Finite Group Databasebeta

← Group #10691479

Character table — Group #10691479

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order12224444223444444666121212121212121212121212444444444466121212121212121212121212121212121212121212128888888824242424242424242424242424242424224444442488
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
χ91111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−i-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−i1-1i−i
χ101111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−i-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−i−iii-11−ii
χ111111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−i-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-11-1ii−i−i-11−ii
χ121111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−i-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-11-11−i−iii1-1i−i
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11-1−i−iii−i−iii-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii1-1−ii
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11-1−i−iii−i−iii-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-11-11ii−i−i-11i−i
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11-1−i−iii−i−iii-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-11-1−i−iii-11i−i
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11-1−i−iii−i−iii-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-11-11ii−i−i1-1−ii
χ172222222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
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
χ232222222222-122-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−3000000000000
χ242222222222-122-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−333000000000000
χ252222222222-122-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−333000000000000
χ262222222222-122-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−3000000000000
χ2722222222-2-22-2-22222222222222222222-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000002-2-2200000000
χ2822222222-2-22-2-22222222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-222-200000000
χ2922222222-2-22-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-22222000000000000000000000000000000000000000000002i−2i2i−2i0000
χ3022222222-2-22-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-22222-2-2-2-2-220000000022-2-2-2-222000000000000000000000000000000000000000022-2-200000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-22222-2-2-2-2-220000000022-2-2-2-2220000000000000000000000000000000000000000-2-22200000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-222222-20000000022-2-222-2-2000000000000000000000000000000000000000000002-2-220000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-222222-20000000022-2-222-2-200000000000000000000000000000000000000000000-222-20000
χ352222-2-2-2-2-2-2222-2-222222-2-2-2-2-2-2-2-22222-222i2i−2i−2i−2i−2i2i2i-2-222-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ362222-2-2-2-2-2-2222-2-222222-2-2-2-2-2-2-2-22222-22−2i−2i2i2i2i2i−2i−2i-2-222-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ372222-2-2-2-2-2-2-12222-2-2-1-1-11111-1-1-1-111112-22i2i−2i−2i2i2i−2i−2i11-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii000000000000
χ382222-2-2-2-2-2-2-12222-2-2-1-1-11111-1-1-1-111112-22i2i−2i−2i2i2i−2i−2i11-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000
χ392222-2-2-2-2-2-2-12222-2-2-1-1-11111-1-1-1-111112-2−2i−2i2i2i−2i−2i2i2i11-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000
χ402222-2-2-2-2-2-2-12222-2-2-1-1-11111-1-1-1-111112-2−2i−2i2i2i−2i−2i2i2i11-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000
χ412222-2-2-2-2-2-2-122-2-222-1-1-111111111-1-1-1-1-222i2i−2i−2i−2i−2i2i2i11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000033−3−3−3−333i3i3−i3−i3−i3−i3i3i3000000000000
χ422222-2-2-2-2-2-2-122-2-222-1-1-111111111-1-1-1-1-222i2i−2i−2i−2i−2i2i2i11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000−3−33333−3−3−i3−i3i3i3i3i3−i3−i3000000000000
χ432222-2-2-2-2-2-2-122-2-222-1-1-111111111-1-1-1-1-22−2i−2i2i2i2i2i−2i−2i11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii0000000033−3−3−3−333−i3−i3i3i3i3i3−i3−i3000000000000
