Finite Group Databasebeta

← Group #11781594

Character table — Group #11781594

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222222224444444444444444466668888888888888888888888812121212121212121212121212122424242424242424242436363636484848144
order1222334444666666121212123466612121212121212121212121288888812121212122424242424242424242424242424242488888824242424242424248824242424242424244444412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-1-1-111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1
χ61111111111111111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11
χ71111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111-1
χ92222222-22-222222222222-22222-2-2-222222-2-2-2000000-2-2-2-2-2000000000000000000000000000000000000000022-2-20000
χ102222222-22-222222222222-22222-2-2-222222-2-2-2000000-2-2-2-2-20000000000000000000000000000000000000000-2-2220000
χ11222222-22-22222222-2-2-2-22-2222-2-2-22-2-2-2-2-2222222200-222-2-20000000000000000-2-200002222-2-2-2-2000000000000000000
χ12222222-22-22222222-2-2-2-22-2222-2-2-22-2-2-2-2-2222-2-2-2-200-222-2-20000000000000000220000-2-2-2-22222000000000000000000
χ13222222-2-2-2-2222222-2-2-2-222222-222-2-2-2-2-2-2-2-2-20000002-2-2220000000000000000002i2i−2i−2i000000000000002i2i−2i−2i00000000
χ14222222-2-2-2-2222222-2-2-2-222222-222-2-2-2-2-2-2-2-2-20000002-2-222000000000000000000−2i−2i2i2i00000000000000−2i−2i2i2i00000000
χ1522222-12222222-1-1-12222-12-1-1-1-122-1-1-1-1-1-122-1000022-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100222200000000000000-1-1-1-100002-1-10
χ1622222-12222222-1-1-12222-12-1-1-1-122-1-1-1-1-1-122-1000022-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-20000000000000011110000-2110
χ1722222-12222222-1-1-12222-12-1-1-1-122-1-1-1-1-1-122-10000-2-2-1-1-1-1-1-2-2-2-211111111111100222200000000000000-1-1-1-10000-2110
χ1822222-12222222-1-1-12222-12-1-1-1-122-1-1-1-1-1-122-10000-2-2-1-1-1-1-1-2-2-2-211111111111100-2-2-2-200000000000000111100002-1-10
χ1922222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-1122111111-2-21000000-111-1-10000333333−3−3−3−3−3−3002i2i−2i−2i00000000000000−i−iii00000−i3i30
χ2022222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-1122111111-2-21000000-111-1-10000333333−3−3−3−3−3−300−2i−2i2i2i00000000000000ii−i−i00000i3−i30
χ2122222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-1122111111-2-21000000-111-1-10000−3−3−3−3−3−3333333002i2i−2i−2i00000000000000−i−iii00000i3−i30
χ2222222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-1122111111-2-21000000-111-1-10000−3−3−3−3−3−333333300−2i−2i2i2i00000000000000ii−i−i00000−i3i30
χ232222-122222-1-1-1222-1-1-1-1-12-1-1-12-1-12-1-12-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ242222-122222-1-1-1222-1-1-1-1-12-1-1-12-1-12-1-12-1-1-1-122222-2-22-1-1-1-11111-2-21111-2-21111220000-1-1-1-1-1-1-1-1-2-21111000000000000
χ252222-122222-1-1-1222-1-1-1-1-12-1-1-12-1-12-1-12-1-1-1-12-2-2-2-2222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2000011111111-2-21111000000000000
χ262222-122222-1-1-1222-1-1-1-1-12-1-1-12-1-12-1-12-1-1-1-12-2-2-2-2-2-22-1-1-1-11111-2-21111-2-21111-2-200001111111122-1-1-1-1000000000000
χ272222-12-22-22-1-1-12221111-1-2-1-1-1-211211-211-1-12222200-2-1-11133−3−30033−3−30033−3−3-2-20000-1-1-1-111110033−3−3000000000000
χ282222-12-22-22-1-1-12221111-1-2-1-1-1-211211-211-1-12222200-2-1-111−3−33300−3−33300−3−333-2-20000-1-1-1-1111100−3−333000000000000
χ292222-12-22-22-1-1-12221111-1-2-1-1-1-211211-211-1-12-2-2-2-200-2-1-11133−3−30033−3−30033−3−32200001111-1-1-1-100−3−333000000000000
χ302222-12-22-22-1-1-12221111-1-2-1-1-1-211211-211-1-12-2-2-2-200-2-1-111−3−33300−3−33300−3−3332200001111-1-1-1-10033−3−3000000000000
χ3122-2-2220-2022-2-2-2-220000202-2-2000-2000002-222i2i−2i−2i2−202-2002−22−22−22−22−22−22−22−20000002i2i−2i−2i0000−i2i2−i2i2−i2i2000000000000
χ3222-2-2220-2022-2-2-2-220000202-2-2000-2000002-222i2i−2i−2i−2202-200−22−22−22−22−22−22−22−220000002i2i−2i−2i0000i2−i2i2−i2i2−i2000000000000
χ3322-2-2220-2022-2-2-2-220000202-2-2000-2000002-22−2i−2i2i2i2−202-2002−22−22−22−22−22−22−22−2000000−2i−2i2i2i0000i2−i2i2−i2i2−i2000000000000
χ3422-2-2220-2022-2-2-2-220000202-2-2000-2000002-22−2i−2i2i2i−2202-200−22−22−22−22−22−22−22−22000000−2i−2i2i2i0000−i2i2−i2i2−i2i2000000000000
