Finite Group Databasebeta

← Group #10691487

Character table — Group #10691487

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order122244442234444446666666121212121212121244444444441212121212121212121212121212121212121212121212124444444412121212121212121212121212121212888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111111-1-11-1-111-1-11111-1-1-1-11-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-1-1-111111-1-11-1-111-1-11111-1-1-1-11-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-11−ii
χ111111-1-1-1-1-1-111111-1-11-1-111-1-11111-1-1-1-11-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121111-1-1-1-1-1-111111-1-11-1-111-1-11111-1-1-1-11-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131111-1-1-1-1-1-111111-1-11-1-111-1-11111-1-1-1-11-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141111-1-1-1-1-1-111111-1-11-1-111-1-11111-1-1-1-11-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151111-1-1-1-1-1-111111-1-11-1-111-1-11111-1-1-1-11-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111-1-1-1-1-1-111111-1-11-1-111-1-11111-1-1-1-11-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i1-1−ii
χ172222222222222-2-2-2-2222222222222222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-2222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ192222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ202222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ212222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ232222222222-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ242222222222-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ252222222222-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000
χ262222222222-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000
χ2722222222-2-22-2-222222-2-222-2-2-2-2-2-22222-2-2000000000000000022-2-222-2-2000000002-22-200002-22-22-22-200000000000000000000
χ2822222222-2-22-2-222222-2-222-2-2-2-2-2-22222-2-2000000000000000022-2-222-2-200000000-22-220000-22-22-22-2200000000000000000000
χ2922222222-2-22-2-2-2-2-2-22-2-222-2-2-2-2-2-22222220000000000000000-2-222-2-2220000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i000000000000
χ3022222222-2-22-2-2-2-2-2-22-2-222-2-2-2-2-2-22222220000000000000000-2-222-2-222000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000
χ3122222222-2-2-1-2-22222-111-1-1111111-1-1-1-1-2-20000000033−3−333−3−3-1-111-1-11133−3−333−3−32-22-20000-11-11-11-113−3−333−3−33000000000000
χ3222222222-2-2-1-2-22222-111-1-1111111-1-1-1-1-2-20000000033−3−333−3−3-1-111-1-11133−3−333−3−3-22-2200001-11-11-11-1−333−3−333−3000000000000
χ3322222222-2-2-1-2-22222-111-1-1111111-1-1-1-1-2-200000000−3−333−3−333-1-111-1-111−3−333−3−3332-22-20000-11-11-11-11−333−3−333−3000000000000
χ3422222222-2-2-1-2-22222-111-1-1111111-1-1-1-1-2-200000000−3−333−3−333-1-111-1-111−3−333−3−333-22-2200001-11-11-11-13−3−333−3−33000000000000
χ3522222222-2-2-1-2-2-2-2-2-2-111-1-1111111-1-1-1-1220000000033−3−333−3−311-1-111-1-1−3−333−3−33300002i−2i2i−2i−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii000000000000
χ3622222222-2-2-1-2-2-2-2-2-2-111-1-1111111-1-1-1-1220000000033−3−333−3−311-1-111-1-1−3−333−3−3330000−2i2i−2i2ii3−i3−i3i3i3−i3−i3i3i−ii−ii−ii−i000000000000
χ3722222222-2-2-1-2-2-2-2-2-2-111-1-1111111-1-1-1-12200000000−3−333−3−33311-1-111-1-133−3−333−3−300002i−2i2i−2ii3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii000000000000
χ3822222222-2-2-1-2-2-2-2-2-2-111-1-1111111-1-1-1-12200000000−3−333−3−33311-1-111-1-133−3−333−3−30000−2i2i−2i2i−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i000000000000
