Finite Group Databasebeta

← Group #10822394

Character table — Group #10822394

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222444422222234444446666666121212121212121266668888888812121212242424242424242424242424242424242244666688881212121224242424242424242222444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-11-1-1-1-1111111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-11-1-1-1-1111111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ111111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-11-1-1-1-1111111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ121111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-11-1-1-1-1111111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ131111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ141111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ151111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-21111111111110000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111112222-1-1-1-1-2-2-2-2-1-1-1-1111111110000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2-2-2111122221111-1-1-1-1-1-1-1-10000000000000000
χ212222222222-2-2-2-2222-2-2-2-222-2-2-2-222222-2-2-2-222-2-200000000-2-2220000000000000000000000002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i0000000000000000
χ222222222222-2-2-2-2222-2-2-2-222-2-2-2-222222-2-2-2-222-2-200000000-2-222000000000000000000000000−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ232222222222-2-2-2-2-122-2-2-2-2-1-11111-1-1-1-1-11111-1-1110000000011-1-13333−3−3−3−33333−3−3−3−30000−i3i3−i3i32i−2i2i−2i−i3i3−i3i3−i−iii−i−iii0000000000000000
χ242222222222-2-2-2-2-122-2-2-2-2-1-11111-1-1-1-1-11111-1-1110000000011-1-13333−3−3−3−33333−3−3−3−30000i3−i3i3−i3−2i2i−2i2ii3−i3i3−i3ii−i−iii−i−i0000000000000000
χ252222222222-2-2-2-2-122-2-2-2-2-1-11111-1-1-1-1-11111-1-1110000000011-1-1−3−3−3−33333−3−3−3−333330000−i3i3−i3i3−2i2i−2i2i−i3i3−i3i3ii−i−iii−i−i0000000000000000
χ262222222222-2-2-2-2-122-2-2-2-2-1-11111-1-1-1-1-11111-1-1110000000011-1-1−3−3−3−33333−3−3−3−333330000i3−i3i3−i32i−2i2i−2ii3−i3i3−i3−i−iii−i−iii0000000000000000
χ2722222222-2-222-2-22-2-222-2-2222222222222222-2-2-2-222-2-222-2-2-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000
χ2822222222-2-222-2-22-2-222-2-2222222222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
χ2922222222-2-222-2-2-1-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111122-2-222-2-21111-1-111-1-111-1-111-1-1110000−i3i3i3−i30000i3−i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ3022222222-2-222-2-2-1-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111122-2-222-2-21111-1-111-1-111-1-111-1-1110000i3−i3−i3i30000−i3i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ3122222222-2-222-2-2-1-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-222-2-222111111-1-111-1-111-1-111-1-10000−i3i3i3−i30000i3−i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ3222222222-2-222-2-2-1-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-222-2-222111111-1-111-1-111-1-111-1-10000i3−i3−i3i30000−i3i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ3322222222-2-2-2-2222-2-2-2-22222-2-2-2-222222-2-2-2-2-2-2220000000022-2-200000000000000002-2-2222-2-20000-2-222000000000000000000000000
