Finite Group Databasebeta

← Group #11714752

Character table — Group #11714752

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size11222336668888888824242424112223366688888888242424241122233666888888882424242411222336668888888824242424
order1248822488361212242424242444224882248866121224242424244422488224886612122424242424442248822488661212242424242444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-1111111111111111111-1-1-1-1111111111111111111-1-1-1-1111111111111111111-1-1-1-1
χ3111-1-1111-1-11111-1-1-1-11-11-1111-1-1111-1-11111-1-1-1-11-11-1111-1-1111-1-11111-1-1-1-11-11-1111-1-1111-1-11111-1-1-1-11-11-1
χ4111-1-1111-1-11111-1-1-1-1-11-11111-1-1111-1-11111-1-1-1-1-11-11111-1-1111-1-11111-1-1-1-1-11-11111-1-1111-1-11111-1-1-1-1-11-11
χ52222222222-1-1-1-1-1-1-1-100002222222222-1-1-1-1-1-1-1-100002222222222-1-1-1-1-1-1-1-100002222222222-1-1-1-1-1-1-1-10000
χ6222-2-2222-2-2-1-1-1-111110000222-2-2222-2-2-1-1-1-111110000222-2-2222-2-2-1-1-1-111110000222-2-2222-2-2-1-1-1-111110000
χ722-20022-20022-2-20000000022-20022-20022-2-20000000022-20022-20022-2-20000000022-20022-20022-2-200000000
χ822-20022-200-1-11133−3−3000022-20022-200-1-11133−3−3000022-20022-200-1-11133−3−3000022-20022-200-1-11133−3−30000
χ922-20022-200-1-111−3−333000022-20022-200-1-111−3−333000022-20022-200-1-111−3−333000022-20022-200-1-111−3−3330000
χ102-20−i2i22-20−i2i22-200−i2i2−i2i200002-20−i2i22-20−i2i22-200−i2i2−i2i200002-20−i2i22-20−i2i22-200−i2i2−i2i200002-20−i2i22-20−i2i22-200−i2i2−i2i20000
χ112-20−i2i22-20−i2i2-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300002-20−i2i22-20−i2i2-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300002-20−i2i22-20−i2i2-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300002-20−i2i22-20−i2i2-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ122-20−i2i22-20−i2i2-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700002-20−i2i22-20−i2i2-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700002-20−i2i22-20−i2i2-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700002-20−i2i22-20−i2i2-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ132-20i2−i22-20i2−i22-200i2−i2i2−i200002-20i2−i22-20i2−i22-200i2−i2i2−i200002-20i2−i22-20i2−i22-200i2−i2i2−i200002-20i2−i22-20i2−i22-200i2−i2i2−i20000
χ142-20i2−i22-20i2−i2-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300002-20i2−i22-20i2−i2-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300002-20i2−i22-20i2−i2-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300002-20i2−i22-20i2−i2-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ152-20i2−i22-20i2−i2-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700002-20i2−i22-20i2−i2-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700002-20i2−i22-20i2−i2-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700002-20i2−i22-20i2−i2-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ1633333-1-1-1-1-10000000011-1-133333-1-1-1-1-10000000011-1-133333-1-1-1-1-10000000011-1-133333-1-1-1-1-10000000011-1-1
χ1733333-1-1-1-1-100000000-1-11133333-1-1-1-1-100000000-1-11133333-1-1-1-1-100000000-1-11133333-1-1-1-1-100000000-1-111
χ18333-3-3-1-1-111000000001-1-11333-3-3-1-1-111000000001-1-11333-3-3-1-1-111000000001-1-11333-3-3-1-1-111000000001-1-11
χ19333-3-3-1-1-11100000000-111-1333-3-3-1-1-11100000000-111-1333-3-3-1-1-11100000000-111-1333-3-3-1-1-11100000000-111-1
χ2066-600-2-220000000000000066-600-2-220000000000000066-600-2-220000000000000066-600-2-2200000000000000
