311-ζ138-ζ137-ζ139-ζ133-ζ13ζ139+ζ133+ζ13ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137ζ139+ζ133+ζ13ζ136+ζ135+ζ132ζ136+ζ135+ζ132ζ1312+ζ1310+ζ134ζ1311+ζ138+ζ137    complex lifted from C2×C13⋊C3
ρ216000-3-3√5/2-3+3√5/2002ζ139+2ζ133+2ζ132ζ136+2ζ135+2ζ1322ζ1312+2ζ1310+2ζ1342ζ1311+2ζ138+2ζ13700000000ζ54ζ1312+ζ54ζ1310+ζ54ζ134+ζ5ζ1312+ζ5ζ1310+ζ5ζ134ζ53ζ139+ζ53ζ133+ζ53ζ13+ζ52ζ139+ζ52ζ133+ζ52ζ13ζ53ζ136+ζ53ζ135+ζ53ζ132+ζ52ζ136+ζ52ζ135+ζ52ζ132ζ53ζ1312+ζ53ζ1310+ζ53ζ134+ζ52ζ1312+ζ52ζ1310+ζ52ζ134ζ53ζ1311+ζ53ζ138+ζ53ζ137+ζ52ζ1311+ζ52ζ138+ζ52ζ137ζ54ζ1311+ζ54ζ138+ζ54ζ137+ζ5ζ1311+ζ5ζ138+ζ5ζ137ζ54ζ139+ζ54ζ133+ζ54ζ13+ζ5ζ139+ζ5ζ133+ζ5ζ13ζ54ζ136+ζ54ζ135+ζ54ζ132+ζ5ζ136+ζ5ζ135+ζ5ζ132    complex faithful
ρ226000-3+3√5/2-3-3√5/2002ζ139+2ζ133+2ζ132ζ136+2ζ135+2ζ1322ζ1312+2ζ1310+2ζ1342ζ1311+2ζ138+2ζ13700000000ζ53ζ1312+ζ53ζ1310+ζ53ζ134+ζ52ζ1312+ζ52ζ1310+ζ52ζ134ζ54ζ139+ζ54ζ133+ζ54ζ13+ζ5ζ139+ζ5ζ133+ζ5ζ13ζ54ζ136+ζ54ζ135+ζ54ζ132+ζ5ζ136+ζ5ζ135+ζ5ζ132ζ54ζ1312+ζ54ζ1310+ζ54ζ134+ζ5ζ1312+ζ5ζ1310+ζ5ζ134ζ54ζ1311+ζ54ζ138+ζ54ζ137+ζ5ζ1311+ζ5ζ138+ζ5ζ137ζ53ζ1311+ζ53ζ138+ζ53ζ137+ζ52ζ1311+ζ52ζ138+ζ52ζ137ζ53ζ139+ζ53ζ133+ζ53ζ13+ζ52ζ139+ζ52ζ133+ζ52ζ13ζ53ζ136+ζ53ζ135+ζ53ζ132+ζ52ζ136+ζ52ζ135+ζ52ζ132    complex faithful
