Finite Group Databasebeta

← Group #10693647

Character table — Group #10693647

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order122244442234444446666666121212121212121244444444441212121212121212121212121212121212121212121212128888888824242424242424242424242424242424888888882488
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
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-11-1i−i
χ101111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1−i−iii-1-111-11−ii
χ111111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-11111ii−i−i11-1-1-11−ii
χ121111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-11111−i−iii-1-1111-1i−i
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-111iiii−i−i−i−i-1-1-1-11111ii−i−i-1-1111-1−ii
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-111iiii−i−i−i−i-1-1-1-11111−i−iii11-1-1-11i−i
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111-11i−i
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-11-1−ii
χ172222222222222-2-2-2-2222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-2222222222222222-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
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
χ212222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ232222222222-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ242222222222-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ252222222222-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-222111111111111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000
χ262222222222-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-222111111111111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000
χ2722222222-2-22-2-22222222-2-2-2-2-2-222-2-222-2-20000000022-2-222-2-200000000000000002-22-200002-22-22-22-200000000000000000000
χ2822222222-2-22-2-22222222-2-2-2-2-2-222-2-222-2-20000000022-2-222-2-20000000000000000-22-220000-22-22-22-2200000000000000000000
χ2922222222-2-22-2-2-2-2-2-2222-2-2-2-2-2-222-2-2222200000000-2-222-2-222000000000000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i000000000000
χ3022222222-2-22-2-2-2-2-2-2222-2-2-2-2-2-222-2-2222200000000-2-222-2-22200000000000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000
χ3122222222-2-2-1-2-22222-1-1-1111111-1-111-1-1-2-200000000-1-111-1-11133−3−333−3−333−3−333−3−32-22-20000-11-11-11-113−3−333−3−33000000000000
χ3222222222-2-2-1-2-22222-1-1-1111111-1-111-1-1-2-200000000-1-111-1-11133−3−333−3−333−3−333−3−3-22-2200001-11-11-11-1−333−3−333−3000000000000
χ3322222222-2-2-1-2-22222-1-1-1111111-1-111-1-1-2-200000000-1-111-1-111−3−333−3−333−3−333−3−3332-22-20000-11-11-11-11−333−3−333−3000000000000
χ3422222222-2-2-1-2-22222-1-1-1111111-1-111-1-1-2-200000000-1-111-1-111−3−333−3−333−3−333−3−333-22-2200001-11-11-11-13−3−333−3−33000000000000
χ3522222222-2-2-1-2-2-2-2-2-2-1-1-1111111-1-111-1-1220000000011-1-111-1-133−3−3−3−33333−3−3−3−33300002i−2i2i−2i−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii000000000000
χ3622222222-2-2-1-2-2-2-2-2-2-1-1-1111111-1-111-1-1220000000011-1-111-1-133−3−3−3−33333−3−3−3−3330000−2i2i−2i2ii3−i3−i3i3i3−i3−i3i3i−ii−ii−ii−i000000000000
χ3722222222-2-2-1-2-2-2-2-2-2-1-1-1111111-1-111-1-1220000000011-1-111-1-1−3−33333−3−3−3−33333−3−300002i−2i2i−2ii3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii000000000000
χ3822222222-2-2-1-2-2-2-2-2-2-1-1-1111111-1-111-1-1220000000011-1-111-1-1−3−33333−3−3−3−33333−3−30000−2i2i−2i2i−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i000000000000
χ392222-2-2-2-2222-2-222-2-22222222-2-2-2-2-2-2-2-2-220000000022-2-2-2-22200000000000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ402222-2-2-2-2222-2-222-2-22222222-2-2-2-2-2-2-2-2-220000000022-2-2-2-2220000000000000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ412222-2-2-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-22-200000000-2-22222-2-2000000000000000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i000000000000
χ422222-2-2-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-22-200000000-2-22222-2-200000000000000000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i000000000000
χ432222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-111111111-2200000000-1-11111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i32i−2i−2i2i0000−ii−iii−ii−i−333−33−3−33000000000000
χ442222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-111111111-2200000000-1-11111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−2i2i2i−2i0000i−ii−i−ii−ii3−3−33−333−3000000000000
χ452222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-111111111-2200000000-1-11111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i32i−2i−2i2i0000−ii−iii−ii−i3−3−33−333−3000000000000
