Finite Group Databasebeta

← Group #13165986

Character table — Group #13165986

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222222222222222266881212121212121212121212121212121212121212121212121212161616161616161616161616161616161624242424242424242436108144144216216
order12333346666121212121212121224364466661212121212121212121212121212121212121212333366661212121212121212128242424242424242442121248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1
χ311111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111
χ5222222222222222222222-1-100222222220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000022-1-100
χ6222222222222222222222-1-100222222220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000-2-21100
χ7222222-22222-2-2-2-2-2-2-2-2-222200-2-2-2-22222000000000000000022222222-2-2-2-2-2-2-2-2-2000000000000000
χ8222222-22222-2-2-2-2-2-2-2-2-22-1-100-2-2-2-222220000000000000000-1-1-1-1-1-1-1-111111111100000000000−i3i300
χ9222222-22222-2-2-2-2-2-2-2-2-22-1-100-2-2-2-222220000000000000000-1-1-1-1-1-1-1-111111111100000000000i3−i300
χ10222-1-1-122-1-1-122-1-1-1-1-1-12222222-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12-1-1-12-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1000000
χ11222-1-1-122-1-1-122-1-1-1-1-1-12222-2-22-1-1-12-1-1-1-2-2-2-21111111111112-1-1-12-1-1-1222-1-1-1-1-1-1-2-2-2111111000000
χ12222-1-1-1-22-1-1-1-2-2111111-222200-21112-1-1-10000333333−3−3−3−3−3−32-1-1-12-1-1-1-2-2-2111111000333−3−3−3000000
χ13222-1-1-1-22-1-1-1-2-2111111-222200-21112-1-1-10000−3−3−3−3−3−33333332-1-1-12-1-1-1-2-2-2111111000−3−3−3333000000
χ1422-12-1-12-12-1-1-1-122-1-1-1-1222222-12-1-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1-12-1-1-12-1-12-1-122-1-1-1-12-1-12-1-12-1-1000000
χ1522-12-1-12-12-1-1-1-122-1-1-1-12222-2-2-12-1-1-12-1-11111-2-21111-2-21111-12-1-1-12-1-12-1-122-1-1-1-1-211-211-211000000
χ1622-12-1-1-2-12-1-111-2-21111-2222001-211-12-1-133−3−30033−3−30033−3−3-12-1-1-12-1-1-211-2-2111103−303−303−3000000
χ1722-12-1-1-2-12-1-111-2-21111-2222001-211-12-1-1−3−33300−3−33300−3−333-12-1-1-12-1-1-211-2-211110−330−330−33000000
χ1822-1-12-12-1-12-1-1-1-1-122-1-1222222-1-12-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-122-1-12-1-1-12-12-1-1-1-122-1-12-1-1-12-1-1-12000000
χ1922-1-12-12-1-12-1-1-1-1-122-1-12222-2-2-1-12-1-1-12-1111111-2-2111111-2-2-1-12-1-1-12-12-1-1-1-122-1-1-2111-2111-2000000
χ2022-1-12-1-2-1-12-11111-2-211-22220011-21-1-12-133−3−3−3−3003333−3−300-1-12-1-1-12-1-21111-2-21103−3−3033−30000000
χ2122-1-12-1-2-1-12-11111-2-211-22220011-21-1-12-1−3−3333300−3−3−3−33300-1-12-1-1-12-1-21111-2-2110−3330−3−330000000
χ2222-1-1-122-1-1-12-1-1-1-1-1-122222222-1-1-12-1-1-12-1-1-1-1-1-1-1-122-1-122-1-1-1-1-12-1-1-122-1-1-1-1-1-1222-1-1-1-12-12-1000000
χ2322-1-1-122-1-1-12-1-1-1-1-1-1222222-2-2-1-1-12-1-1-1211111111-2-211-2-211-1-1-12-1-1-122-1-1-1-1-1-122-21111-21-21000000
χ2422-1-1-12-2-1-1-12111111-2-2-222200111-2-1-1-1233−3−333−3−300−3−30033-1-1-12-1-1-12-2111111-2-203−33−30−303000000
χ2522-1-1-12-2-1-1-12111111-2-2-222200111-2-1-1-12−3−333−3−333003300−3−3-1-1-12-1-1-12-2111111-2-20−33−33030−3000000
χ263333333333333333333-1-10011-1-1-1-1-1-1-1-1111111111111111100000000000000000-1-1-1-1-1-1-1-1-13-100-11
χ273333333333333333333-1-10011-1-1-1-1-1-1-1-1111111111111111100000000000000000-1-1-1-1-1-1-1-1-1-31001-1
χ283333333333333333333-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000001111111113-1001-1
χ293333333333333333333-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000111111111-3100-11
