Finite Group Databasebeta

← Group #72343126

Character table — Group #72343126

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111166881212121224242424242424242424323232323232323248484848111166881212121224242424242424242424323232323232323248484848
order12442488224424448888883612122424242444442244248822442444888888661212242424244444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1
χ3111111-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-111
χ511-1-11-1i−i1-11-11-11-1i−ii−ii−i11-1-1ii−i−i1-1i−i11-1-11-1i−i1-11-11-11-1i−ii−ii−i11-1-1ii−i−i1-1i−i
χ611-1-11-1i−i1-11-1-11-11−iii−i−ii11-1-1ii−i−i-11−ii11-1-11-1i−i1-11-1-11-11−iii−i−ii11-1-1ii−i−i-11−ii
χ711-1-11-1−ii1-11-11-11-1−ii−ii−ii11-1-1−i−iii1-1−ii11-1-11-1−ii1-11-11-11-1−ii−ii−ii11-1-1−i−iii1-1−ii
χ811-1-11-1−ii1-11-1-11-11i−i−iii−i11-1-1−i−iii-11i−i11-1-11-1−ii1-11-1-11-11i−i−iii−i11-1-1−i−iii-11i−i
χ92222222222220000002200-1-1-1-1-1-1-1-100002222222222220000002200-1-1-1-1-1-1-1-10000
χ10222222-2-22222000000-2-200-1-1-1-111110000222222-2-22222000000-2-200-1-1-1-111110000
χ1122-2-22-22i−2i2-22-20000002i−2i00-1-111−i−iii000022-2-22-22i−2i2-22-20000002i−2i00-1-111−i−iii0000
χ1222-2-22-2−2i2i2-22-2000000−2i2i00-1-111ii−i−i000022-2-22-2−2i2i2-22-2000000−2i2i00-1-111ii−i−i0000
χ1333333333-1-1-1-1111111-1-11100000000-1-1-1-133333333-1-1-1-1111111-1-11100000000-1-1-1-1
χ1433333333-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000111133333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000001111
χ15333333-3-3-1-1-1-11111-1-111-1-100000000-1-111333333-3-3-1-1-1-11111-1-111-1-100000000-1-111
χ16333333-3-3-1-1-1-1-1-1-1-11111110000000011-1-1333333-3-3-1-1-1-1-1-1-1-11111110000000011-1-1
χ1733-3-33-33i−3i-11-111-11-1i−i−iii−i00000000-11−ii33-3-33-33i−3i-11-111-11-1i−i−iii−i00000000-11−ii
χ1833-3-33-33i−3i-11-11-11-11−ii−ii−ii000000001-1i−i33-3-33-33i−3i-11-11-11-11−ii−ii−ii000000001-1i−i
χ1933-3-33-3−3i3i-11-111-11-1−iii−i−ii00000000-11i−i33-3-33-3−3i3i-11-111-11-1−iii−i−ii00000000-11i−i
χ2033-3-33-3−3i3i-11-11-11-11i−ii−ii−i000000001-1−ii33-3-33-3−3i3i-11-11-11-11i−ii−ii−i000000001-1−ii
χ216666-2-2002-2-2222-2-20000000000000000006666-2-2002-2-2222-2-2000000000000000000
χ226666-2-2002-2-22-2-2220000000000000000006666-2-2002-2-22-2-222000000000000000000
χ236666-2-200-222-200002200-2-20000000000006666-2-200-222-200002200-2-2000000000000
χ246666-2-200-222-20000-2-200220000000000006666-2-200-222-20000-2-20022000000000000
χ2566-6-6-220022-2-22-2-2200000000000000000066-6-6-220022-2-22-2-22000000000000000000
χ2666-6-6-220022-2-2-222-200000000000000000066-6-6-220022-2-2-222-2000000000000000000
χ2766-6-6-2200-2-22200002i−2i00−2i2i00000000000066-6-6-2200-2-22200002i−2i00−2i2i000000000000
χ2866-6-6-2200-2-2220000−2i2i002i−2i00000000000066-6-6-2200-2-2220000−2i2i002i−2i000000000000
χ298-88i−8i0000000000000000002-22i−2i000000008-88i−8i0000000000000000002-22i−2i00000000
χ308-88i−8i000000000000000000-11−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300008-88i−8i000000000000000000-11−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ318-88i−8i000000000000000000-11−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300008-88i−8i000000000000000000-11−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ328-8−8i8i0000000000000000002-2−2i2i000000008-8−8i8i0000000000000000002-2−2i2i00000000
χ338-8−8i8i000000000000000000-11i−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300008-8−8i8i000000000000000000-11i−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ348-8−8i8i000000000000000000-11i−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300008-8−8i8i000000000000000000-11i−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ351111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ36111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111