χ216-60−3i23i2-220i2−i20000000000006-60−3i23i2-220i2−i20000000000006-60−3i23i2-220i2−i20000000000006-60−3i23i2-220i2−i2000000000000
χ226-603i2−3i2-220−i2i20000000000006-603i2−3i2-220−i2i20000000000006-603i2−3i2-220−i2i20000000000006-603i2−3i2-220−i2i2000000000000
χ231111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ24111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ25111-1-1111-1-11111-1-1-1-11-11-1-1-1-111-1-1-111-1-1-1-11111-11-11111-1-1111-1-11111-1-1-1-11-11-1-1-1-111-1-1-111-1-1-1-11111-11-11
χ26111-1-1111-1-11111-1-1-1-1-11-11-1-1-111-1-1-111-1-1-1-111111-11-1111-1-1111-1-11111-1-1-1-1-11-11-1-1-111-1-1-111-1-1-1-111111-11-1
χ272222222222-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-2-21111111100002222222222-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-2-2111111110000
χ28222-2-2222-2-2-1-1-1-111110000-2-2-222-2-2-2221111-1-1-1-10000222-2-2222-2-2-1-1-1-111110000-2-2-222-2-2-2221111-1-1-1-10000
χ2922-20022-20022-2-200000000-2-2200-2-2200-2-2220000000022-20022-20022-2-200000000-2-2200-2-2200-2-22200000000
χ3022-20022-200-1-11133−3−30000-2-2200-2-220011-1-1−3−333000022-20022-200-1-11133−3−30000-2-2200-2-220011-1-1−3−3330000
χ3122-20022-200-1-111−3−3330000-2-2200-2-220011-1-133−3−3000022-20022-200-1-111−3−3330000-2-2200-2-220011-1-133−3−30000
χ322-20−i2i22-20−i2i22-200−i2i2−i2i20000-220i2−i2-220i2−i2-2200i2−i2i2−i200002-20−i2i22-20−i2i22-200−i2i2−i2i20000-220i2−i2-220i2−i2-2200i2−i2i2−i20000
χ332-20−i2i22-20−i2i2-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000-220i2−i2-220i2−i21-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300002-20−i2i22-20−i2i2-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000-220i2−i2-220i2−i21-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ342-20−i2i22-20−i2i2-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000-220i2−i2-220i2−i21-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700002-20−i2i22-20−i2i2-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000-220i2−i2-220i2−i21-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ352-20i2−i22-20i2−i22-200i2−i2i2−i20000-220−i2i2-220−i2i2-2200−i2i2−i2i200002-20i2−i22-20i2−i22-200i2−i2i2−i20000-220−i2i2-220−i2i2-2200−i2i2−i2i20000
χ362-20i2−i22-20i2−i2-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000-220−i2i2-220−i2i21-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300002-20i2−i22-20i2−i2-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000-220−i2i2-220−i2i21-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ372-20i2−i22-20i2−i2-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000-220−i2i2-220−i2i21-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700002-20i2−i22-20i2−i2-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000-220−i2i2-220−i2i21-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ3833333-1-1-1-1-10000000011-1-1-3-3-3-3-31111100000000-1-11133333-1-1-1-1-10000000011-1-1-3-3-3-3-31111100000000-1-111
χ3933333-1-1-1-1-100000000-1-111-3-3-3-3-3111110000000011-1-133333-1-1-1-1-100000000-1-111-3-3-3-3-3111110000000011-1-1
χ40333-3-3-1-1-111000000001-1-11-3-3-333111-1-100000000-111-1333-3-3-1-1-111000000001-1-11-3-3-333111-1-100000000-111-1
χ41333-3-3-1-1-11100000000-111-1-3-3-333111-1-1000000001-1-11333-3-3-1-1-11100000000-111-1-3-3-333111-1-1000000001-1-11
χ4266-600-2-2200000000000000-6-660022-20000000000000066-600-2-2200000000000000-6-660022-200000000000000
χ436-60−3i23i2-220i2−i2000000000000-6603i2−3i22-20−i2i20000000000006-60−3i23i2-220i2−i2000000000000-6603i2−3i22-20−i2i2000000000000