ρ236000-3+3√5/2-3-3√5/2002ζ136+2ζ135+2ζ1322ζ1312+2ζ1310+2ζ1342ζ1311+2ζ138+2ζ1372ζ139+2ζ133+2ζ1300000000ζ53ζ1311+ζ53ζ138+ζ53ζ137+ζ52ζ1311+ζ52ζ138+ζ52ζ137ζ54ζ136+ζ54ζ135+ζ54ζ132+ζ5ζ136+ζ5ζ135+ζ5ζ132ζ54ζ1312+ζ54ζ1310+ζ54ζ134+ζ5ζ1312+ζ5ζ1310+ζ5ζ134ζ54ζ1311+ζ54ζ138+ζ54ζ137+ζ5ζ1311+ζ5ζ138+ζ5ζ137ζ54ζ139+ζ54ζ133+ζ54ζ13+ζ5ζ139+ζ5ζ133+ζ5ζ13ζ53ζ139+ζ53ζ133+ζ53ζ13+ζ52ζ139+ζ52ζ133+ζ52ζ13ζ53ζ136+ζ53ζ135+ζ53ζ132+ζ52ζ136+ζ52ζ135+ζ52ζ132ζ53ζ1312+ζ53ζ1310+ζ53ζ134+ζ52ζ1312+ζ52ζ1310+ζ52ζ134    complex faithful
ρ246000-3-3√5/2-3+3√5/2002ζ1311+2ζ138+2ζ1372ζ139+2ζ133+2ζ132ζ136+2ζ135+2ζ1322ζ1312+2ζ1310+2ζ13400000000ζ54ζ136+ζ54ζ135+ζ54ζ132+ζ5ζ136+ζ5ζ135+ζ5ζ132ζ53ζ1311+ζ53ζ138+ζ53ζ137+ζ52ζ1311+ζ52ζ138+ζ52ζ137ζ53ζ139+ζ53ζ133+ζ53ζ13+ζ52ζ139+ζ52ζ133+ζ52ζ13ζ53ζ136+ζ53ζ135+ζ53ζ132+ζ52ζ136+ζ52ζ135+ζ52ζ132ζ53ζ1312+ζ53ζ1310+ζ53ζ134+ζ52ζ1312+ζ52ζ1310+ζ52ζ134ζ54ζ1312+ζ54ζ1310+ζ54ζ134+ζ5ζ1312+ζ5ζ1310+ζ5ζ134ζ54ζ1311+ζ54ζ138+ζ54ζ137+ζ5ζ1311+ζ5ζ138+ζ5ζ137ζ54ζ139+ζ54ζ133+ζ54ζ13+ζ5ζ139+ζ5ζ133+ζ5ζ13    complex faithful
ρ256000-3+3√5/2-3-3√5/2002ζ1311+2ζ138+2ζ1372ζ139+2ζ133+2ζ132ζ136+2ζ135+2ζ1322ζ1312+2ζ1310+2ζ13400000000ζ53ζ136+ζ53ζ135+ζ53ζ132+ζ52ζ136+ζ52ζ135+ζ52ζ132ζ54ζ1311+ζ54ζ138+ζ54ζ137+ζ5ζ1311+ζ5ζ138+ζ5ζ137ζ54ζ139+ζ54ζ133+ζ54ζ13+ζ5ζ139+ζ5ζ133+ζ5ζ13ζ54ζ136+ζ54ζ135+ζ54ζ132+ζ5ζ136+ζ5ζ135+ζ5ζ132ζ54ζ1312+ζ54ζ1310+ζ54ζ134+ζ5ζ1312+ζ5ζ1310+ζ5ζ134ζ53ζ1312+ζ53ζ1310+ζ53ζ134+ζ52ζ1312+ζ52ζ1310+ζ52ζ134ζ53ζ1311+ζ53ζ138+ζ53ζ137+ζ52ζ1311+ζ52ζ138+ζ52ζ137ζ53ζ139+ζ53ζ133+ζ53ζ13+ζ52ζ139+ζ52ζ133+ζ52ζ13    complex faithful