χ3422222222-2-2-2-2222-2-2-2-22222-2-2-2-222222-2-2-2-2-2-2220000000022-2-20000000000000000-222-2-2-222000022-2-2000000000000000000000000
χ3522222222-2-2-2-222-1-2-2-2-222-1-11111-1-1-1-1-1111111-1-100000000-1-11133−3−3−3−33333−3−3−3−3332-2-22-1-111000011-1-13−3−333−3−330000000000000000
χ3622222222-2-2-2-222-1-2-2-2-222-1-11111-1-1-1-1-1111111-1-100000000-1-11133−3−3−3−33333−3−3−3−333-222-211-1-10000-1-111−333−3−333−30000000000000000
χ3722222222-2-2-2-222-1-2-2-2-222-1-11111-1-1-1-1-1111111-1-100000000-1-111−3−33333−3−3−3−33333−3−32-2-22-1-111000011-1-1−333−3−333−30000000000000000
χ3822222222-2-2-2-222-1-2-2-2-222-1-11111-1-1-1-1-1111111-1-100000000-1-111−3−33333−3−3−3−33333−3−3-222-211-1-10000-1-1113−3−333−3−330000000000000000
χ392222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-20000000000000000000000002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-2000000000000000000000000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-10000000011113333−3−3−3−3−3−3−3−333330000−i3i3i3−i32i−2i−2i2i−i3i3i3−i3−i−iiiii−i−i0000000000000000
χ422222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-10000000011113333−3−3−3−3−3−3−3−333330000i3−i3−i3i3−2i2i2i−2ii3−i3−i3i3ii−i−i−i−iii0000000000000000
χ432222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1000000001111−3−3−3−333333333−3−3−3−30000−i3i3i3−i3−2i2i2i−2i−i3i3i3−i3ii−i−i−i−iii0000000000000000
χ442222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1000000001111−3−3−3−333333333−3−3−3−30000i3−i3−i3i32i−2i−2i2ii3−i3−i3i3−i−iiiii−i−i0000000000000000
χ452222-2-2-2-222-2-2-2-2-1-2-22222-1-11111-11111-1-1-1-1-1-1112222-2-2-2-2-1-111-1-1-1-1-1-1-1-1111111112-22-2-1-11122-2-2-1-111-1-1-1-111110000000000000000
χ462222-2-2-2-222-2-2-2-2-1-2-22222-1-11111-11111-1-1-1-1-1-1112222-2-2-2-2-1-111-1-1-1-1-1-1-1-111111111-22-2211-1-1-2-22211-1-11111-1-1-1-10000000000000000
χ472222-2-2-2-222-2-2-2-2-1-2-22222-1-11111-11111-1-1-1-1-1-111-2-2-2-22222-1-11111111111-1-1-1-1-1-1-1-12-22-2-1-111-2-222-1-1111111-1-1-1-10000000000000000
χ482222-2-2-2-222-2-2-2-2-1-2-22222-1-11111-11111-1-1-1-1-1-111-2-2-2-22222-1-11111111111-1-1-1-1-1-1-1-1-22-2211-1-122-2-211-1-1-1-1-1-111110000000000000000
χ492222-2-2-2-2-2-222-2-2222-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000022-2-222220000-2-2-2-2000000000000000000000000
χ502222-2-2-2-2-2-222-2-2222-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000-2-222-2-2-2-200002222000000000000000000000000
χ512222-2-2-2-2-2-222-2-2-122-2-222-1-1-1-1-1-1-111111111111100000000-1-1-1-133−3−3−3−333−3−33333−3−322-2-2-1-1-1-1000011113−3−33−333−30000000000000000
χ522222-2-2-2-2-2-222-2-2-122-2-222-1-1-1-1-1-1-111111111111100000000-1-1-1-133−3−3−3−333−3−33333−3−3-2-22211110000-1-1-1-1−333−33−3−330000000000000000
χ532222-2-2-2-2-2-222-2-2-122-2-222-1-1-1-1-1-1-111111111111100000000-1-1-1-1−3−33333−3−333−3−3−3−33322-2-2-1-1-1-100001111−333−33−3−330000000000000000