χ442222-2-2-2-2-2-2-122-2-222-1-1-111111111-1-1-1-1-22−2i−2i2i2i2i2i−2i−2i11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii00000000−3−33333−3−3i3i3−i3−i3−i3−i3i3i3000000000000
χ452-2-2222-2-22-222-200002-2-222-2-2000000000000002i−2i2i−2i2-22-2000000002i2i−2i−2i00002i2i−2i−2i2−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ462-2-2222-2-22-222-200002-2-222-2-2000000000000002i−2i2i−2i2-22-2000000002i2i−2i−2i00002i2i−2i−2i−22−22i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ472-2-2222-2-22-222-200002-2-222-2-200000000000000−2i2i−2i2i2-22-200000000−2i−2i2i2i0000−2i−2i2i2i2−22−2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ482-2-2222-2-22-222-200002-2-222-2-200000000000000−2i2i−2i2i2-22-200000000−2i−2i2i2i0000−2i−2i2i2i−22−22−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ492-2-2222-2-22-2-12-20000-111-1-11133−3−333−3−30000002i−2i2i−2i-11-113−33−3−i3−i3i3i3−i−iii−i3−i3i3i3−i−iii2−22−2−i2i2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ502-2-2222-2-22-2-12-20000-111-1-11133−3−333−3−30000002i−2i2i−2i-11-113−33−3−i3−i3i3i3−i−iii−i3−i3i3i3−i−iii−22−22i2−i2i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ512-2-2222-2-22-2-12-20000-111-1-11133−3−333−3−3000000−2i2i−2i2i-11-113−33−3i3i3−i3−i3ii−i−ii3i3−i3−i3ii−i−i2−22−2i2−i2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ522-2-2222-2-22-2-12-20000-111-1-11133−3−333−3−3000000−2i2i−2i2i-11-113−33−3i3i3−i3−i3ii−i−ii3i3−i3−i3ii−i−i−22−22−i2i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ532-2-2222-2-22-2-12-20000-111-1-111−3−333−3−3330000002i−2i2i−2i-11-11−33−33i3i3−i3−i3−i−iiii3i3−i3−i3−i−iii2−22−2−i2i2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ542-2-2222-2-22-2-12-20000-111-1-111−3−333−3−3330000002i−2i2i−2i-11-11−33−33i3i3−i3−i3−i−iiii3i3−i3−i3−i−iii−22−22i2−i2i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ552-2-2222-2-22-2-12-20000-111-1-111−3−333−3−333000000−2i2i−2i2i-11-11−33−33−i3−i3i3i3ii−i−i−i3−i3i3i3ii−i−i2−22−2i2−i2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ562-2-2222-2-22-2-12-20000-111-1-111−3−333−3−333000000−2i2i−2i2i-11-11−33−33−i3−i3i3i3ii−i−i−i3−i3i3i3ii−i−i−22−22−i2i2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ572-2-22-2-222-2222-200002-2-2-2-222000000000000002-2-22-222-20000000022-2-20000-2-2222−2−22−222−22−22−2−22−22−22−222−22−2000000000000
χ582-2-22-2-222-2222-200002-2-2-2-222000000000000002-2-22-222-20000000022-2-20000-2-222−222−22−2−22−22−222−22−22−22−2−22−22000000000000
χ592-2-22-2-222-2222-200002-2-2-2-22200000000000000-222-2-222-200000000-2-222000022-2-22−2−222−2−222−22−2−22−222−22−2−22−22000000000000
χ602-2-22-2-222-2222-200002-2-2-2-22200000000000000-222-2-222-200000000-2-222000022-2-2−222−2−222−2−22−222−22−2−22−222−22−2000000000000
χ612-2-22-2-222-22-12-20000-11111-1-133−3−3−3−3330000002-2-221-1-113−3−33−3−333-1-11133−3−311-1-12−2−22−222−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ622-2-22-2-222-22-12-20000-11111-1-133−3−3−3−3330000002-2-221-1-113−3−33−3−333-1-11133−3−311-1-1−222−22−2−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ632-2-22-2-222-22-12-20000-11111-1-133−3−3−3−333000000-222-21-1-113−3−3333−3−311-1-1−3−333-1-1112−2−222−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ642-2-22-2-222-22-12-20000-11111-1-133−3−3−3−333000000-222-21-1-113−3−3333−3−311-1-1−3−333-1-111−222−2−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ652-2-22-2-222-22-12-20000-11111-1-1−3−33333−3−30000002-2-221-1-11−333−333−3−3-1-111−3−33311-1-12−2−22−222−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ662-2-22-2-222-22-12-20000-11111-1-1−3−33333−3−30000002-2-221-1-11−333−333−3−3-1-111−3−33311-1-1−222−22−2−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ672-2-22-2-222-22-12-20000-11111-1-1−3−33333−3−3000000-222-21-1-11−333−3−3−33311-1-133−3−3-1-1112−2−222−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ682-2-22-2-222-22-12-20000-11111-1-1−3−33333−3−3000000-222-21-1-11−333−3−3−33311-1-133−3−3-1-111−222−2−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.