Finite Group Databasebeta

← Group #10697106

Character table — Group #10697106

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444448888888888888888888888884848484848484848
order12222234444444466612121212121212121212121244668888888812121212121224242424242424242424242424242424888888882424242424242424242424242424242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-111
χ9222222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22-2220000000022-2-2-2-200000000000000000000000000000000000000000000002i−2i
χ10222222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22-2220000000022-2-2-2-20000000000000000000000000000000000000000000000−2i2i
χ112222222-2-22-2-2222222-2-2-2-22222-2-2-2-2-2-22200000000-2-222-2-20000000000000000000022-2-2000000002222-2-2-2-200000000
χ122222222-2-22-2-2222222-2-2-2-22222-2-2-2-2-2-22200000000-2-222-2-200000000000000000000-2-22200000000-2-2-2-2222200000000
χ132222222-2-2-222-2-2-2222-2-2-2-2-2-2-2-22222-222200000000-2-2-2-222000000000000000000000000000000000000000002-200000
χ142222222-2-2-222-2-2-2222-2-2-2-2-2-2-2-22222-222200000000-2-2-2-22200000000000000000000000000000000000000000-2200000
χ15222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ16222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000
χ17222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000
χ18222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000
χ19222222-1-2-22-2-2222-1-1-11111-1-1-1-11111-2-2-1-10000000011-1-11133333333−3−3−3−3−3−3−3−3000022-2-23333−3−3−3−3-1-1-1-1111100000000
χ20222222-1-2-22-2-2222-1-1-11111-1-1-1-11111-2-2-1-10000000011-1-11133333333−3−3−3−3−3−3−3−30000-2-222−3−3−3−333331111-1-1-1-100000000
χ21222222-1-2-22-2-2222-1-1-11111-1-1-1-11111-2-2-1-10000000011-1-111−3−3−3−3−3−3−3−333333333000022-2-2−3−3−3−33333-1-1-1-1111100000000
χ22222222-1-2-22-2-2222-1-1-11111-1-1-1-11111-2-2-1-10000000011-1-111−3−3−3−3−3−3−3−3333333330000-2-2223333−3−3−3−31111-1-1-1-100000000
χ232222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-22-2-22222-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ242222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-22-2-2-2-2-2-22222-2-22222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ252222-2-2222-22222-2222222222222222-2-2-2-200000000-2-2-2-2-2-20000000000000000000000000000000000000000200-20000
χ262222-2-2222-22222-2222222222222222-2-2-2-200000000-2-2-2-2-2-20000000000000000000000000000000000000000-20020000
χ272222-2-22-2-2222-2-22222-2-2-2-2-2-2-2-222222-2-2-2000000002222-2-2000000000000000022-2-2000022-2-222-2-20000000000000000
χ282222-2-22-2-2222-2-22222-2-2-2-2-2-2-2-222222-2-2-2000000002222-2-20000000000000000-2-2220000-2-222-2-2220000000000000000
χ292222-2-22-2-2-2-2-222-2222-2-2-2-22222-2-2-2-222-2-20000000022-2-222000000000000000000000000000000000000000000002-200
χ302222-2-22-2-2-2-2-222-2222-2-2-2-22222-2-2-2-222-2-20000000022-2-22200000000000000000000000000000000000000000000-2200
χ312222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-22112222-2-2-2-211-1-1-1-1-1-1-1-11111-1-1-1-111110000000033−3−3−3−33333−3−333−3−300000000
χ322222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-22112222-2-2-2-211-1-1-1-1-1-1-1-11111-1-1-1-1111100000000−3−33333−3−3−3−333−3−33300000000
χ332222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-2211-2-2-2-2222211-1-1-1-11111-1-1-1-11111-1-1-1-10000000033−3−3−3−333−3−333−3−33300000000
χ342222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-2211-2-2-2-2222211-1-1-1-11111-1-1-1-11111-1-1-1-100000000−3−33333−3−333−3−333−3−300000000
χ352222-2-2-1-2-2222-2-22-1-1-111111111-1-1-1-12-21100000000-1-1-1-1113333−3−3−3−3−3−3−3−3333322-2-20000-1-111-1-111−3−33333−3−300000000
χ362222-2-2-1-2-2222-2-22-1-1-111111111-1-1-1-12-21100000000-1-1-1-1113333−3−3−3−3−3−3−3−33333-2-222000011-1-111-1-133−3−3−3−33300000000
χ372222-2-2-1-2-2222-2-22-1-1-111111111-1-1-1-12-21100000000-1-1-1-111−3−3−3−333333333−3−3−3−322-2-20000-1-111-1-11133−3−3−3−33300000000
χ382222-2-2-1-2-2222-2-22-1-1-111111111-1-1-1-12-21100000000-1-1-1-111−3−3−3−333333333−3−3−3−3-2-222000011-1-111-1-1−3−33333−3−300000000
χ392-2-222-22002002-2-22-2-2000022-2-20000002-2−i2−i2i2i2−i2−i2i2i2002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2002-2−i2i2−i2i2−i2i2−i2i200002-22-200000000
χ402-2-222-22002002-2-22-2-2000022-2-20000002-2−i2−i2i2i2−i2−i2i2i2002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2−i2i2−i200-22i2−i2i2−i2i2−i2i2−i20000-22-2200000000
χ412-2-222-22002002-2-22-2-2000022-2-20000002-2i2i2−i2−i2i2i2−i2−i2002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2i2−i2i200-22−i2i2−i2i2−i2i2−i2i20000-22-2200000000
χ422-2-222-22002002-2-22-2-2000022-2-20000002-2i2i2−i2−i2i2i2−i2−i2002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2002-2i2−i2i2−i2i2−i2i2−i200002-22-200000000
χ432-2-222-2-1002002-2-2-11133−3−3-1-11133−3−300-11−i2−i2i2i2−i2−i2i2i23−3-113−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−i2i2−i2i2002-2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ73−33−3-11-1100000000
