Finite Group Databasebeta

← Group #10693836

Character table — Group #10693836

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order122222223444444446666666888888881212121212121212448888121212121212121224242424242424242424242424242424888888882424242424242424242424242424242444444444888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91-1-1111-1-111-1-1-1111-1-1-1-1-11111111-1-1-1-111-1-1-1-1111-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−ii−ii−i
χ101-1-1111-1-111-1-1-1111-1-1-1-1-11111111-1-1-1-111-1-1-1-1111-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−ii−ii
χ111-1-1111-1-111-1-1-1111-1-1-1-1-11111111-1-1-1-111-1-1-1-1111-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−i−ii−ii
χ121-1-1111-1-111-1-1-1111-1-1-1-1-11111111-1-1-1-111-1-1-1-1111-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−i−i−iiiiii−ii−i
χ131-1-1111-1-111-1-1-1111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiiii−i−ii
χ141-1-1111-1-111-1-1-1111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i−iii−i
χ151-1-1111-1-111-1-1-1111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−i−i−i−i−iiiii−iii−i
χ161-1-1111-1-111-1-1-1111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iiiiiii−i−i−i−ii−i−ii
χ17222222222222-2-2-22-222222220000000022222222-2-20000-2-2-2-2-2-2-2-200000000000000000000000000000000000000002222-2-2-2-2000000000000
χ18222222222222-2-2-22-222222220000000022222222-2-20000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-2-2-22222000000000000
χ19222222222-2-2-2222-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ20222222222-2-2-2222-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222200000000-2-2-2-2-2-2-2-222000022-2-222-2-20000000000000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i0000
χ22222222222-2-2-2-2-2-2-2-2222222200000000-2-2-2-2-2-2-2-222000022-2-222-2-2000000000000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000
χ2322222222-122222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ2722222222-1-2-2-2222-22-1-1-1-1-1-1-12222222211111111-2-2-2-2-2-211-1-111-1-1-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−300000000000000000000
χ2822222222-1-2-2-2222-22-1-1-1-1-1-1-12222222211111111-2-2-2-2-2-211-1-111-1-1-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−33300000000000000000000
χ2922222222-1-2-2-2222-22-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-2-2222211-1-111-1-11111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−33300000000000000000000
χ3022222222-1-2-2-2222-22-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-2-2222211-1-111-1-11111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−300000000000000000000
χ312222-2-2-2-2200022-20-222-2-22-2-222-2-222-2-200000000000000002-2002-222-2-2000022-2-200002−22−22−22−22−22−22−22−22−22−22−22−200000000000000000000
χ322222-2-2-2-2200022-20-222-2-22-2-222-2-222-2-200000000000000002-2002-222-2-2000022-2-20000−22−22−22−22−22−22−22−22−22−22−22−2200000000000000000000
χ332222-2-2-2-2200022-20-222-2-22-2-2-2-222-2-22200000000000000002-2002-2-2-2220000-2-22200002−22−2−22−222−22−22−22−2−22−22−22−2200000000000000000000
χ342222-2-2-2-2200022-20-222-2-22-2-2-2-222-2-22200000000000000002-2002-2-2-2220000-2-2220000−22−222−22−2−22−22−22−222−22−22−22−200000000000000000000
χ352222-2-2-2-2-100022-20-2-1-111-11122-2-222-2-23−333−3−33−30000003−3-113−3-11-1-11133−3−3-1-11133−3−32−22−22−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000000000
χ362222-2-2-2-2-100022-20-2-1-111-11122-2-222-2-23−333−3−33−30000003−3-113−3-11-1-11133−3−3-1-11133−3−3−22−22−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000000000