χ30444-2-2-244-2-2-244-2-2-2-2-2-244-2-2004-2-2-24-2-2-20000000000000000-2111-2111-2-2-2111111000000000000000
χ31444-2-2-2-44-2-2-2-4-4222222-44-2-200-42224-2-2-20000000000000000-2111-2111222-1-1-1-1-1-1000000000000000
χ3244-24-2-24-24-2-2-2-244-2-2-2-244-2-200-24-2-2-24-2-200000000000000001-2111-211-211-2-21111000000000000000
χ3344-24-2-2-4-24-2-222-4-42222-44-2-2002-422-24-2-200000000000000001-2111-2112-1-122-1-1-1-1000000000000000
χ3444-2-24-24-2-24-2-2-2-2-244-2-244-2-200-2-24-2-2-24-2000000000000000011-2111-21-21111-2-211000000000000000
χ3544-2-24-2-4-2-24-22222-4-422-44-2-20022-42-2-24-2000000000000000011-2111-212-1-1-1-122-1-1000000000000000
χ3644-2-2-244-2-2-24-2-2-2-2-2-24444-2-200-2-2-24-2-2-240000000000000000111-2111-2-2111111-2-2000000000000000
χ3744-2-2-24-4-2-2-24222222-4-4-44-2-200222-4-2-2-240000000000000000111-2111-22-1-1-1-1-1-122000000000000000
χ384-444440-4-4-4-40000000000-222i−2i000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i-2-2-2-22222000000000000000000000000
χ394-444440-4-4-4-40000000000-22−2i2i00000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i-2-2-2-22222000000000000000000000000
χ404-44-2-2-20-42220023−2323−2323−2300-222i−2i000000002i−2i2i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11-21112-1-1-10003−33−33−3000000000000000
χ414-44-2-2-20-42220023−2323−2323−2300-22−2i2i00000000−2i2i−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11-21112-1-1-10003−33−33−3000000000000000
χ424-44-2-2-20-422200−2323−2323−232300-222i−2i000000002i−2i2i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11-21112-1-1-1000−33−33−33000000000000000
χ434-44-2-2-20-422200−2323−2323−232300-22−2i2i00000000−2i2i−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11-21112-1-1-1000−33−33−33000000000000000
χ444-4-24-2-202-42223−230023−23−232300-222i−2i00000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ112i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ112i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ111-211-12-1-103−3003−3−33000000000000000
χ454-4-24-2-202-42223−230023−23−232300-22−2i2i00000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ111-211-12-1-103−3003−3−33000000000000000
χ464-4-24-2-202-422−232300−232323−2300-222i−2i00000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ112i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ112i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ111-211-12-1-10−3300−333−3000000000000000
χ474-4-24-2-202-422−232300−232323−2300-22−2i2i00000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ111-211-12-1-10−3300−333−3000000000000000
χ484-4-2-24-2022-4223−23−23230023−2300-222i−2i00000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ112i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ112i−2i11-21-1-12-103−3−33003−3000000000000000
χ494-4-2-24-2022-4223−23−23230023−2300-22−2i2i00000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−2i2i11-21-1-12-103−3−33003−3000000000000000
χ504-4-2-24-2022-42−232323−2300−232300-222i−2i00000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ112i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ112i−2i11-21-1-12-10−333−300−33000000000000000
χ514-4-2-24-2022-42−232323−2300−232300-22−2i2i00000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−2i2i11-21-1-12-10−333−300−33000000000000000
χ524-4-2-2-240222-423−2323−23−23230000-222i−2i00000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ112i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ112i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11111-2-1-1-1203−33−3−3300000000000000000
