Finite Group Databasebeta

← Group #10714301

Character table — Group #10714301

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444448888888888888888888888884848484848484848
order1222223444466688881212121224242424242424244444668888881212121212121212121224242424242424242424242416161616161616164848484848484848484848484848484824444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ8111111111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ922222222222222-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1022222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-222222-2-2-2-2-2-2-2-22-2-2-2-22222222200000000000000000000000000000000
χ11222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ12222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000
χ13222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-2-2-111111111-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000
χ14222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-2-2-111111111-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000
χ15222222-12222-1-1-1-2-2-2-2-1-1-1-1111111112222-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111000000003333−3−3−3−33333−3−3−3−300000000
χ16222222-12222-1-1-1-2-2-2-2-1-1-1-1111111112222-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000−3−3−3−33333−3−3−3−3333300000000
χ17222222-12222-1-1-1-2-2-2-2-1-1-1-111111111-2-2-2-2-1-1-2-22222-111111111-11111-1-1-1-1-1-1-1-1000000003333−3−3−3−3−3−3−3−3333300000000
χ18222222-12222-1-1-1-2-2-2-2-1-1-1-111111111-2-2-2-2-1-1-2-22222-111111111-11111-1-1-1-1-1-1-1-100000000−3−3−3−333333333−3−3−3−300000000
χ192222-2-2222-2-222222222222222222220000-2-2-2-20000-200000000-2-2-2-2-2000000000000000000000000000000000000002i−2i
χ202222-2-2222-2-222222222222222222220000-2-2-2-20000-200000000-2-2-2-2-200000000000000000000000000000000000000−2i2i
χ212222-2-2222-2-2222-2-2-2-22222-2-2-2-2-2-2-2-20000-2-2220000-200000000-22222000000000000000000000000000000002-2000000
χ222222-2-2222-2-2222-2-2-2-22222-2-2-2-2-2-2-2-20000-2-2220000-200000000-2222200000000000000000000000000000000-22000000
χ232222-2-22-2-2222220000-2-2-2-2000000000000-2-20022-2-2200000000200002222-2-2-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ242222-2-22-2-2222220000-2-2-2-2000000000000-2-20022-2-2200000000200002222-2-2-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ252222-2-22-2-2222220000-2-2-2-2000000000000-2-200-2-22220000000020000-2-2-2-22222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ262222-2-22-2-2222220000-2-2-2-2000000000000-2-200-2-22220000000020000-2-2-2-22222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ272222-2-2-1-2-222-1-1-1000011113333−3−3−3−30000110022-2-2-13333−3−3−3−3-133−3−3-1-1-1-11111−i2−i2i2i2−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000
χ282222-2-2-1-2-222-1-1-1000011113333−3−3−3−30000110022-2-2-13333−3−3−3−3-133−3−3-1-1-1-11111i2i2−i2−i2i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000
χ292222-2-2-1-2-222-1-1-1000011113333−3−3−3−300001100-2-222-1−3−3−3−33333-133−3−31111-1-1-1-1−i2−i2i2i2i2i2−i2−i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000