χ462222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-111111111-2200000000-1-11111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3−2i2i2i−2i0000i−ii−i−ii−ii−333−33−3−33000000000000
χ472222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-1111111112-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300002i−2i−2i2i−333−33−3−33−ii−iii−ii−i000000000000
χ482222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-1111111112-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000−2i2i2i−2i3−3−33−333−3i−ii−i−ii−ii000000000000
χ492222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-1111111112-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300002i−2i−2i2i3−3−33−333−3−ii−iii−ii−i000000000000
χ502222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-1111111112-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000−2i2i2i−2i−333−33−3−33i−ii−i−ii−ii000000000000
χ512222-2-2-2-2-2-2222-2-222222-2-2-2-222-2-222-2-2-222i2i−2i−2i−2i−2i2i2i-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ522222-2-2-2-2-2-2222-2-222222-2-2-2-222-2-222-2-2-22−2i−2i2i2i2i2i−2i−2i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ532222-2-2-2-2-2-2-12222-2-2-1-1-11111-1-111-1-1112-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii2i2i−2i−2i22-2-2−i−i−i−iiiii-1-1-1-11111000000000000
χ542222-2-2-2-2-2-2-12222-2-2-1-1-11111-1-111-1-1112-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−2i−2i2i2i-2-222iiii−i−i−i−i1111-1-1-1-1000000000000
χ552222-2-2-2-2-2-2-12222-2-2-1-1-11111-1-111-1-1112-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i2i2i−2i−2i-2-222−i−i−i−iiiii1111-1-1-1-1000000000000
χ562222-2-2-2-2-2-2-12222-2-2-1-1-11111-1-111-1-1112-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−2i−2i2i2i22-2-2iiii−i−i−i−i-1-1-1-11111000000000000
χ572222-2-2-2-2-2-2-122-2-222-1-1-11111-1-111-1-111-222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000033−3−3−3−333−i3−i3i3i3i3i3−i3−i3000000000000
χ582222-2-2-2-2-2-2-122-2-222-1-1-11111-1-111-1-111-222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000−3−33333−3−3i3i3−i3−i3−i3−i3i3i3000000000000
χ592222-2-2-2-2-2-2-122-2-222-1-1-11111-1-111-1-111-22−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000033−3−3−3−333i3i3−i3−i3−i3−i3i3i3000000000000
χ602222-2-2-2-2-2-2-122-2-222-1-1-11111-1-111-1-111-22−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000−3−33333−3−3−i3−i3i3i3i3i3−i3−i3000000000000
χ612-2-2222-2-22-222-200002-2-222-2-222-2-2-2-22200002i−2i002i−2i0000000000002i−2i2i−2i00002i−2i2i−2i0000000000000000000000002−22−2−i2i2−i2i20000
χ622-2-2222-2-22-222-200002-2-222-2-222-2-2-2-22200002i−2i002i−2i0000000000002i−2i2i−2i00002i−2i2i−2i000000000000000000000000−22−22i2−i2i2−i20000
χ632-2-2222-2-22-222-200002-2-222-2-222-2-2-2-2220000−2i2i00−2i2i000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000000000002−22−2i2−i2i2−i20000
χ642-2-2222-2-22-222-200002-2-222-2-222-2-2-2-2220000−2i2i00−2i2i000000000000−2i2i−2i2i0000−2i2i−2i2i000000000000000000000000−22−22−i2i2−i2i20000
χ652-2-22-2-222-2222-200002-2-2-2-2222222-2-2-2-200002-200-220000000000002-22-20000-22-22000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ662-2-22-2-222-2222-200002-2-2-2-2222222-2-2-2-200002-200-220000000000002-22-20000-22-22000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ672-2-22-2-222-2222-200002-2-2-2-2222222-2-2-2-20000-22002-2000000000000-22-2200002-22-2000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ682-2-22-2-222-2222-200002-2-2-2-2222222-2-2-2-20000-22002-2000000000000-22-2200002-22-2000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ6944-4-44i−4i4i−4i004000000-44-40000004i−4i004i−4i002+2i−2−2i002−2i−2+2i00000000002+2i−2−2i2+2i−2−2i00002−2i−2+2i2−2i−2+2i0000000000000000000000000000000000000000
χ7044-4-44i−4i4i−4i004000000-44-40000004i−4i004i−4i00−2−2i2+2i00−2+2i2−2i0000000000−2−2i2+2i−2−2i2+2i0000−2+2i2−2i−2+2i2−2i0000000000000000000000000000000000000000
χ7144-4-44i−4i4i−4i00-20000002-22−2i32i3−2i32i323−23−2i2i23−23−2i2i002+2i−2−2i002−2i−2+2i0000000000−2ζ4+2ζ142ζ4−2ζ14−2ζ20+2ζ222ζ20−2ζ220000−2ζ20−2ζ222ζ20+2ζ22−2ζ4−2ζ142ζ4+2ζ140000000000000000000000000000000000000000
χ7244-4-44i−4i4i−4i00-20000002-22−2i32i3−2i32i323−23−2i2i23−23−2i2i00−2−2i2+2i00−2+2i2−2i00000000002ζ4−2ζ14−2ζ4+2ζ142ζ20−2ζ22−2ζ20+2ζ2200002ζ20+2ζ22−2ζ20−2ζ222ζ4+2ζ14−2ζ4−2ζ140000000000000000000000000000000000000000
χ7344-4-44i−4i4i−4i00-20000002-222i3−2i32i3−2i3−2323−2i2i−2323−2i2i002+2i−2−2i002−2i−2+2i0000000000−2ζ20+2ζ222ζ20−2ζ22−2ζ4+2ζ142ζ4−2ζ140000−2ζ4−2ζ142ζ4+2ζ14−2ζ20−2ζ222ζ20+2ζ220000000000000000000000000000000000000000
χ7444-4-44i−4i4i−4i00-20000002-222i3−2i32i3−2i3−2323−2i2i−2323−2i2i00−2−2i2+2i00−2+2i2−2i00000000002ζ20−2ζ22−2ζ20+2ζ222ζ4−2ζ14−2ζ4+2ζ1400002ζ4+2ζ14−2ζ4−2ζ142ζ20+2ζ22−2ζ20−2ζ220000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.