χ534-4-2-2-240222-423−2323−23−23230000-22−2i2i00000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11111-2-1-1-1203−33−3−3300000000000000000
χ544-4-2-2-240222-4−2323−232323−230000-222i−2i00000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ112i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ112i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11111-2-1-1-120−33−333−300000000000000000
χ554-4-2-2-240222-4−2323−232323−230000-22−2i2i00000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11111-2-1-1-120−33−333−300000000000000000
χ56666666-66666-6-6-6-6-6-6-6-62-200002222-2-2-2-2000000000000000000000000000000000000000000000000
χ57666-3-3-366-3-3-366-3-3-3-3-3-3-2-20022-2111-21112222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000-2-2-2111111000000
χ58666-3-3-366-3-3-366-3-3-3-3-3-3-2-200-2-2-2111-2111-2-2-2-211111111111100000000000000000222-1-1-1-1-1-1000000
χ59666-3-3-3-66-3-3-3-6-63333332-200002-1-1-1-21110000333333−3−3−3−3−3−300000000000000000000−3−3−3333000000
χ60666-3-3-3-66-3-3-3-6-63333332-200002-1-1-1-21110000−3−3−3−3−3−333333300000000000000000000333−3−3−3000000
χ6166-36-3-36-36-3-3-3-366-3-3-3-3-2-200221-2111-211-1-1-1-122-1-1-1-122-1-1-1-100000000000000000-211-211-211000000
χ6266-36-3-36-36-3-3-3-366-3-3-3-3-2-200-2-21-2111-2111111-2-21111-2-21111000000000000000002-1-12-1-12-1-1000000
χ6366-36-3-3-6-36-3-333-6-633332-20000-12-1-11-21133−3−30033−3−30033−3−3000000000000000000−330−330−33000000
χ6466-36-3-3-6-36-3-333-6-633332-20000-12-1-11-211−3−33300−3−33300−3−3330000000000000000003−303−303−3000000
χ6566-3-36-36-3-36-3-3-3-3-366-3-3-2-2002211-2111-21-1-1-1-1-1-122-1-1-1-1-1-12200000000000000000-2111-2111-2000000
χ6666-3-36-36-3-36-3-3-3-3-366-3-3-2-200-2-211-2111-21111111-2-2111111-2-2000000000000000002-1-1-12-1-1-12000000
χ6766-3-36-3-6-3-36-33333-6-6332-20000-1-12-111-2133−3−3−3−3003333−3−300000000000000000000−3330−3−330000000
χ6866-3-36-3-6-3-36-33333-6-6332-20000-1-12-111-21−3−3333300−3−3−3−333000000000000000000003−3−3033−30000000
χ6966-3-3-366-3-3-36-3-3-3-3-3-366-2-20022111-2111-2-1-1-1-1-1-1-1-122-1-122-1-100000000000000000-21111-21-21000000
χ7066-3-3-366-3-3-36-3-3-3-3-3-366-2-200-2-2111-2111-211111111-2-211-2-211000000000000000002-1-1-1-12-12-1000000
χ7166-3-3-36-6-3-3-36333333-6-62-20000-1-1-12111-233−3−333−3−300−3−30033000000000000000000−33−33030−3000000
χ7266-3-3-36-6-3-3-36333333-6-62-20000-1-1-12111-2−3−333−3−333003300−3−30000000000000000003−33−30−303000000
χ738-888880-8-8-8-800000000002-2000000000000000000000000002222-2-2-2-2000000000000000000000000
χ748-88-4-4-40-84440043−4343−4343−43002-2000000000000000000000000002-1-1-1-2111000−33−33−33000000000000000
χ758-88-4-4-40-844400−4343−4343−4343002-2000000000000000000000000002-1-1-1-21110003−33−33−3000000000000000
χ768-8-48-4-404-84443−430043−43−4343002-200000000000000000000000000-12-1-11-2110−3300−333−3000000000000000
χ778-8-48-4-404-844−434300−434343−43002-200000000000000000000000000-12-1-11-21103−3003−3−33000000000000000
χ788-8-4-48-4044-8443−43−43430043−43002-200000000000000000000000000-1-12-111-210−333−300−33000000000000000
χ798-8-4-48-4044-84−434343−4300−4343002-200000000000000000000000000-1-12-111-2103−3−33003−3000000000000000
χ808-8-4-4-480444-843−4343−43−434300002-200000000000000000000000000-1-1-12111-20−33−333−300000000000000000
χ818-8-4-4-480444-8−4343−434343−4300002-200000000000000000000000000-1-1-12111-203−33−3−3300000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.