ρ266000-3+3√5/2-3-3√5/2002ζ1312+2ζ1310+2ζ1342ζ1311+2ζ138+2ζ1372ζ139+2ζ133+2ζ132ζ136+2ζ135+2ζ13200000000ζ53ζ139+ζ53ζ133+ζ53ζ13+ζ52ζ139+ζ52ζ133+ζ52ζ13ζ54ζ1312+ζ54ζ1310+ζ54ζ134+ζ5ζ1312+ζ5ζ1310+ζ5ζ134ζ54ζ1311+ζ54ζ138+ζ54ζ137+ζ5ζ1311+ζ5ζ138+ζ5ζ137ζ54ζ139+ζ54ζ133+ζ54ζ13+ζ5ζ139+ζ5ζ133+ζ5ζ13ζ54ζ136+ζ54ζ135+ζ54ζ132+ζ5ζ136+ζ5ζ135+ζ5ζ132ζ53ζ136+ζ53ζ135+ζ53ζ132+ζ52ζ136+ζ52ζ135+ζ52ζ132ζ53ζ1312+ζ53ζ1310+ζ53ζ134+ζ52ζ1312+ζ52ζ1310+ζ52ζ134ζ53ζ1311+ζ53ζ138+ζ53ζ137+ζ52ζ1311+ζ52ζ138+ζ52ζ137    complex faithful
ρ276000-3-3√5/2-3+3√5/2002ζ136+2ζ135+2ζ1322ζ1312+2ζ1310+2ζ1342ζ1311+2ζ138+2ζ1372ζ139+2ζ133+2ζ1300000000ζ54ζ1311+ζ54ζ138+ζ54ζ137+ζ5ζ1311+ζ5ζ138+ζ5ζ137ζ53ζ136+ζ53ζ135+ζ53ζ132+ζ52ζ136+ζ52ζ135+ζ52ζ132ζ53ζ1312+ζ53ζ1310+ζ53ζ134+ζ52ζ1312+ζ52ζ1310+ζ52ζ134ζ53ζ1311+ζ53ζ138+ζ53ζ137+ζ52ζ1311+ζ52ζ138+ζ52ζ137ζ53ζ139+ζ53ζ133+ζ53ζ13+ζ52ζ139+ζ52ζ133+ζ52ζ13ζ54ζ139+ζ54ζ133+ζ54ζ13+ζ5ζ139+ζ5ζ133+ζ5ζ13ζ54ζ136+ζ54ζ135+ζ54ζ132+ζ5ζ136+ζ5ζ135+ζ5ζ132ζ54ζ1312+ζ54ζ1310+ζ54ζ134+ζ5ζ1312+ζ5ζ1310+ζ5ζ134    complex faithful
ρ286000-3-3√5/2-3+3√5/2002ζ1312+2ζ1310+2ζ1342ζ1311+2ζ138+2ζ1372ζ139+2ζ133+2ζ132ζ136+2ζ135+2ζ13200000000ζ54ζ139+ζ54ζ133+ζ54ζ13+ζ5ζ139+ζ5ζ133+ζ5ζ13ζ53ζ1312+ζ53ζ1310+ζ53ζ134+ζ52ζ1312+ζ52ζ1310+ζ52ζ134ζ53ζ1311+ζ53ζ138+ζ53ζ137+ζ52ζ1311+ζ52ζ138+ζ52ζ137ζ53ζ139+ζ53ζ133+ζ53ζ13+ζ52ζ139+ζ52ζ133+ζ52ζ13ζ53ζ136+ζ53ζ135+ζ53ζ132+ζ52ζ136+ζ52ζ135+ζ52ζ132ζ54ζ136+ζ54ζ135+ζ54ζ132+ζ5ζ136+ζ5ζ135+ζ5ζ132ζ54ζ1312+ζ54ζ1310+ζ54ζ134+ζ5ζ1312+ζ5ζ1310+ζ5ζ134ζ54ζ1311+ζ54ζ138+ζ54ζ137+ζ5ζ1311+ζ5ζ138+ζ5ζ137    complex faithful