χ392222-2-2-2-2222-2-222-2-22222222-2-2-2-2-2-2-2-2-22000000000000000022-2-2-2-222000000002-2-2200002-22-2-22-2200000000000000000000
χ402222-2-2-2-2222-2-222-2-22222222-2-2-2-2-2-2-2-2-22000000000000000022-2-2-2-22200000000-222-20000-22-222-22-200000000000000000000
χ412222-2-2-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-22-20000000000000000-2-22222-2-20000000000002-2-22000000002-22-2-22-22000000000000
χ422222-2-2-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-22-20000000000000000-2-22222-2-2000000000000-222-200000000-22-222-22-2000000000000
χ432222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-111111111-2200000000−i3−i3i3i3i3i3−i3−i3-1-11111-1-1−i3−i3i3i3i3i3−i3−i32-2-220000-11-111-11-1−i3i3i3−i3i3−i3−i3i3000000000000
χ442222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-111111111-2200000000−i3−i3i3i3i3i3−i3−i3-1-11111-1-1−i3−i3i3i3i3i3−i3−i3-222-200001-11-1-11-11i3−i3−i3i3−i3i3i3−i3000000000000
χ452222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-111111111-2200000000i3i3−i3−i3−i3−i3i3i3-1-11111-1-1i3i3−i3−i3−i3−i3i3i32-2-220000-11-111-11-1i3−i3−i3i3−i3i3i3−i3000000000000
χ462222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-111111111-2200000000i3i3−i3−i3−i3−i3i3i3-1-11111-1-1i3i3−i3−i3−i3−i3i3i3-222-200001-11-1-11-11−i3i3i3−i3i3−i3−i3i3000000000000
χ472222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-1111111112-200000000−i3−i3i3i3i3i3−i3−i311-1-1-1-111i3i3−i3−i3−i3−i3i3i300002-2-22−i3i3i3−i3i3−i3−i3i3-11-111-11-1000000000000
χ482222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-1111111112-200000000−i3−i3i3i3i3i3−i3−i311-1-1-1-111i3i3−i3−i3−i3−i3i3i30000-222-2i3−i3−i3i3−i3i3i3−i31-11-1-11-11000000000000
χ492222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-1111111112-200000000i3i3−i3−i3−i3−i3i3i311-1-1-1-111−i3−i3i3i3i3i3−i3−i300002-2-22i3−i3−i3i3−i3i3i3−i3-11-111-11-1000000000000
χ502222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-1111111112-200000000i3i3−i3−i3−i3−i3i3i311-1-1-1-111−i3−i3i3i3i3i3−i3−i30000-222-2−i3i3i3−i3i3−i3−i3i31-11-1-11-11000000000000
χ512222-2-2-2-2-2-2222-2-2222-2-222-2-22222-2-2-2-2-222i2i−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ522222-2-2-2-2-2-2222-2-2222-2-222-2-22222-2-2-2-2-22−2i−2i2i2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-2-2-222222i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ532222-2-2-2-2-2-2-12222-2-2-111-1-111-1-1-1-111112-22i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii000000000000
χ542222-2-2-2-2-2-2-12222-2-2-111-1-111-1-1-1-111112-22i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000
χ552222-2-2-2-2-2-2-12222-2-2-111-1-111-1-1-1-111112-2−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000
χ562222-2-2-2-2-2-2-12222-2-2-111-1-111-1-1-1-111112-2−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000
χ572222-2-2-2-2-2-2-122-2-222-111-1-111-1-1-1-11111-222i2i−2i−2i−2i−2i2i2i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i00000000−i3−i3i3i3i3i3−i3−i333−3−3−3−333000000000000
χ582222-2-2-2-2-2-2-122-2-222-111-1-111-1-1-1-11111-222i2i−2i−2i−2i−2i2i2i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i00000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−3000000000000
χ592222-2-2-2-2-2-2-122-2-222-111-1-111-1-1-1-11111-22−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii00000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−3000000000000
χ602222-2-2-2-2-2-2-122-2-222-111-1-111-1-1-1-11111-22−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii00000000i3i3−i3−i3−i3−i3i3i333−3−3−3−333000000000000