χ372222-2-2-2-2-100022-20-2-1-111-11122-2-222-2-2−33−3−333−33000000−33-11−33-11-1-111−3−333-1-111−3−3332−22−22−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000000000
χ382222-2-2-2-2-100022-20-2-1-111-11122-2-222-2-2−33−3−333−33000000−33-11−33-11-1-111−3−333-1-111−3−333−22−22−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000000000
χ392222-2-2-2-2-100022-20-2-1-111-111-2-222-2-2223−333−3−33−30000003−3-113−3-1111-1-1−3−33311-1-1−3−3332−22−2−22−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000000000
χ402222-2-2-2-2-100022-20-2-1-111-111-2-222-2-2223−333−3−33−30000003−3-113−3-1111-1-1−3−33311-1-1−3−333−22−222−22−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000000000
χ412222-2-2-2-2-100022-20-2-1-111-111-2-222-2-222−33−3−333−33000000−33-11−33-1111-1-133−3−311-1-133−3−32−22−2−22−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000000000
χ422222-2-2-2-2-100022-20-2-1-111-111-2-222-2-222−33−3−333−33000000−33-11−33-1111-1-133−3−311-1-133−3−3−22−222−22−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000000000
χ4322-2-22-22-2222-2000-202-22-2-22-22−22−22−22−2222-22-2-2-2002−22−2000000002−22−22−22−22−22−22−22−20000000000000000000000002-22-200002−22−22−22−20000
χ4422-2-22-22-2222-2000-202-22-2-22-22−22−22−22−2222-22-2-2-2002−22−2000000002−22−22−22−22−22−22−22−2000000000000000000000000-22-220000−22−22−22−220000
χ4522-2-22-22-2222-2000-202-22-2-22-2−22−22−22−22222-22-2-2-200−22−2200000000−22−22−22−22−22−22−22−220000000000000000000000002-22-20000−22−22−22−220000
χ4622-2-22-22-2222-2000-202-22-2-22-2−22−22−22−22222-22-2-2-200−22−2200000000−22−22−22−22−22−22−22−22000000000000000000000000-22-2200002−22−22−22−20000
χ4722-2-22-22-22-2-22000202-22-2-22-22−22−22−22−2-2-2-22-222200−22−22000000002−22−2−22−222−22−2−22−2200000000000000000000000000002i−2i2i−2i−i2i2i2−i2−i2i2i2−i20000
χ4822-2-22-22-22-2-22000202-22-2-22-22−22−22−22−2-2-2-22-222200−22−22000000002−22−2−22−222−22−2−22−220000000000000000000000000000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i20000
χ4922-2-22-22-22-2-22000202-22-2-22-2−22−22−22−22-2-2-22-2222002−22−200000000−22−222−22−2−22−222−22−200000000000000000000000000002i−2i2i−2ii2−i2−i2i2i2−i2−i2i20000
χ5022-2-22-22-22-2-22000202-22-2-22-2−22−22−22−22-2-2-22-2222002−22−200000000−22−222−22−2−22−222−22−20000000000000000000000000000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i20000
χ512-22-22-2-2222-22000-20-22-22-22-22−22−2−22−2222-22-22-2-2002−2−22000000002−22−22−22−2−22−22−22−220000000000000000000000002i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i20000
χ522-22-22-2-2222-22000-20-22-22-22-22−22−2−22−2222-22-22-2-2002−2−22000000002−22−22−22−2−22−22−22−22000000000000000000000000−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i20000
χ532-22-22-2-2222-22000-20-22-22-22-2−22−222−22−222-22-22-2-200−222−200000000−22−22−22−222−22−22−22−20000000000000000000000002i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i20000
χ542-22-22-2-2222-22000-20-22-22-22-2−22−222−22−222-22-22-2-200−222−200000000−22−22−22−222−22−22−22−2000000000000000000000000−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i20000
χ552-22-22-2-222-22-200020-22-22-22-22−22−2−22−22-2-22-22-22200−222−2000000002−22−2−22−22−22−222−22−200000000000000000000000000002-2-22−222−22−2−220000
χ562-22-22-2-222-22-200020-22-22-22-22−22−2−22−22-2-22-22-22200−222−2000000002−22−2−22−22−22−222−22−20000000000000000000000000000-222-22−2−22−222−20000
χ572-22-22-2-222-22-200020-22-22-22-2−22−222−22−2-2-22-22-222002−2−2200000000−22−222−22−22−22−2−22−2200000000000000000000000000002-2-222−2−22−222−20000
χ582-22-22-2-222-22-200020-22-22-22-2−22−222−22−2-2-22-22-222002−2−2200000000−22−222−22−22−22−2−22−220000000000000000000000000000-222-2−222−22−2−220000
