Finite Group Databasebeta

← Group #10697113

Character table — Group #10697113

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444448888888888888888888888884848484848484848
order12222234444444466612121212121212121212121244668888888812121212121224242424242424242424242424242424888888882424242424242424242424242424242444444488
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
χ112222222-2-2222-2-22222-2-2-2-22222-2-2-2-2-2-22200000000-2-222-2-2000000000000000022-2-200002222-2-2-2-20000000000000000
χ122222222-2-2222-2-22222-2-2-2-22222-2-2-2-2-2-22200000000-2-222-2-20000000000000000-2-2220000-2-2-2-222220000000000000000
χ132222222-2-2-2-2-222-2222-2-2-2-2-2-2-2-22222-222200000000-2-2-2-222000000000000000000000000000000000000000000002-200
χ142222222-2-2-2-2-222-2222-2-2-2-2-2-2-2-22222-222200000000-2-2-2-22200000000000000000000000000000000000000000000-2200
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
χ19222222-1-2-2222-2-22-1-1-11111-1-1-1-11111-2-2-1-10000000011-1-11133333333−3−3−3−3−3−3−3−322-2-20000-1-1-1-111113333−3−3−3−300000000
χ20222222-1-2-2222-2-22-1-1-11111-1-1-1-11111-2-2-1-10000000011-1-11133333333−3−3−3−3−3−3−3−3-2-22200001111-1-1-1-1−3−3−3−3333300000000
χ21222222-1-2-2222-2-22-1-1-11111-1-1-1-11111-2-2-1-10000000011-1-111−3−3−3−3−3−3−3−33333333322-2-20000-1-1-1-11111−3−3−3−3333300000000
χ22222222-1-2-2222-2-22-1-1-11111-1-1-1-11111-2-2-1-10000000011-1-111−3−3−3−3−3−3−3−333333333-2-22200001111-1-1-1-13333−3−3−3−300000000
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
χ272222-2-22-2-22-2-2222222-2-2-2-2-2-2-2-222222-2-2-2000000002222-2-20000000000000000000022-2-20000000022-2-222-2-200000000
χ282222-2-22-2-22-2-2222222-2-2-2-2-2-2-2-222222-2-2-2000000002222-2-200000000000000000000-2-22200000000-2-222-2-22200000000
χ292222-2-22-2-2-222-2-2-2222-2-2-2-22222-2-2-2-222-2-20000000022-2-222000000000000000000000000000000000000000002-200000
χ302222-2-22-2-2-222-2-2-2222-2-2-2-22222-2-2-2-222-2-20000000022-2-22200000000000000000000000000000000000000000-2200000
χ312222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-22112222-2-2-2-211-1-1-1-1-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−3−3−33300000000
χ322222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-22112222-2-2-2-211-1-1-1-1-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−33333−3−300000000
χ332222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-2211-2-2-2-2222211-1-1-1-11111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−33333−3−300000000
χ342222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-2211-2-2-2-2222211-1-1-1-11111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−3−3−33300000000
χ352222-2-2-1-2-22-2-2222-1-1-111111111-1-1-1-12-21100000000-1-1-1-1113333−3−3−3−3−3−3−3−33333000022-2-2−3−33333−3−3-1-111-1-11100000000
χ362222-2-2-1-2-22-2-2222-1-1-111111111-1-1-1-12-21100000000-1-1-1-1113333−3−3−3−3−3−3−3−333330000-2-22233−3−3−3−33311-1-111-1-100000000
χ372222-2-2-1-2-22-2-2222-1-1-111111111-1-1-1-12-21100000000-1-1-1-111−3−3−3−333333333−3−3−3−3000022-2-233−3−3−3−333-1-111-1-11100000000
χ382222-2-2-1-2-22-2-2222-1-1-111111111-1-1-1-12-21100000000-1-1-1-111−3−3−3−333333333−3−3−3−30000-2-222−3−33333−3−311-1-111-1-100000000
χ392-22-22-2200-22-20022-2-2000022-2-20000002-2−i2−i2i2i2−i2−i2i2i2002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i2−22−200002i−2i2i−2i2−22−22−22−200000000
χ402-22-22-2200-22-20022-2-2000022-2-20000002-2−i2−i2i2i2−i2−i2i2i2002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i−22−220000−2i2i−2i2i−22−22−22−2200000000
χ412-22-22-2200-22-20022-2-2000022-2-20000002-2i2i2−i2−i2i2i2−i2−i2002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i−22−2200002i−2i2i−2i−22−22−22−2200000000
χ422-22-22-2200-22-20022-2-2000022-2-20000002-2i2i2−i2−i2i2i2−i2−i2002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i2−22−20000−2i2i−2i2i2−22−22−22−200000000
χ432-22-22-2-100-22-2002-11133−3−3-1-11133−3−300-11−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−ζ23002i−2i2−22−2−i3i3−i3i3−ii−iiζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000