χ3522-2-2-120-202-111-2-223−33−3-10-11103−3-23−303−3-1122i2i−2i−2i2−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000−i−iii−i3−i3i3i3−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ3622-2-2-120-202-111-2-223−33−3-10-11103−3-23−303−3-1122i2i−2i−2i−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000−i−iii−i3−i3i3i3i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ3722-2-2-120-202-111-2-223−33−3-10-11103−3-23−303−3-112−2i−2i2i2i2−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000ii−i−ii3i3−i3−i3i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ3822-2-2-120-202-111-2-223−33−3-10-11103−3-23−303−3-112−2i−2i2i2i−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000ii−i−ii3i3−i3−i3−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ3922-2-2-120-202-111-2-22−33−33-10-1110−33-2−330−33-1122i2i−2i−2i2−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000−i−iiii3i3−i3−i3−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ4022-2-2-120-202-111-2-22−33−33-10-1110−33-2−330−33-1122i2i−2i−2i−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000−i−iiii3i3−i3−i3i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ4122-2-2-120-202-111-2-22−33−33-10-1110−33-2−330−33-112−2i−2i2i2i2−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000ii−i−i−i3−i3i3i3i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ4222-2-2-120-202-111-2-22−33−33-10-1110−33-2−330−33-112−2i−2i2i2i−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000ii−i−i−i3−i3i3i3−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ432-22-22220-20-22-22-2-222-2-220-22-2200022-2-2-20002−22−2000000000000000000000002−22−22−22−22−22−22−20000002−22−22-2000000
χ442-22-22220-20-22-22-2-222-2-220-22-2200022-2-2-20002−22−2000000000000000000000002−2−22−222−22−22−22−2000000−22−22-22000000
χ452-22-22220-20-22-22-2-222-2-220-22-2200022-2-2-2000−22−2200000000000000000000000−222−22−2−22−22−22−220000002−22−2-22000000
χ462-22-22220-20-22-22-2-222-2-220-22-2200022-2-2-2000−22−2200000000000000000000000−22−22−22−22−22−22−22000000−22−222-2000000
χ472-22-222-2020-22-22-2-2-2-22220-22-2-2000-2-22220002−22−200000000000000000000000−22−i2i2i2−i22−22−2−22−22000000−i2i2i2−i2002i−2i0000
χ482-22-222-2020-22-22-2-2-2-22220-22-2-2000-2-22220002−22−200000000000000000000000−22i2−i2−i2i22−22−2−22−22000000i2−i2−i2i200−2i2i0000
χ492-22-222-2020-22-22-2-2-2-22220-22-2-2000-2-2222000−22−22000000000000000000000002−2−i2i2i2−i2−22−222−22−2000000−i2i2i2−i200−2i2i0000
χ502-22-222-2020-22-22-2-2-2-22220-22-2-2000-2-2222000−22−22000000000000000000000002−2i2−i2−i2i2−22−222−22−2000000i2−i2−i2i2002i−2i0000
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χ554444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-211-211-2-2-2000044-21111-2-2-2-2-2-21111-2-2111100000000000000000000000000000000
χ564444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-211-211-2-2-20000-4-4-21111222222-1-1-1-122-1-1-1-100000000000000000000000000000000
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χ594444-2-2-44-44-2-2-2-2-2-222221-4111222-2-1-12-1-1-2-2-2000000211-1-12323−23−2300−3−33300−3−33300000000000000000000000000000000
χ604444-2-2-44-44-2-2-2-2-2-222221-4111222-2-1-12-1-1-2-2-2000000211-1-1−23−2323230033−3−30033−3−300000000000000000000000000000000
χ614444-2-2-4-4-4-4-2-2-2-2-2-22222141112-2-22-1-12-1-1222000000-2-1-11100002323−3−3−3−3−23−23333300000000000000000000000000000000
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χ7144-4-4-2-2040-4-22222-223−2323−23101-1-10−2323-2−330−332-220000000-113−30000−66−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ236−6ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ2300000000000000000000000000000000
χ7244-4-4-2-2040-4-22222-2−2323−2323101-1-1023−23-23−303−32-220000000-11−3300006−6−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−662ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ2300000000000000000000000000000000
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χ914-4-44-24000022-2-44-4−232323−23-2022-20000−2323023−230002i2−2i2−2i22i200000000000000000000000000000−i2i2i2−i2i6−i6−i6i6000000000000000000
χ928-88-8-4-480-804-44-444-4-44420-22-2-4000224-2-200000000000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-80804-44-44444-4-420-22-24000-2-2-42200000000000000000000000000000000000000000000000000000000000000
χ948-8-888-40000-8-884-440000-4044-400000000000000000000000000000000000000000000000000000000000000000000000
χ958-8-88-4-4000044-44-4443−43−434320-2-220000−2323023−2300000000000000000000000000000000000000000000000000000000000000
χ968-8-88-4-4000044-44-44−434343−4320-2-22000023−230−232300000000000000000000000000000000000000000000000000000000000000

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