χ542222-2-2-2-2-2-222-2-2-122-2-222-1-1-1-1-1-1-111111111111100000000-1-1-1-1−3−33333−3−333−3−3−3−333-2-22211110000-1-1-1-13−3−33−333−30000000000000000
χ552222-2-2-2-2-2-2-2-22222222-2-222-2-2-2-22-2-2-2-22222-2-22222-2-2-2-222-2-22222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-22222222-2-222-2-2-2-22-2-2-2-22222-2-222-2-22222-2-2-2-222-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000
χ572222-2-2-2-2-2-2-2-222-12222-2-2-1-11111-11111-1-1-1-111-1-122-2-2-2-22211-1-1-1-111-1-11111-1-111-1-10000−i3i3−i3i30000i3−i3i3−i3−i3i3−i3i3i3−i3i3−i30000000000000000
χ582222-2-2-2-2-2-2-2-222-12222-2-2-1-11111-11111-1-1-1-111-1-122-2-2-2-22211-1-1-1-111-1-11111-1-111-1-10000i3−i3i3−i30000−i3i3−i3i3i3−i3i3−i3−i3i3−i3i30000000000000000
χ592222-2-2-2-2-2-2-2-222-12222-2-2-1-11111-11111-1-1-1-111-1-1-2-22222-2-211-1-111-1-111-1-1-1-111-1-1110000−i3i3−i3i30000i3−i3i3−i3i3−i3i3−i3−i3i3−i3i30000000000000000
χ602222-2-2-2-2-2-2-2-222-12222-2-2-1-11111-11111-1-1-1-111-1-1-2-22222-2-211-1-111-1-111-1-1-1-111-1-1110000i3−i3i3−i30000−i3i3−i3i3−i3i3−i3i3i3−i3i3−i30000000000000000
χ612-2-2222-2-22-22-22-222-22-22-2-2-222-2-2222-2-222-2-22-22-2000000002-22-20000000000000000000000000000000000000000002-2002-200000000
χ622-2-2222-2-22-22-22-222-22-22-2-2-222-2-2222-2-222-2-22-22-2000000002-22-2000000000000000000000000000000000000000000-2200-2200000000
χ632-2-2222-2-22-2-22-2222-2-22-22-2-2-2-222222-2-2-2-2222-2-2200000000-222-20000000000000000000000000000000000000000000000002-22-20000
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χ662-2-2222-2-2-222-2-222-222-2-22-2-222-2-2222-2-222-2-2-22-2200000000-22-220000000000000000000000000000000000000000-2200-220000000000
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χ8544-4-4−4i4i−4i4i000000-2000000-22−2i32i3−2i32i322i−2i2i−2i−2323−232300000022−22002i2−2i20000002ζ5−2ζ7−2ζ5+2ζ7002ζ13−2ζ23−2ζ13+2ζ2300−2ζ13−2ζ232ζ13+2ζ2300−2ζ5−2ζ72ζ5+2ζ70000000000000000000000000000000000000000
χ8644-4-4−4i4i−4i4i000000-2000000-22−2i32i3−2i32i322i−2i2i−2i−2323−2323000000−222200−2i22i2000000−2ζ5+2ζ72ζ5−2ζ700−2ζ13+2ζ232ζ13−2ζ23002ζ13+2ζ23−2ζ13−2ζ23002ζ5+2ζ7−2ζ5−2ζ70000000000000000000000000000000000000000
χ8744-4-4−4i4i−4i4i000000-2000000-222i3−2i32i3−2i322i−2i2i−2i23−2323−2300000022−22002i2−2i20000002ζ13−2ζ23−2ζ13+2ζ23002ζ5−2ζ7−2ζ5+2ζ700−2ζ5−2ζ72ζ5+2ζ700−2ζ13−2ζ232ζ13+2ζ230000000000000000000000000000000000000000
χ8844-4-4−4i4i−4i4i000000-2000000-222i3−2i32i3−2i322i−2i2i−2i23−2323−23000000−222200−2i22i2000000−2ζ13+2ζ232ζ13−2ζ2300−2ζ5+2ζ72ζ5−2ζ7002ζ5+2ζ7−2ζ5−2ζ7002ζ13+2ζ23−2ζ13−2ζ230000000000000000000000000000000000000000
χ894-44-44i−4i−4i4i0000004000000-440000-44i−4i−4i4i0000000022−2200−2i22i200000022−220022−2200−2i22i200−2i22i2000000000000000000000000000000000000000000
χ904-44-44i−4i−4i4i0000004000000-440000-44i−4i−4i4i00000000−2222002i2−2i2000000−222200−2222002i2−2i2002i2−2i2000000000000000000000000000000000000000000
χ914-44-44i−4i−4i4i000000-20000002-2−2i32i32i3−2i32−2i2i2i−2i23−23−2323000022−2200−2i22i20000002ζ13−2ζ23−2ζ13+2ζ23002ζ5−2ζ7−2ζ5+2ζ7002ζ5+2ζ7−2ζ5−2ζ7002ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000000000000000000000