χ446-603i2−3i2-220−i2i2000000000000-660−3i23i22-20i2−i20000000000006-603i2−3i2-220−i2i2000000000000-660−3i23i22-20i2−i2000000000000
χ4511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ46111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ47111-1-1111-1-11111-1-1-1-11-11-1111-1-1111-1-11111-1-1-1-11-11-1-1-1-111-1-1-111-1-1-1-11111-11-11-1-1-111-1-1-111-1-1-1-11111-11-11
χ48111-1-1111-1-11111-1-1-1-1-11-11111-1-1111-1-11111-1-1-1-1-11-11-1-1-111-1-1-111-1-1-1-111111-11-1-1-1-111-1-1-111-1-1-1-111111-11-1
χ492222222222-1-1-1-1-1-1-1-100002222222222-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-2-2111111110000-2-2-2-2-2-2-2-2-2-2111111110000
χ50222-2-2222-2-2-1-1-1-111110000222-2-2222-2-2-1-1-1-111110000-2-2-222-2-2-2221111-1-1-1-10000-2-2-222-2-2-2221111-1-1-1-10000
χ5122-20022-20022-2-20000000022-20022-20022-2-200000000-2-2200-2-2200-2-22200000000-2-2200-2-2200-2-22200000000
χ5222-20022-200-1-11133−3−3000022-20022-200-1-11133−3−30000-2-2200-2-220011-1-1−3−3330000-2-2200-2-220011-1-1−3−3330000
χ5322-20022-200-1-111−3−333000022-20022-200-1-111−3−3330000-2-2200-2-220011-1-133−3−30000-2-2200-2-220011-1-133−3−30000
χ542-20−i2i22-20−i2i22-200−i2i2−i2i200002-20−i2i22-20−i2i22-200−i2i2−i2i20000-220i2−i2-220i2−i2-2200i2−i2i2−i20000-220i2−i2-220i2−i2-2200i2−i2i2−i20000
χ552-20−i2i22-20−i2i2-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300002-20−i2i22-20−i2i2-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000-220i2−i2-220i2−i21-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000-220i2−i2-220i2−i21-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ562-20−i2i22-20−i2i2-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700002-20−i2i22-20−i2i2-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000-220i2−i2-220i2−i21-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000-220i2−i2-220i2−i21-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ572-20i2−i22-20i2−i22-200i2−i2i2−i200002-20i2−i22-20i2−i22-200i2−i2i2−i20000-220−i2i2-220−i2i2-2200−i2i2−i2i20000-220−i2i2-220−i2i2-2200−i2i2−i2i20000
χ582-20i2−i22-20i2−i2-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300002-20i2−i22-20i2−i2-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000-220−i2i2-220−i2i21-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000-220−i2i2-220−i2i21-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ592-20i2−i22-20i2−i2-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700002-20i2−i22-20i2−i2-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000-220−i2i2-220−i2i21-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000-220−i2i2-220−i2i21-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ6033333-1-1-1-1-10000000011-1-133333-1-1-1-1-10000000011-1-1-3-3-3-3-31111100000000-1-111-3-3-3-3-31111100000000-1-111
χ6133333-1-1-1-1-100000000-1-11133333-1-1-1-1-100000000-1-111-3-3-3-3-3111110000000011-1-1-3-3-3-3-3111110000000011-1-1
χ62333-3-3-1-1-111000000001-1-11333-3-3-1-1-111000000001-1-11-3-3-333111-1-100000000-111-1-3-3-333111-1-100000000-111-1
χ63333-3-3-1-1-11100000000-111-1333-3-3-1-1-11100000000-111-1-3-3-333111-1-1000000001-1-11-3-3-333111-1-1000000001-1-11
χ6466-600-2-220000000000000066-600-2-2200000000000000-6-660022-200000000000000-6-660022-200000000000000
χ656-60−3i23i2-220i2−i20000000000006-60−3i23i2-220i2−i2000000000000-6603i2−3i22-20−i2i2000000000000-6603i2−3i22-20−i2i2000000000000
χ666-603i2−3i2-220−i2i20000000000006-603i2−3i2-220−i2i2000000000000-660−3i23i22-20i2−i2000000000000-660−3i23i22-20i2−i2000000000000