χ442-22-22-2-100-22-2002-11133−3−3-1-11133−3−300-11−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−ζ2300−2i2i−22−22i3−i3i3−i3i−ii−i−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000
χ452-22-22-2-100-22-2002-11133−3−3-1-11133−3−300-11i2i2−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+ζ23002i−2i−22−22−i3i3−i3i3−ii−ii−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000
χ462-22-22-2-100-22-2002-11133−3−3-1-11133−3−300-11i2i2−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+ζ2300−2i2i2−22−2i3−i3i3−i3i−ii−iζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000
χ472-22-22-2-100-22-2002-111−3−333-1-111−3−33300-11−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−ζ7002i−2i2−22−2i3−i3i3−i3−ii−iiζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000
χ482-22-22-2-100-22-2002-111−3−333-1-111−3−33300-11−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−ζ700−2i2i−22−22−i3i3−i3i3i−ii−i−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000
χ492-22-22-2-100-22-2002-111−3−333-1-111−3−33300-11i2i2−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+ζ7002i−2i−22−22i3−i3i3−i3−ii−ii−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000
χ502-22-22-2-100-22-2002-111−3−333-1-111−3−33300-11i2i2−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+ζ700−2i2i2−22−2−i3i3−i3i3i−ii−iζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000
χ512-22-2-22200-2-220022-2-20000-2-222000000-22−i2−i2i2i2i2i2−i2−i2002-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22i−2i002−2−22−2i2i2i−2i00002−2−222−2−2200000000
χ522-22-2-22200-2-220022-2-20000-2-222000000-22−i2−i2i2i2i2i2−i2−i2002-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−2i2i00−222−22i−2i−2i2i0000−222−2−222−200000000
χ532-22-2-22200-2-220022-2-20000-2-222000000-22i2i2−i2−i2−i2−i2i2i2002-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22i−2i00−222−2−2i2i2i−2i0000−222−2−222−200000000
χ542-22-2-22200-2-220022-2-20000-2-222000000-22i2i2−i2−i2−i2−i2i2i2002-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−2i2i002−2−222i−2i−2i2i00002−2−222−2−2200000000
χ552-22-2-22-100-2-22002-11133−3−311-1-1−3−333001-1−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+ζ232i−2i002−2−22i−i−ii−i3i3i3−i3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ562-22-2-22-100-2-22002-11133−3−311-1-1−3−333001-1−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+ζ23−2i2i00−222−2−iii−ii3−i3−i3i3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ572-22-2-22-100-2-22002-11133−3−311-1-1−3−333001-1i2i2−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−ζ232i−2i00−222−2i−i−ii−i3i3i3−i3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ582-22-2-22-100-2-22002-11133−3−311-1-1−3−333001-1i2i2−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−ζ23−2i2i002−2−22−iii−ii3−i3−i3i3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ592-22-2-22-100-2-22002-111−3−33311-1-133−3−3001-1−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+ζ72i−2i002−2−22i−i−iii3−i3−i3i3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ602-22-2-22-100-2-22002-111−3−33311-1-133−3−3001-1−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+ζ7−2i2i00−222−2−iii−i−i3i3i3−i3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ612-22-2-22-100-2-22002-111−3−33311-1-133−3−3001-1i2i2−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−ζ72i−2i00−222−2i−i−iii3−i3−i3i3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ622-22-2-22-100-2-22002-111−3−33311-1-133−3−3001-1i2i2−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−ζ7−2i2i002−2−22−iii−i−i3i3i3−i3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ63444444-244-4-4-4-4-4-4-2-2-2-2-2-2-2222222224-4-2-200000000-2-22222000000000000000000000000000000000000000000000000
χ64444444-2-4-4-4-4-444-4-2-2-222222222-2-2-2-2-44-2-2000000002222-2-2000000000000000000000000000000000000000000000000
χ654444-4-4-244-44444-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-42200000000222222000000000000000000000000000000000000000000000000
χ664444-4-4-2-4-4-444-4-4-4-2-2-22222-2-2-2-22222442200000000-2-222-2-2000000000000000000000000000000000000000000000000
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.