χ37111111-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ38111111-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1
χ3911-1-11-1i−i1-11-11-11-1i−ii−ii−i11-1-1ii−i−i1-1i−i-1-111-11−ii-11-11-11-11−ii−ii−ii-1-111−i−iii-11−ii
χ4011-1-11-1i−i1-11-1-11-11−iii−i−ii11-1-1ii−i−i-11−ii-1-111-11−ii-11-111-11-1i−i−iii−i-1-111−i−iii1-1i−i
χ4111-1-11-1−ii1-11-11-11-1−ii−ii−ii11-1-1−i−iii1-1−ii-1-111-11i−i-11-11-11-11i−ii−ii−i-1-111ii−i−i-11i−i
χ4211-1-11-1−ii1-11-1-11-11i−i−iii−i11-1-1−i−iii-11i−i-1-111-11i−i-11-111-11-1−iii−i−ii-1-111ii−i−i1-1−ii
χ432222222222220000002200-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-2-2-2-2000000-2-200111111110000
χ44222222-2-22222000000-2-200-1-1-1-111110000-2-2-2-2-2-222-2-2-2-200000022001111-1-1-1-10000
χ4522-2-22-22i−2i2-22-20000002i−2i00-1-111−i−iii0000-2-222-22−2i2i-22-22000000−2i2i0011-1-1ii−i−i0000
χ4622-2-22-2−2i2i2-22-2000000−2i2i00-1-111ii−i−i0000-2-222-222i−2i-22-220000002i−2i0011-1-1−i−iii0000
χ4733333333-1-1-1-1111111-1-11100000000-1-1-1-1-3-3-3-3-3-3-3-31111-1-1-1-1-1-111-1-1000000001111
χ4833333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000001111-3-3-3-3-3-3-3-31111111111111100000000-1-1-1-1
χ49333333-3-3-1-1-1-11111-1-111-1-100000000-1-111-3-3-3-3-3-3331111-1-1-1-111-1-1110000000011-1-1
χ50333333-3-3-1-1-1-1-1-1-1-11111110000000011-1-1-3-3-3-3-3-33311111111-1-1-1-1-1-100000000-1-111
χ5133-3-33-33i−3i-11-111-11-1i−i−iii−i00000000-11−ii-3-333-33−3i3i1-11-1-11-11−iii−i−ii000000001-1i−i
χ5233-3-33-33i−3i-11-11-11-11−ii−ii−ii000000001-1i−i-3-333-33−3i3i1-11-11-11-1i−ii−ii−i00000000-11−ii
χ5333-3-33-3−3i3i-11-111-11-1−iii−i−ii00000000-11i−i-3-333-333i−3i1-11-1-11-11i−i−iii−i000000001-1−ii
χ5433-3-33-3−3i3i-11-11-11-11i−ii−ii−i000000001-1−ii-3-333-333i−3i1-11-11-11-1−ii−ii−ii00000000-11i−i
χ556666-2-2002-2-2222-2-2000000000000000000-6-6-6-62200-222-2-2-222000000000000000000
χ566666-2-2002-2-22-2-222000000000000000000-6-6-6-62200-222-222-2-2000000000000000000
χ576666-2-200-222-200002200-2-2000000000000-6-6-6-622002-2-220000-2-20022000000000000
χ586666-2-200-222-20000-2-20022000000000000-6-6-6-622002-2-2200002200-2-2000000000000
χ5966-6-6-220022-2-22-2-22000000000000000000-6-6662-200-2-222-222-2000000000000000000
χ6066-6-6-220022-2-2-222-2000000000000000000-6-6662-200-2-2222-2-22000000000000000000
χ6166-6-6-2200-2-22200002i−2i00−2i2i000000000000-6-6662-20022-2-20000−2i2i002i−2i000000000000
χ6266-6-6-2200-2-2220000−2i2i002i−2i000000000000-6-6662-20022-2-200002i−2i00−2i2i000000000000
χ638-88i−8i0000000000000000002-22i−2i00000000-88−8i8i000000000000000000-22−2i2i00000000
χ648-88i−8i000000000000000000-11−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000-88−8i8i0000000000000000001-1i−iζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ658-88i−8i000000000000000000-11−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000-88−8i8i0000000000000000001-1i−i−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ668-8−8i8i0000000000000000002-2−2i2i00000000-888i−8i000000000000000000-222i−2i00000000
χ678-8−8i8i000000000000000000-11i−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000-888i−8i0000000000000000001-1−ii−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ688-8−8i8i000000000000000000-11i−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000-888i−8i0000000000000000001-1−iiζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.