χ592-2-2222-2-222-2-22-2-222-2-2-2-22220000000022-2-2-2-222-220000-2-22222-2-200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ602-2-2222-2-222-2-22-2-222-2-2-2-22220000000022-2-2-2-222-220000-2-22222-2-20000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ612-2-2222-2-22-2222-2-2-22-2-2-2-222200000000-2-22222-2-22-200002222-2-2-2-200000000000000000000000000000000000000000000000022-2-2-2-2220000
χ622-2-2222-2-22-2222-2-2-22-2-2-2-222200000000-2-22222-2-22-200002222-2-2-2-2000000000000000000000000000000000000000000000000-2-22222-2-20000
χ632-2-2222-2-22-222-222-2-2-2-2-2-22222222-2-2-2-2-2-22222-2-2-22-2-222-2-2-2-222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ642-2-2222-2-22-222-222-2-2-2-2-2-2222-2-2-2-22222-2-22222-2-2-2222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000
χ652-2-2222-2-2-12-2-2-2222-21111-1-1-12222-2-2-2-2-1-11111-1-12-222-2-2-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-1111100000000000000000000
χ662-2-2222-2-2-12-2-2-2222-21111-1-1-12222-2-2-2-2-1-11111-1-12-222-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-100000000000000000000
χ672-2-2222-2-2-12-2-2-2222-21111-1-1-1-2-2-2-22222-1-11111-1-12-2-2-222-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000
χ682-2-2222-2-2-12-2-2-2222-21111-1-1-1-2-2-2-22222-1-11111-1-12-2-2-222-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000
χ692-2-2222-2-2-1-222-222-2-21111-1-1-12222-2-2-2-211-1-1-1-111-22-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−33300000000000000000000
χ702-2-2222-2-2-1-222-222-2-21111-1-1-12222-2-2-2-211-1-1-1-111-22-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−300000000000000000000
χ712-2-2222-2-2-1-222-222-2-21111-1-1-1-2-2-2-2222211-1-1-1-111-2222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−300000000000000000000
χ722-2-2222-2-2-1-222-222-2-21111-1-1-1-2-2-2-2222211-1-1-1-111-2222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−33300000000000000000000
χ732-2-22-2-2222000-22-202-2-2222-2-222-2-2-2-2220000000000000000-22002-222-2-20000-2-22200002−2−222−2−222−22−2−22−222−22−2−22−2200000000000000000000
χ742-2-22-2-2222000-22-202-2-2222-2-222-2-2-2-2220000000000000000-22002-222-2-20000-2-2220000−222−2−222−2−22−222−22−2−22−222−22−200000000000000000000
χ752-2-22-2-2222000-22-202-2-2222-2-2-2-22222-2-20000000000000000-22002-2-2-222000022-2-200002−2−22−222−22−22−2−22−22−22−222−22−200000000000000000000
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χ9344-4-44-44-4-2-4-4400040-22-222-22−2222−2222−2222−2222222-22-2-2-20022−2222−22000000002−22−2−22−222−22−2−22−2200000000000000000000000000000000000000000000
χ9444-4-4-44-444000000004-4-44-4-4422−22−222222−22−2222000000000000000000000022−22−2222000022−22−2222000000000000000000000000000000000000000000000000
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χ1044-44-4-444-4400000000-444-4-4-4422−22−2222−222222−22000000000000000000000022−22−22220000−222222−22000000000000000000000000000000000000000000000000
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χ1114-4-4444-4-4-2-4444-4-4-442222-2-2-20000000022-2-2-2-2224-40000-2-2-2-22222000000000000000000000000000000000000000000000000000000000000
χ1124-4-44-4-44440004-440-4-4-4444-4-40000000000000000000000004-400-44000000000000000000000000000000000000000000000000000000000000
χ1134-4-44-4-444-20004-440-422-2-2-2220000000023−23−23−23232323−23000000−2323-2223−232-2000000000000000000000000000000000000000000000000000000000000
χ1144-4-44-4-444-20004-440-422-2-2-22200000000−23232323−23−23−232300000023−23-22−23232-2000000000000000000000000000000000000000000000000000000000000

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