Finite Group Databasebeta

← Group #13180875

Character table — Group #13180875

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122223344666688121216161616161616161836363636363636363636363654727211222233446666881212161616161616161618363636363636363636363636547272
order123366223666663666333366664224466661212121241212226666226666666666666666664224466661212121241212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111
χ311111111111111111111111111-11-11-111-1-111-1-1-1-1-111111111111111111111111111-11-11-111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-11-11-1-111-1-111-1-1-111111111111111111111111111-1-11-11-1-111-1-111-1-1-1
χ522222222222222-1-122-1-1-1-1-1-1-1-120000000000002-1-122222222222222-1-122-1-1-1-1-1-1-1-120000000000002-1-1
χ622222222222222-1-122-1-1-1-1-1-1-1-1-2000000000000-21122222222222222-1-122-1-1-1-1-1-1-1-1-2000000000000-211
χ7222-12-122-1-12-12-122-1-12-1-1-12-1-1-10020200-1-100-1-1000222-12-122-1-12-12-122-1-12-1-1-12-1-1-10020200-1-100-1-1000
χ8222-12-122-1-12-12-122-1-12-1-1-12-1-1-100-20-200110011000222-12-122-1-12-12-122-1-12-1-1-12-1-1-100-20-200110011000
χ922-12-1222-1-1-12-1222-1-1-12-1-1-12-1-102020-1-100-1-10000022-12-1222-1-1-12-1222-1-1-12-1-1-12-1-102020-1-100-1-100000
χ1022-12-1222-1-1-12-1222-1-1-12-1-1-12-1-10-20-201100110000022-12-1222-1-1-12-1222-1-1-12-1-1-12-1-10-20-2011001100000
χ112-222-2-2-222-2-2-2222-22-22222-2-2-2-200000000000000002-222-2-2-222-2-2-2222-22-22222-2-2-2-20000000000000000
χ122-222-2-2-222-2-2-222-112-2-1-1-1-11111000000000000003−32-222-2-2-222-2-2-222-112-2-1-1-1-11111000000000000003−3
χ132-222-2-2-222-2-2-222-112-2-1-1-1-1111100000000000000−332-222-2-2-222-2-2-222-112-2-1-1-1-1111100000000000000−33
χ142-22-1-21-22-11-212-12-2-112-1-1-1-21110000000−i3i300−i3i30002-22-1-21-22-11-212-12-2-112-1-1-1-21110000000−i3i300−i3i3000
χ152-22-1-21-22-11-212-12-2-112-1-1-1-21110000000i3−i300i3−i30002-22-1-21-22-11-212-12-2-112-1-1-1-21110000000i3−i300i3−i3000
χ162-2-121-2-22-111-2-122-2-11-12-1-11-21100000−i3i300−i3i3000002-2-121-2-22-111-2-122-2-11-12-1-11-21100000−i3i300−i3i300000
χ172-2-121-2-22-111-2-122-2-11-12-1-11-21100000i3−i300i3−i3000002-2-121-2-22-111-2-122-2-11-12-1-11-21100000i3−i300i3−i300000
χ18333333-1-133-1-1-1-100-1-100000000311-1-11111-1-1-1-1-100333333-1-133-1-1-1-100-1-100000000311-1-11111-1-1-1-1-100
χ19333333-1-133-1-1-1-100-1-1000000003-1-111-1-1-1-11111-100333333-1-133-1-1-1-100-1-1000000003-1-111-1-1-1-11111-100
χ20333333-1-133-1-1-1-100-1-100000000-31-1-1111-1-1-1-111100333333-1-133-1-1-1-100-1-100000000-31-1-1111-1-1-1-111100
χ21333333-1-133-1-1-1-100-1-100000000-3-111-1-1-11111-1-1100333333-1-133-1-1-1-100-1-100000000-3-111-1-1-11111-1-1100
χ22444-24-244-2-24-24-2-2-2-2-2-2111-21110000000000000000444-24-244-2-24-24-2-2-2-2-2-2111-21110000000000000000
χ2344-24-2444-2-2-24-24-2-2-2-21-2111-211000000000000000044-24-2444-2-2-24-24-2-2-2-21-2111-2110000000000000000
χ2444-2-2-2-24411-2-2-2-24411-2-211-2-211000000000000000044-2-2-2-24411-2-2-2-24411-2-211-2-2110000000000000000
χ2544-2-2-2-24411-2-2-2-2-2-21111−1−3i32−1+3i3211−1−3i32−1+3i32000000000000000044-2-2-2-24411-2-2-2-2-2-21111−1−3i32−1+3i3211−1−3i32−1+3i320000000000000000
χ2644-2-2-2-24411-2-2-2-2-2-21111−1+3i32−1−3i3211−1+3i32−1−3i32000000000000000044-2-2-2-24411-2-2-2-2-2-21111−1+3i32−1−3i3211−1+3i32−1−3i320000000000000000
χ274-44-2-42-44-22-424-2-22-22-21112-1-1-100000000000000004-44-2-42-44-22-424-2-22-22-21112-1-1-10000000000000000