χ302222-2-2-1-2-222-1-1-1000011113333−3−3−3−300001100-2-222-1−3−3−3−33333-133−3−31111-1-1-1-1i2i2−i2−i2−i2−i2i2i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000
χ312222-2-2-1-2-222-1-1-100001111−3−3−3−333330000110022-2-2-1−3−3−3−33333-1−3−333-1-1-1-11111−i2−i2i2i2−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000
χ322222-2-2-1-2-222-1-1-100001111−3−3−3−333330000110022-2-2-1−3−3−3−33333-1−3−333-1-1-1-11111i2i2−i2−i2i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000
χ332222-2-2-1-2-222-1-1-100001111−3−3−3−3333300001100-2-222-13333−3−3−3−3-1−3−3331111-1-1-1-1−i2−i2i2i2i2i2−i2−i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000
χ342222-2-2-1-2-222-1-1-100001111−3−3−3−3333300001100-2-222-13333−3−3−3−3-1−3−3331111-1-1-1-1i2i2−i2−i2−i2−i2i2i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000
χ352-2-222-22-22-22-2-2222-2-2-2-22222-2-222-2-200002-22-20000200000000-22-22-20000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i00000000
χ362-2-222-22-22-22-2-2222-2-2-2-22222-2-222-2-200002-22-20000200000000-22-22-2000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i00000000
χ372-2-222-22-22-22-2-22-2-222-2-222-2-222-2-22200002-2-220000200000000-2-22-22000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i0000000000000000
χ382-2-222-22-22-22-2-22-2-222-2-222-2-222-2-22200002-2-220000200000000-2-22-2200000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ392-2-222-2-1-22-2211-122-2-211-1-1-1-111-1-1110000-112-20000-133−3−333−3−31-11-1133−3−333−3−300002i−2i2i−2i−i3i3−i3i3i3−i3i3−i3−ii−ii−ii−ii00000000
χ402-2-222-2-1-22-2211-122-2-211-1-1-1-111-1-1110000-112-20000-133−3−333−3−31-11-1133−3−333−3−30000−2i2i−2i2ii3−i3i3−i3−i3i3−i3i3i−ii−ii−ii−i00000000
χ412-2-222-2-1-22-2211-122-2-211-1-1-1-111-1-1110000-112-20000-1−3−333−3−3331-11-11−3−333−3−33300002i−2i2i−2ii3−i3i3−i3−i3i3−i3i3−ii−ii−ii−ii00000000
χ422-2-222-2-1-22-2211-122-2-211-1-1-1-111-1-1110000-112-20000-1−3−333−3−3331-11-11−3−333−3−3330000−2i2i−2i2i−i3i3−i3i3i3−i3i3−i3i−ii−ii−ii−i00000000
χ432-2-222-2-1-22-2211-1-2-22211-1-111-1-111-1-10000-11-220000-133−3−333−3−311-11-1−3−333−3−3332i−2i2i−2i0000−ii−ii−ii−iii3−i3i3−i3−i3i3−i3i300000000
χ442-2-222-2-1-22-2211-1-2-22211-1-111-1-111-1-10000-11-220000-133−3−333−3−311-11-1−3−333−3−333−2i2i−2i2i0000i−ii−ii−ii−i−i3i3−i3i3i3−i3i3−i300000000
χ452-2-222-2-1-22-2211-1-2-22211-1-111-1-111-1-10000-11-220000-1−3−333−3−33311-11-133−3−333−3−32i−2i2i−2i0000−ii−ii−ii−ii−i3i3−i3i3i3−i3i3−i300000000
χ462-2-222-2-1-22-2211-1-2-22211-1-111-1-111-1-10000-11-220000-1−3−333−3−33311-11-133−3−333−3−3−2i2i−2i2i0000i−ii−ii−ii−ii3−i3i3−i3−i3i3−i3i300000000
χ472-2-22-2222-2-22-2-22000022-2-20000000022-2-2-22000000222-2-2-2-222-20000000000002−2−222−2−222−2−222−2−222−2−222−2−2200000000
χ482-2-22-2222-2-22-2-22000022-2-20000000022-2-2-22000000222-2-2-2-222-2000000000000−222−2−222−2−222−2−222−2−222−2−222−200000000
χ492-2-22-2222-2-22-2-22000022-2-200000000-2-222-220000002-2-22222-2-2-20000000000002−2−22−222−22−2−222−2−22−222−2−222−200000000
χ502-2-22-2222-2-22-2-22000022-2-200000000-2-222-220000002-2-22222-2-2-2000000000000−222−22−2−22−222−2−222−22−2−222−2−2200000000
χ512-2-22-222-222-2-2-2222-2-2-2-22222-2-222-2-20000-22-220000-2000000002-22-2200000000000000000000000000000000002-20000