χ924-44-44i−4i−4i4i000000-20000002-2−2i32i32i3−2i32−2i2i2i−2i23−23−23230000−2222002i2−2i2000000−2ζ13+2ζ232ζ13−2ζ2300−2ζ5+2ζ72ζ5−2ζ700−2ζ5−2ζ72ζ5+2ζ700−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000000000000000000000
χ934-44-44i−4i−4i4i000000-20000002-22i3−2i3−2i32i32−2i2i2i−2i−232323−23000022−2200−2i22i20000002ζ5−2ζ7−2ζ5+2ζ7002ζ13−2ζ23−2ζ13+2ζ23002ζ13+2ζ23−2ζ13−2ζ23002ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000000000000000
χ944-44-44i−4i−4i4i000000-20000002-22i3−2i3−2i32i32−2i2i2i−2i−232323−230000−2222002i2−2i2000000−2ζ5+2ζ72ζ5−2ζ700−2ζ13+2ζ232ζ13−2ζ2300−2ζ13−2ζ232ζ13+2ζ2300−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000000000000000000000
χ954-44-4−4i4i4i−4i0000004000000-440000-4−4i4i4i−4i0000000022−22002i2−2i200000022−220022−22002i2−2i2002i2−2i2000000000000000000000000000000000000000000
χ964-44-4−4i4i4i−4i0000004000000-440000-4−4i4i4i−4i00000000−222200−2i22i2000000−222200−222200−2i22i200−2i22i2000000000000000000000000000000000000000000
χ974-44-4−4i4i4i−4i000000-20000002-2−2i32i32i3−2i322i−2i−2i2i−232323−23000022−22002i2−2i20000002ζ5−2ζ7−2ζ5+2ζ7002ζ13−2ζ23−2ζ13+2ζ2300−2ζ13−2ζ232ζ13+2ζ2300−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000000000000000000000
χ984-44-4−4i4i4i−4i000000-20000002-2−2i32i32i3−2i322i−2i−2i2i−232323−230000−222200−2i22i2000000−2ζ5+2ζ72ζ5−2ζ700−2ζ13+2ζ232ζ13−2ζ23002ζ13+2ζ23−2ζ13−2ζ23002ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000000000000000
χ994-44-4−4i4i4i−4i000000-20000002-22i3−2i3−2i32i322i−2i−2i2i23−23−2323000022−22002i2−2i20000002ζ13−2ζ23−2ζ13+2ζ23002ζ5−2ζ7−2ζ5+2ζ700−2ζ5−2ζ72ζ5+2ζ700−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000000000000000000000
χ1004-44-4−4i4i4i−4i000000-20000002-22i3−2i3−2i32i322i−2i−2i2i23−23−23230000−222200−2i22i2000000−2ζ13+2ζ232ζ13−2ζ2300−2ζ5+2ζ72ζ5−2ζ7002ζ5+2ζ7−2ζ5−2ζ7002ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000000000000000000000
χ1014-4-4444-4-44-44-44-4-24-44-44-422-2-222-2-2-222-2-222-22-2200000000-22-2200000000000000000000000000000000000000000000000000000000
χ1024-4-4444-4-44-4-44-44-24-4-44-442222-2-2-2-2-22222-2-2-222-2000000002-2-2200000000000000000000000000000000000000000000000000000000
χ1034-4-4444-4-4-444-4-44-2-444-4-4422-2-222-2-2-222-2-2222-22-2000000002-22-200000000000000000000000000000000000000000000000000000000
χ1044-4-4444-4-4-44-444-4-2-44-444-42222-2-2-2-2-22222-2-22-2-2200000000-222-200000000000000000000000000000000000000000000000000000000
χ1054-4-44-4-4444-44-44-4-2-44-44-4422-2-222-222-2-222-2-2-22-22000000002-22-200000000000000000000000000000000000000000000000000000000
χ1064-4-44-4-4444-4-44-44-2-444-44-42222-2-2-222-2-2-2-222-222-200000000-222-200000000000000000000000000000000000000000000000000000000
χ1074-4-44-4-444-444-4-44-24-4-444-422-2-222-222-2-222-2-22-22-200000000-22-2200000000000000000000000000000000000000000000000000000000
χ1084-4-44-4-444-44-444-4-24-44-4-442222-2-2-222-2-2-2-2222-2-22000000002-2-2200000000000000000000000000000000000000000000000000000000

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