χ284-4-242-4-44-222-4-24-22-221-211-12-1-100000000000000004-4-242-4-44-222-4-24-22-221-211-12-1-10000000000000000
χ294-4-2-222-441-122-2-24-41-1-2-21122-1-100000000000000004-4-2-222-441-122-2-24-41-1-2-21122-1-10000000000000000
χ304-4-2-222-441-122-2-2-221-111−1−3i32−1+3i32-1-11+3i321−3i3200000000000000004-4-2-222-441-122-2-2-221-111−1−3i32−1+3i32-1-11+3i321−3i320000000000000000
χ314-4-2-222-441-122-2-2-221-111−1+3i32−1−3i32-1-11−3i321+3i3200000000000000004-4-2-222-441-122-2-2-221-111−1+3i32−1−3i32-1-11−3i321+3i320000000000000000
χ32666-36-3-2-2-3-3-21-210011000000000020-200-1-10011000666-36-3-2-2-3-3-21-210011000000000020-200-1-10011000
χ33666-36-3-2-2-3-3-21-2100110000000000-202001100-1-1000666-36-3-2-2-3-3-21-2100110000000000-202001100-1-1000
χ3466-36-36-2-2-3-31-21-2001100000000020-20-1-100110000066-36-36-2-2-3-31-21-2001100000000020-20-1-1001100000
χ3566-36-36-2-2-3-31-21-20011000000000-20201100-1-10000066-36-36-2-2-3-31-21-20011000000000-20201100-1-100000
χ366-666-6-62-26-622-2-200-220000000000000000000000006-666-6-62-26-622-2-200-22000000000000000000000000
χ376-66-3-632-2-332-1-21001-1000000000000000−i3i300i3−i30006-66-3-632-2-332-1-21001-1000000000000000−i3i300i3−i3000
χ386-66-3-632-2-332-1-21001-1000000000000000i3−i300−i3i30006-66-3-632-2-332-1-21001-1000000000000000i3−i300−i3i3000
χ396-6-363-62-2-33-121-2001-10000000000000−i3i300i3−i3000006-6-363-62-2-33-121-2001-10000000000000−i3i300i3−i300000
χ406-6-363-62-2-33-121-2001-10000000000000i3−i300−i3i3000006-6-363-62-2-33-121-2001-10000000000000i3−i300−i3i300000
χ411212-6-6-6-6-4-433222200-1-10000000000000000000000001212-6-6-6-6-4-433222200-1-1000000000000000000000000
χ4212-12-6-6664-43-3-2-22200-1100000000000000000000000012-12-6-6664-43-3-2-22200-11000000000000000000000000
χ43111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ44111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1
χ4511111111111111111111111111-11-11-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-111-1-111111
χ4611111111111111111111111111-1-11-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111-1-111-1-1111
χ4722222222222222-1-122-1-1-1-1-1-1-1-120000000000002-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-211-2-211111111-2000000000000-211
χ4822222222222222-1-122-1-1-1-1-1-1-1-1-2000000000000-211-2-2-2-2-2-2-2-2-2-2-2-2-2-211-2-21111111120000000000002-1-1
χ49222-12-122-1-12-12-122-1-12-1-1-12-1-1-10020200-1-100-1-1000-2-2-21-21-2-211-21-21-2-211-2111-211100-20-200110011000
χ50222-12-122-1-12-12-122-1-12-1-1-12-1-1-100-20-200110011000-2-2-21-21-2-211-21-21-2-211-2111-21110020200-1-100-1-1000
χ5122-12-1222-1-1-12-1222-1-1-12-1-1-12-1-102020-1-100-1-100000-2-21-21-2-2-2111-21-2-2-2111-2111-2110-20-2011001100000
χ5222-12-1222-1-1-12-1222-1-1-12-1-1-12-1-10-20-2011001100000-2-21-21-2-2-2111-21-2-2-2111-2111-21102020-1-100-1-100000
χ532-222-2-2-222-2-2-2222-22-22222-2-2-2-20000000000000000-22-2-2222-2-2222-2-2-22-22-2-2-2-222220000000000000000
χ542-222-2-2-222-2-2-222-112-2-1-1-1-11111000000000000003−3-22-2-2222-2-2222-2-21-1-221111-1-1-1-100000000000000−33
χ552-222-2-2-222-2-2-222-112-2-1-1-1-1111100000000000000−33-22-2-2222-2-2222-2-21-1-221111-1-1-1-1000000000000003−3
χ562-22-1-21-22-11-212-12-2-112-1-1-1-21110000000−i3i300−i3i3000-22-212-12-21-12-1-21-221-1-21112-1-1-10000000i3−i300i3−i3000
