Finite Group Databasebeta

← Group #72341330

Character table — Group #72341330

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size116812122424242424323232324848116812122424242424323232324848116812122424242424323232324848116812122424242424323232324848
order1222242444436664844444444444121212124822222424444666648444444444441212121248
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111-1-11-1-11111-1-1111111-1-11-1-11111-1-1111111-1-11-1-11111-1-1111111-1-11-1-11111-1-1
χ3111-1111-1-11-111-1-1-11111-1111-1-11-111-1-1-11111-1111-1-11-111-1-1-11111-1111-1-11-111-1-1-11
χ4111-111-11-1-1111-1-11-1111-111-11-1-1111-1-11-1111-111-11-1-1111-1-11-1111-111-11-1-1111-1-11-1
χ522222200200-1-1-1-10022222200200-1-1-1-10022222200200-1-1-1-10022222200200-1-1-1-100
χ6222-22200-200-1-11100222-22200-200-1-11100222-22200-200-1-11100222-22200-200-1-11100
χ73333-1-111-1110000-1-13333-1-111-1110000-1-13333-1-111-1110000-1-13333-1-111-1110000-1-1
χ83333-1-1-1-1-1-1-10000113333-1-1-1-1-1-1-10000113333-1-1-1-1-1-1-10000113333-1-1-1-1-1-1-1000011
χ9333-3-1-11-111-100001-1333-3-1-11-111-100001-1333-3-1-11-111-100001-1333-3-1-11-111-100001-1
χ10333-3-1-1-111-110000-11333-3-1-1-111-110000-11333-3-1-1-111-110000-11333-3-1-1-111-110000-11
χ1166-202-20200-200000066-202-20200-200000066-202-20200-200000066-202-20200-2000000
χ1266-202-20-200200000066-202-20-200200000066-202-20-200200000066-202-20-2002000000
χ1366-20-22200-2000000066-20-22200-2000000066-20-22200-2000000066-20-22200-20000000
χ1466-20-22-2002000000066-20-22-2002000000066-20-22-2002000000066-20-22-20020000000
χ158-80000000002-200008-80000000002-200008-80000000002-200008-80000000002-20000
χ168-8000000000-11i3−i3008-8000000000-11i3−i3008-8000000000-11i3−i3008-8000000000-11i3−i300
χ178-8000000000-11−i3i3008-8000000000-11−i3i3008-8000000000-11−i3i3008-8000000000-11−i3i300
χ1811111111111111111iiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ19111111-1-11-1-11111-1-1iiiiii−i−ii−i−iiiii−i−i-1-1-1-1-1-111-111-1-1-1-111−i−i−i−i−i−iii−iii−i−i−i−iii
χ20111-1111-1-11-111-1-1-11iii−iiii−i−ii−iii−i−i−ii-1-1-11-1-1-111-11-1-1111-1−i−i−ii−i−i−iii−ii−i−iiii−i
χ21111-111-11-1-1111-1-11-1iii−iii−ii−i−iiii−i−ii−i-1-1-11-1-11-111-1-1-111-11−i−i−ii−i−ii−iii−i−i−iii−ii
χ2222222200200-1-1-1-1002i2i2i2i2i2i002i00−i−i−i−i00-2-2-2-2-2-200-200111100−2i−2i−2i−2i−2i−2i00−2i00iiii00
χ23222-22200-200-1-111002i2i2i−2i2i2i00−2i00−i−iii00-2-2-22-2-20020011-1-100−2i−2i−2i2i−2i−2i002i00ii−i−i00
χ243333-1-111-1110000-1-13i3i3i3i−i−iii−iii0000−i−i-3-3-3-311-1-11-1-1000011−3i−3i−3i−3iii−i−ii−i−i0000ii
χ253333-1-1-1-1-1-1-10000113i3i3i3i−i−i−i−i−i−i−i0000ii-3-3-3-311111110000-1-1−3i−3i−3i−3iiiiiiii0000−i−i
χ26333-3-1-11-111-100001-13i3i3i−3i−i−ii−iii−i0000i−i-3-3-3311-11-1-110000-11−3i−3i−3i3iii−ii−i−ii0000−ii
χ27333-3-1-1-111-110000-113i3i3i−3i−i−i−iii−ii0000−ii-3-3-33111-1-11-100001-1−3i−3i−3i3iiii−i−ii−i0000i−i
χ2866-202-20200-20000006i6i−2i02i−2i02i00−2i000000-6-620-220-2002000000−6i−6i2i0−2i2i0−2i002i000000
χ2966-202-20-20020000006i6i−2i02i−2i0−2i002i000000-6-620-220200-2000000−6i−6i2i0−2i2i02i00−2i000000
χ3066-20-22200-200000006i6i−2i0−2i2i2i00−2i0000000-6-6202-2-20020000000−6i−6i2i02i−2i−2i002i0000000
χ3166-20-22-200200000006i6i−2i0−2i2i−2i002i0000000-6-6202-2200-20000000−6i−6i2i02i−2i2i00−2i0000000
χ328-80000000002-200008i−8i0000000002i−2i0000-88000000000-220000−8i8i000000000−2i2i0000
χ338-8000000000-11i3−i3008i−8i000000000−ii−3300-880000000001-1−i3i300−8i8i000000000i−i3−300