χ612-2-2222-2-2-2222-200002-2-2-2-22222-2-222-2-2002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000−i2i2−i2i22−22−20000
χ622-2-2222-2-2-2222-200002-2-2-2-22222-2-222-2-2002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000i2−i2i2−i2−22−220000
χ632-2-2222-2-2-2222-200002-2-2-2-22222-2-222-2-200−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000−i2i2−i2i2−22−220000
χ642-2-2222-2-2-2222-200002-2-2-2-22222-2-222-2-200−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000i2−i2i2−i22−22−20000
χ652-2-22-2-2222-222-20000222-2-2-2-222-2-2-2-222002-2-2200002-22-2-22-220000000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ662-2-22-2-2222-222-20000222-2-2-2-222-2-2-2-222002-2-2200002-22-2-22-220000000000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ672-2-22-2-2222-222-20000222-2-2-2-222-2-2-2-22200-222-20000-22-222-22-20000000000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ682-2-22-2-2222-222-20000222-2-2-2-222-2-2-2-22200-222-20000-22-222-22-20000000000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ6944-4-44i−4i4i−4i004000000-4004-40000004i−4i4i−4i0000002+2i−2−2i2−2i−2+2i00000000000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i000000000000000000000000000000000000
χ7044-4-44i−4i4i−4i004000000-4004-40000004i−4i4i−4i000000−2−2i2+2i−2+2i2−2i0000000000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i000000000000000000000000000000000000
χ7144-4-44i−4i4i−4i00-20000002−2i32i3-22−2i32i323−2323−23−2i2i−2i2i0000002+2i−2−2i2−2i−2+2i0000000000000000−2ζ4+2ζ142ζ4−2ζ14−2ζ20+2ζ222ζ20−2ζ22−2ζ20−2ζ222ζ20+2ζ22−2ζ4−2ζ142ζ4+2ζ14000000000000000000000000000000000000
χ7244-4-44i−4i4i−4i00-20000002−2i32i3-22−2i32i323−2323−23−2i2i−2i2i000000−2−2i2+2i−2+2i2−2i00000000000000002ζ4−2ζ14−2ζ4+2ζ142ζ20−2ζ22−2ζ20+2ζ222ζ20+2ζ22−2ζ20−2ζ222ζ4+2ζ14−2ζ4−2ζ14000000000000000000000000000000000000
χ7344-4-44i−4i4i−4i00-200000022i3−2i3-222i3−2i3−2323−2323−2i2i−2i2i0000002+2i−2−2i2−2i−2+2i0000000000000000−2ζ20+2ζ222ζ20−2ζ22−2ζ4+2ζ142ζ4−2ζ14−2ζ4−2ζ142ζ4+2ζ14−2ζ20−2ζ222ζ20+2ζ22000000000000000000000000000000000000
χ7444-4-44i−4i4i−4i00-200000022i3−2i3-222i3−2i3−2323−2323−2i2i−2i2i000000−2−2i2+2i−2+2i2−2i00000000000000002ζ20−2ζ22−2ζ20+2ζ222ζ4−2ζ14−2ζ4+2ζ142ζ4+2ζ14−2ζ4−2ζ142ζ20+2ζ22−2ζ20−2ζ22000000000000000000000000000000000000
χ7544-4-4−4i4i−4i4i004000000-4004-4000000−4i4i−4i4i0000002−2i−2+2i2+2i−2−2i00000000000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i000000000000000000000000000000000000
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χ7744-4-4−4i4i−4i4i00-20000002−2i32i3-22−2i32i3−2323−23232i−2i2i−2i0000002−2i−2+2i2+2i−2−2i0000000000000000−2ζ4−2ζ142ζ4+2ζ14−2ζ20−2ζ222ζ20+2ζ22−2ζ20+2ζ222ζ20−2ζ22−2ζ4+2ζ142ζ4−2ζ14000000000000000000000000000000000000
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χ974-4-4444-4-4-44-24-40000-22222-2-2-2-222-2-22200−4i4i−4i4i00002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
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χ994-4-44-4-4444-4-24-40000-2-2-22222-2-22222-2-200-444-400002-22-2-22-220000000000000000000000000000000000000000000000000000
χ1004-4-44-4-444-444-4400004-4-4-4-444-4-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-4-444-44-2-440000-22222-2-222-2-222-2-2000000000023−23−2323−232323−230000000000000000000000000000000000000000000000000000
χ1024-4-44-4-444-44-2-440000-22222-2-222-2-222-2-20000000000−232323−2323−23−23230000000000000000000000000000000000000000000000000000

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