χ522-2-22-222-222-2-2-2222-2-2-2-22222-2-222-2-20000-22-220000-2000000002-22-220000000000000000000000000000000000-220000
χ532-2-22-222-222-2-2-22-2-222-2-222-2-222-2-2220000-222-20000-20000000022-22-20000000000000000000000000000000000002-200
χ542-2-22-222-222-2-2-22-2-222-2-222-2-222-2-2220000-222-20000-20000000022-22-2000000000000000000000000000000000000-2200
χ552-2-22-22-12-2-2211-10000-1-11133−3−3−3−33322-2-21-1000000-1-1-11111-1-113−3−33−3−33333−3−32−2−222−2−22ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ562-2-22-22-12-2-2211-10000-1-11133−3−3−3−33322-2-21-1000000-1-1-11111-1-113−3−33−3−33333−3−3−222−2−222−2−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ572-2-22-22-12-2-2211-10000-1-11133−3−3−3−333-2-2221-1000000-111-1-1-1-11113−3−3333−3−3−3−3332−2−22−222−2ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ582-2-22-22-12-2-2211-10000-1-11133−3−3−3−333-2-2221-1000000-111-1-1-1-11113−3−3333−3−3−3−333−222−22−2−22−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ592-2-22-22-12-2-2211-10000-1-111−3−33333−3−322-2-21-1000000-1-1-11111-1-11−333−333−3−3−3−3332−2−222−2−22ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ602-2-22-22-12-2-2211-10000-1-111−3−33333−3−322-2-21-1000000-1-1-11111-1-11−333−333−3−3−3−333−222−2−222−2−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ612-2-22-22-12-2-2211-10000-1-111−3−33333−3−3-2-2221-1000000-111-1-1-1-1111−333−3−3−33333−3−32−2−22−222−2ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ622-2-22-22-12-2-2211-10000-1-111−3−33333−3−3-2-2221-1000000-111-1-1-1-1111−333−3−3−33333−3−3−222−22−2−22−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ634444444-4-4-4-44440000-4-4-4-400000000000044000000-400000000-400000000000000000000000000000000000000000000
χ64444444-2-4-4-4-4-2-2-20000222223232323−23−23−23−230000-2-20000002000000002−23−2323230000000000000000000000000000000000000000
χ65444444-2-4-4-4-4-2-2-200002222−23−23−23−23232323230000-2-200000020000000022323−23−230000000000000000000000000000000000000000
χ664444-4-4-244-4-4-2-2-24444-2-2-2-2-2-2-2-2-2-2-2-2000022-4-40000200000000222220000000000000000000000000000000000000000
χ674444-4-4-244-4-4-2-2-2-4-4-4-4-2-2-2-2222222220000224400002000000002-2-2-2-20000000000000000000000000000000000000000
χ6844-4-400400004-4-4−2i22i2−2i22i20000−2i22i2−2i22i2−2i22i2−2i22i22i−2i2i−2i00000022−2202i−2i2i−2i2i−2i2i−2i00000000022−2222−2200000000000000000000000000000000
χ6944-4-400400004-4-4−2i22i2−2i22i20000−2i22i2−2i22i2−2i22i2−2i22i2−2i2i−2i2i000000−22220−2i2i−2i2i−2i2i−2i2i000000000−2222−222200000000000000000000000000000000
χ7044-4-400400004-4-42i2−2i22i2−2i200002i2−2i22i2−2i22i2−2i22i2−2i22i−2i2i−2i000000−222202i−2i2i−2i2i−2i2i−2i000000000−2222−222200000000000000000000000000000000
χ7144-4-400400004-4-42i2−2i22i2−2i200002i2−2i22i2−2i22i2−2i22i2−2i2−2i2i−2i2i00000022−220−2i2i−2i2i−2i2i−2i2i00000000022−2222−2200000000000000000000000000000000
χ7244-4-400-20000-222−2i22i2−2i22i223−2323−232ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ232i−2i2i−2i00000022−220ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000006−66−6−22−2200000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.