Smallest permutation representation of D5×C13⋊C3
►On 65 points
Generators in S65
(1 53 40 27 14)(2 54 41 28 15)(3 55 42 29 16)(4 56 43 30 17)(5 57 44 31 18)(6 58 45 32 19)(7 59 46 33 20)(8 60 47 34 21)(9 61 48 35 22)(10 62 49 36 23)(11 63 50 37 24)(12 64 51 38 25)(13 65 52 39 26)

(1 14)(2 15)(3 16)(4 17)(5 18)(6 19)(7 20)(8 21)(9 22)(10 23)(11 24)(12 25)(13 26)(27 53)(28 54)(29 55)(30 56)(31 57)(32 58)(33 59)(34 60)(35 61)(36 62)(37 63)(38 64)(39 65)

(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)

(2 4 10)(3 7 6)(5 13 11)(8 9 12)(15 17 23)(16 20 19)(18 26 24)(21 22 25)(28 30 36)(29 33 32)(31 39 37)(34 35 38)(41 43 49)(42 46 45)(44 52 50)(47 48 51)(54 56 62)(55 59 58)(57 65 63)(60 61 64)
 
G:=sub<Sym(65)| (1,53,40,27,14)(2,54,41,28,15)(3,55,42,29,16)(4,56,43,30,17)(5,57,44,31,18)(6,58,45,32,19)(7,59,46,33,20)(8,60,47,34,21)(9,61,48,35,22)(10,62,49,36,23)(11,63,50,37,24)(12,64,51,38,25)(13,65,52,39,26), (1,14)(2,15)(3,16)(4,17)(5,18)(6,19)(7,20)(8,21)(9,22)(10,23)(11,24)(12,25)(13,26)(27,53)(28,54)(29,55)(30,56)(31,57)(32,58)(33,59)(34,60)(35,61)(36,62)(37,63)(38,64)(39,65), (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), (2,4,10)(3,7,6)(5,13,11)(8,9,12)(15,17,23)(16,20,19)(18,26,24)(21,22,25)(28,30,36)(29,33,32)(31,39,37)(34,35,38)(41,43,49)(42,46,45)(44,52,50)(47,48,51)(54,56,62)(55,59,58)(57,65,63)(60,61,64)>;
 
G:=Group( (1,53,40,27,14)(2,54,41,28,15)(3,55,42,29,16)(4,56,43,30,17)(5,57,44,31,18)(6,58,45,32,19)(7,59,46,33,20)(8,60,47,34,21)(9,61,48,35,22)(10,62,49,36,23)(11,63,50,37,24)(12,64,51,38,25)(13,65,52,39,26), (1,14)(2,15)(3,16)(4,17)(5,18)(6,19)(7,20)(8,21)(9,22)(10,23)(11,24)(12,25)(13,26)(27,53)(28,54)(29,55)(30,56)(31,57)(32,58)(33,59)(34,60)(35,61)(36,62)(37,63)(38,64)(39,65), (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), (2,4,10)(3,7,6)(5,13,11)(8,9,12)(15,17,23)(16,20,19)(18,26,24)(21,22,25)(28,30,36)(29,33,32)(31,39,37)(34,35,38)(41,43,49)(42,46,45)(44,52,50)(47,48,51)(54,56,62)(55,59,58)(57,65,63)(60,61,64) );
 
G=PermutationGroup([[(1,53,40,27,14),(2,54,41,28,15),(3,55,42,29,16),(4,56,43,30,17),(5,57,44,31,18),(6,58,45,32,19),(7,59,46,33,20),(8,60,47,34,21),(9,61,48,35,22),(10,62,49,36,23),(11,63,50,37,24),(12,64,51,38,25),(13,65,52,39,26)], [(1,14),(2,15),(3,16),(4,17),(5,18),(6,19),(7,20),(8,21),(9,22),(10,23),(11,24),(12,25),(13,26),(27,53),(28,54),(29,55),(30,56),(31,57),(32,58),(33,59),(34,60),(35,61),(36,62),(37,63),(38,64),(39,65)], [(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)], [(2,4,10),(3,7,6),(5,13,11),(8,9,12),(15,17,23),(16,20,19),(18,26,24),(21,22,25),(28,30,36),(29,33,32),(31,39,37),(34,35,38),(41,43,49),(42,46,45),(44,52,50),(47,48,51),(54,56,62),(55,59,58),(57,65,63),(60,61,64)]])
 

Matrix representation of D5×C13⋊C3 ►in GL5(𝔽1171)

1247000
1015112000
00100
00010
00001
,
1247000
01170000
00100
00010
00001
,
10000
01000
00727621006
0010339
000120
,
7500000
0750000
00520482890
002568761072
00514630946

G:=sub<GL(5,GF(1171))| [1,1015,0,0,0,247,112,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,247,1170,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,72,1,0,0,0,762,0,1,0,0,1006,339,20],[750,0,0,0,0,0,750,0,0,0,0,0,520,256,514,0,0,482,876,630,0,0,890,1072,946] >;
 

D5×C13⋊C3 in GAP, Magma, Sage, TeX 

D_5\times C_{13}\rtimes C_3
 
% in TeX
 
G:=Group("D5xC13:C3");
 
// GroupNames label
 
G:=SmallGroup(390,2);
 
// by ID
 
G=gap.SmallGroup(390,2);
 
# by ID
 
G:=PCGroup([4,-2,-3,-5,-13,290,727]);
 
// Polycyclic
 
G:=Group<a,b,c,d|a^5=b^2=c^13=d^3=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^9>;
 
// generators/relations
 

Export

Subgroup lattice of D5×C13⋊C3 in TeX
Character table of D5×C13⋊C3 in TeX

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