χ572-22-1-21-22-11-212-12-2-112-1-1-1-21110000000i3−i300i3−i3000-22-212-12-21-12-1-21-221-1-21112-1-1-10000000−i3i300−i3i3000
χ582-2-121-2-22-111-2-122-2-11-12-1-11-21100000−i3i300−i3i300000-221-2-122-21-1-121-2-221-11-211-12-1-100000i3−i300i3−i300000
χ592-2-121-2-22-111-2-122-2-11-12-1-11-21100000i3−i300i3−i300000-221-2-122-21-1-121-2-221-11-211-12-1-100000−i3i300−i3i300000
χ60333333-1-133-1-1-1-100-1-100000000311-1-11111-1-1-1-1-100-3-3-3-3-3-311-3-31111001100000000-3-1-111-1-1-1-11111100
χ61333333-1-133-1-1-1-100-1-1000000003-1-111-1-1-1-11111-100-3-3-3-3-3-311-3-31111001100000000-311-1-11111-1-1-1-1100
χ62333333-1-133-1-1-1-100-1-100000000-31-1-1111-1-1-1-111100-3-3-3-3-3-311-3-311110011000000003-111-1-1-11111-1-1-100
χ63333333-1-133-1-1-1-100-1-100000000-3-111-1-1-11111-1-1100-3-3-3-3-3-311-3-3111100110000000031-1-1111-1-1-1-111-100
χ64444-24-244-2-24-24-2-2-2-2-2-2111-21110000000000000000-4-4-42-42-4-422-42-4222222-1-1-12-1-1-10000000000000000
χ6544-24-2444-2-2-24-24-2-2-2-21-2111-2110000000000000000-4-42-42-4-4-4222-42-42222-12-1-1-12-1-10000000000000000
χ6644-2-2-2-24411-2-2-2-24411-2-211-2-2110000000000000000-4-42222-4-4-1-12222-4-4-1-122-1-122-1-10000000000000000
χ6744-2-2-2-24411-2-2-2-2-2-21111−1−3i32−1+3i3211−1−3i32−1+3i320000000000000000-4-42222-4-4-1-1222222-1-1-1-11+3i321−3i32-1-11+3i321−3i320000000000000000
χ6844-2-2-2-24411-2-2-2-2-2-21111−1+3i32−1−3i3211−1+3i32−1−3i320000000000000000-4-42222-4-4-1-1222222-1-1-1-11−3i321+3i32-1-11−3i321+3i320000000000000000
χ694-44-2-42-44-22-424-2-22-22-21112-1-1-10000000000000000-44-424-24-42-24-2-422-22-22-1-1-1-21110000000000000000
χ704-4-242-4-44-222-4-24-22-221-211-12-1-10000000000000000-442-4-244-42-2-242-42-22-2-12-1-11-2110000000000000000
χ714-4-2-222-441-122-2-24-41-1-2-21122-1-10000000000000000-4422-2-24-4-11-2-222-44-1122-1-1-2-2110000000000000000
χ724-4-2-222-441-122-2-2-221-111−1−3i32−1+3i32-1-11+3i321−3i320000000000000000-4422-2-24-4-11-2-2222-2-11-1-11+3i321−3i3211−1−3i32−1+3i320000000000000000
χ734-4-2-222-441-122-2-2-221-111−1+3i32−1−3i32-1-11−3i321+3i320000000000000000-4422-2-24-4-11-2-2222-2-11-1-11−3i321+3i3211−1+3i32−1−3i320000000000000000
χ74666-36-3-2-2-3-3-21-210011000000000020-200-1-10011000-6-6-63-6322332-12-100-1-10000000000-202001100-1-1000
χ75666-36-3-2-2-3-3-21-2100110000000000-202001100-1-1000-6-6-63-6322332-12-100-1-1000000000020-200-1-10011000
χ7666-36-36-2-2-3-31-21-2001100000000020-20-1-1001100000-6-63-63-62233-12-1200-1-1000000000-20201100-1-100000
χ7766-36-36-2-2-3-31-21-20011000000000-20201100-1-100000-6-63-63-62233-12-1200-1-100000000020-20-1-1001100000
χ786-666-6-62-26-622-2-200-22000000000000000000000000-66-6-666-22-66-2-222002-2000000000000000000000000
χ796-66-3-632-2-332-1-21001-1000000000000000−i3i300i3−i3000-66-636-3-223-3-212-100-11000000000000000i3−i300−i3i3000
χ806-66-3-632-2-332-1-21001-1000000000000000i3−i300−i3i3000-66-636-3-223-3-212-100-11000000000000000−i3i300i3−i3000
χ816-6-363-62-2-33-121-2001-10000000000000−i3i300i3−i300000-663-6-36-223-31-2-1200-110000000000000i3−i300−i3i300000
χ826-6-363-62-2-33-121-2001-10000000000000i3−i300−i3i300000-663-6-36-223-31-2-1200-110000000000000−i3i300i3−i300000
χ831212-6-6-6-6-4-433222200-1-1000000000000000000000000-12-12666644-3-3-2-2-2-20011000000000000000000000000
χ8412-12-6-6664-43-3-2-22200-11000000000000000000000000-121266-6-6-44-3322-2-2001-1000000000000000000000000

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