χ442-2-222-2-1002002-2-2-11133−3−3-1-11133−3−300-11−i2−i2i2i2−i2−i2i2i23−3-113−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23i2−i2i2−i200-22−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−33−331-11-100000000
χ452-2-222-2-1002002-2-2-11133−3−3-1-11133−3−300-11i2i2−i2−i2i2i2−i2−i23−3-113−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−i2i2−i2i200-22ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−33−331-11-100000000
χ462-2-222-2-1002002-2-2-11133−3−3-1-11133−3−300-11i2i2−i2−i2i2i2−i2−i23−3-113−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23i2−i2i2−i2002-2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ73−33−3-11-1100000000
χ472-2-222-2-1002002-2-2-111−3−333-1-111−3−33300-11−i2−i2i2i2−i2−i2i2i2−33-11−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−i2i2−i2i2002-2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−33−33-11-1100000000
χ482-2-222-2-1002002-2-2-111−3−333-1-111−3−33300-11−i2−i2i2i2−i2−i2i2i2−33-11−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7i2−i2i2−i200-22−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ233−33−31-11-100000000
χ492-2-222-2-1002002-2-2-111−3−333-1-111−3−33300-11i2i2−i2−i2i2i2−i2−i2−33-11−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−i2i2−i2i200-22ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ233−33−31-11-100000000
χ502-2-222-2-1002002-2-2-111−3−333-1-111−3−33300-11i2i2−i2−i2i2i2−i2−i2−33-11−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7i2−i2i2−i2002-2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−33−33-11-1100000000
χ512-2-22-22200200-22-22-2-20000-2-222000000-22−i2−i2i2i2i2i2−i2−i2002-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2i2i2−i22-200−i2i2i2−i2−i2i2i2−i22-2-22000000000000
χ522-2-22-22200200-22-22-2-20000-2-222000000-22−i2−i2i2i2i2i2−i2−i2002-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2-2200i2−i2−i2i2i2−i2−i2i2-222-2000000000000
χ532-2-22-22200200-22-22-2-20000-2-222000000-22i2i2−i2−i2−i2−i2i2i2002-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2-2200−i2i2i2−i2−i2i2i2−i2-222-2000000000000
χ542-2-22-22200200-22-22-2-20000-2-222000000-22i2i2−i2−i2−i2−i2i2i2002-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2−i2−i2i22-200i2−i2−i2i2i2−i2−i2i22-2-22000000000000
χ552-2-22-22-100200-22-2-11133−3−311-1-1−3−333001-1−i2−i2i2i2i2i2−i2−i2−33-113−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−i2i2i2−i22-200ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23-111-1−333−300000000
χ562-2-22-22-100200-22-2-11133−3−311-1-1−3−333001-1−i2−i2i2i2i2i2−i2−i2−33-113−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23i2−i2−i2i2-2200−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ231-1-113−3−3300000000
χ572-2-22-22-100200-22-2-11133−3−311-1-1−3−333001-1i2i2−i2−i2−i2−i2i2i2−33-113−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−i2i2i2−i2-2200ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ231-1-113−3−3300000000
χ582-2-22-22-100200-22-2-11133−3−311-1-1−3−333001-1i2i2−i2−i2−i2−i2i2i2−33-113−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23i2−i2−i2i22-200−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23-111-1−333−300000000
χ592-2-22-22-100200-22-2-111−3−33311-1-133−3−3001-1−i2−i2i2i2i2i2−i2−i23−3-11−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−i2i2i2−i22-200ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7-111-13−3−3300000000
χ602-2-22-22-100200-22-2-111−3−33311-1-133−3−3001-1−i2−i2i2i2i2i2−i2−i23−3-11−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7i2−i2−i2i2-2200−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ71-1-11−333−300000000
χ612-2-22-22-100200-22-2-111−3−33311-1-133−3−3001-1i2i2−i2−i2−i2−i2i2i23−3-11−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−i2i2i2−i2-2200ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ71-1-11−333−300000000
χ622-2-22-22-100200-22-2-111−3−33311-1-133−3−3001-1i2i2−i2−i2−i2−i2i2i23−3-11−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7i2−i2−i2i22-200−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7-111-13−3−3300000000
χ63444444-244-4-4-4-4-4-4-2-2-2-2-2-2-2222222224-4-2-200000000-2-22222000000000000000000000000000000000000000000000000
χ64444444-2-4-4-444-4-4-4-2-2-222222222-2-2-2-2-44-2-2000000002222-2-2000000000000000000000000000000000000000000000000
χ654444-4-4-244-44444-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-42200000000222222000000000000000000000000000000000000000000000000
χ664444-4-4-2-4-4-4-4-444-4-2-2-22222-2-2-2-22222442200000000-2-222-2-2000000000000000000000000000000000000000000000000
χ6744-4-40044-4000000-44-44-44-4000000000000000022−2222−22000000000022−2222−22000022−2222−2200000000000000000000000000000000
χ6844-4-40044-4000000-44-44-44-40000000000000000−2222−22220000000000−2222−22220000−2222−222200000000000000000000000000000000
χ6944-4-4004-44000000-44-4-44-4400000000000022−2222−22000000000022−2222−22000022−2222−22000000000000000000000000000000000000
χ7044-4-4004-44000000-44-4-44-44000000000000−2222−22220000000000−2222−22220000−2222−2222000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.