χ348-8000000000-11−i3i3008i−8i000000000−ii3−300-880000000001-1i3−i300−8i8i000000000i−i−3300
χ3511111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ36111111-1-11-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-111
χ37111-1111-1-11-111-1-1-11-1-1-11-1-1-111-11-1-1111-1111-1111-1-11-111-1-1-11-1-1-11-1-1-111-11-1-1111-1
χ38111-111-11-1-1111-1-11-1-1-1-11-1-11-111-1-1-111-11111-111-11-1-1111-1-11-1-1-1-11-1-11-111-1-1-111-11
χ3922222200200-1-1-1-100-2-2-2-2-2-200-20011110022222200200-1-1-1-100-2-2-2-2-2-200-200111100
χ40222-22200-200-1-11100-2-2-22-2-20020011-1-100222-22200-200-1-11100-2-2-22-2-20020011-1-100
χ413333-1-111-1110000-1-1-3-3-3-311-1-11-1-10000113333-1-111-1110000-1-1-3-3-3-311-1-11-1-1000011
χ423333-1-1-1-1-1-1-1000011-3-3-3-311111110000-1-13333-1-1-1-1-1-1-1000011-3-3-3-311111110000-1-1
χ43333-3-1-11-111-100001-1-3-3-3311-11-1-110000-11333-3-1-11-111-100001-1-3-3-3311-11-1-110000-11
χ44333-3-1-1-111-110000-11-3-3-33111-1-11-100001-1333-3-1-1-111-110000-11-3-3-33111-1-11-100001-1
χ4566-202-20200-2000000-6-620-220-200200000066-202-20200-2000000-6-620-220-2002000000
χ4666-202-20-2002000000-6-620-220200-200000066-202-20-2002000000-6-620-220200-2000000
χ4766-20-22200-20000000-6-6202-2-2002000000066-20-22200-20000000-6-6202-2-20020000000
χ4866-20-22-20020000000-6-6202-2200-2000000066-20-22-20020000000-6-6202-2200-20000000
χ498-80000000002-20000-88000000000-2200008-80000000002-20000-88000000000-220000
χ508-8000000000-11i3−i300-880000000001-1−i3i3008-8000000000-11i3−i300-880000000001-1−i3i300
χ518-8000000000-11−i3i300-880000000001-1i3−i3008-8000000000-11−i3i300-880000000001-1i3−i300
χ5211111111111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiii
χ53111111-1-11-1-11111-1-1−i−i−i−i−i−iii−iii−i−i−i−iii-1-1-1-1-1-111-111-1-1-1-111iiiiii−i−ii−i−iiiii−i−i
χ54111-1111-1-11-111-1-1-11−i−i−ii−i−i−iii−ii−i−iiii−i-1-1-11-1-1-111-11-1-1111-1iii−iiii−i−ii−iii−i−i−ii
χ55111-111-11-1-1111-1-11-1−i−i−ii−i−ii−iii−i−i−iii−ii-1-1-11-1-11-111-1-1-111-11iii−iii−ii−i−iiii−i−ii−i
χ5622222200200-1-1-1-100−2i−2i−2i−2i−2i−2i00−2i00iiii00-2-2-2-2-2-200-2001111002i2i2i2i2i2i002i00−i−i−i−i00
χ57222-22200-200-1-11100−2i−2i−2i2i−2i−2i002i00ii−i−i00-2-2-22-2-20020011-1-1002i2i2i−2i2i2i00−2i00−i−iii00
χ583333-1-111-1110000-1-1−3i−3i−3i−3iii−i−ii−i−i0000ii-3-3-3-311-1-11-1-10000113i3i3i3i−i−iii−iii0000−i−i
χ593333-1-1-1-1-1-1-1000011−3i−3i−3i−3iiiiiiii0000−i−i-3-3-3-311111110000-1-13i3i3i3i−i−i−i−i−i−i−i0000ii
χ60333-3-1-11-111-100001-1−3i−3i−3i3iii−ii−i−ii0000−ii-3-3-3311-11-1-110000-113i3i3i−3i−i−ii−iii−i0000i−i
χ61333-3-1-1-111-110000-11−3i−3i−3i3iiii−i−ii−i0000i−i-3-3-33111-1-11-100001-13i3i3i−3i−i−i−iii−ii0000−ii
χ6266-202-20200-2000000−6i−6i2i0−2i2i0−2i002i000000-6-620-220-20020000006i6i−2i02i−2i02i00−2i000000
χ6366-202-20-2002000000−6i−6i2i0−2i2i02i00−2i000000-6-620-220200-20000006i6i−2i02i−2i0−2i002i000000
χ6466-20-22200-20000000−6i−6i2i02i−2i−2i002i0000000-6-6202-2-200200000006i6i−2i0−2i2i2i00−2i0000000
χ6566-20-22-20020000000−6i−6i2i02i−2i2i00−2i0000000-6-6202-2200-200000006i6i−2i0−2i2i−2i002i0000000
χ668-80000000002-20000−8i8i000000000−2i2i0000-88000000000-2200008i−8i0000000002i−2i0000
χ678-8000000000-11i3−i300−8i8i000000000i−i3−300-880000000001-1−i3i3008i−8i000000000−ii−3300
χ688-8000000000-11−i3i300−8i8i000000000i−i−3300-880000000001-1i3−i3008i−8i000000000−ii3−300

Here i is the imaginary unit (i² = −1).