χ671111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111
χ68111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1
χ69111-1-1111-1-11111-1-1-1-11-11-1-1-1-111-1-1-111-1-1-1-11111-11-11-1-1-111-1-1-111-1-1-1-11111-11-11111-1-1111-1-11111-1-1-1-11-11-1
χ70111-1-1111-1-11111-1-1-1-1-11-11-1-1-111-1-1-111-1-1-1-111111-11-1-1-1-111-1-1-111-1-1-1-111111-11-1111-1-1111-1-11111-1-1-1-1-11-11
χ712222222222-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-2-2111111110000-2-2-2-2-2-2-2-2-2-21111111100002222222222-1-1-1-1-1-1-1-10000
χ72222-2-2222-2-2-1-1-1-111110000-2-2-222-2-2-2221111-1-1-1-10000-2-2-222-2-2-2221111-1-1-1-10000222-2-2222-2-2-1-1-1-111110000
χ7322-20022-20022-2-200000000-2-2200-2-2200-2-22200000000-2-2200-2-2200-2-2220000000022-20022-20022-2-200000000
χ7422-20022-200-1-11133−3−30000-2-2200-2-220011-1-1−3−3330000-2-2200-2-220011-1-1−3−333000022-20022-200-1-11133−3−30000
χ7522-20022-200-1-111−3−3330000-2-2200-2-220011-1-133−3−30000-2-2200-2-220011-1-133−3−3000022-20022-200-1-111−3−3330000
χ762-20−i2i22-20−i2i22-200−i2i2−i2i20000-220i2−i2-220i2−i2-2200i2−i2i2−i20000-220i2−i2-220i2−i2-2200i2−i2i2−i200002-20−i2i22-20−i2i22-200−i2i2−i2i20000
χ772-20−i2i22-20−i2i2-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000-220i2−i2-220i2−i21-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000-220i2−i2-220i2−i21-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300002-20−i2i22-20−i2i2-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ782-20−i2i22-20−i2i2-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000-220i2−i2-220i2−i21-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000-220i2−i2-220i2−i21-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700002-20−i2i22-20−i2i2-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ792-20i2−i22-20i2−i22-200i2−i2i2−i20000-220−i2i2-220−i2i2-2200−i2i2−i2i20000-220−i2i2-220−i2i2-2200−i2i2−i2i200002-20i2−i22-20i2−i22-200i2−i2i2−i20000
χ802-20i2−i22-20i2−i2-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000-220−i2i2-220−i2i21-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000-220−i2i2-220−i2i21-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300002-20i2−i22-20i2−i2-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ812-20i2−i22-20i2−i2-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000-220−i2i2-220−i2i21-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000-220−i2i2-220−i2i21-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700002-20i2−i22-20i2−i2-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ8233333-1-1-1-1-10000000011-1-1-3-3-3-3-31111100000000-1-111-3-3-3-3-31111100000000-1-11133333-1-1-1-1-10000000011-1-1
χ8333333-1-1-1-1-100000000-1-111-3-3-3-3-3111110000000011-1-1-3-3-3-3-3111110000000011-1-133333-1-1-1-1-100000000-1-111
χ84333-3-3-1-1-111000000001-1-11-3-3-333111-1-100000000-111-1-3-3-333111-1-100000000-111-1333-3-3-1-1-111000000001-1-11
χ85333-3-3-1-1-11100000000-111-1-3-3-333111-1-1000000001-1-11-3-3-333111-1-1000000001-1-11333-3-3-1-1-11100000000-111-1
χ8666-600-2-2200000000000000-6-660022-200000000000000-6-660022-20000000000000066-600-2-2200000000000000
χ876-60−3i23i2-220i2−i2000000000000-6603i2−3i22-20−i2i2000000000000-6603i2−3i22-20−i2i20000000000006-60−3i23i2-220i2−i2000000000000
χ886-603i2−3i2-220−i2i2000000000000-660−3i23i22-20i2−i2000000000000-660−3i23i22-20i2−i20000000000006-603i2−3i2-220−i2i2000000000000

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