Finite Group Databasebeta

← Group #10698050

Character table — Group #10698050

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444448888888888888888888888884848484848484848
order12222222223444466666661212121212121212444444444466661212121212121212121212121212121212121212888888882424242424242424242424242424242422444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1111-1-1
χ922222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1022222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ112222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ122222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000
χ132222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000
χ142222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000
χ152222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111000000003333−3−3−3−33333−3−3−3−300000000
χ162222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000−3−3−3−33333−3−3−3−3333300000000
χ172222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1000000003333−3−3−3−3−3−3−3−3333300000000
χ182222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-100000000−3−3−3−333333333−3−3−3−300000000
χ19222222-2-2-2-222222222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000022-2-2000022-2-222-2-20000000000000000
χ20222222-2-2-2-222222222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000-2-2220000-2-222-2-2220000000000000000
χ21222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-22222000000000000000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i00000000
χ22222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i00000000
χ23222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i322-2-20000-1-111-1-111−i3−i3i3i3i3i3−i3−i300000000
χ24222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-2-222000011-1-111-1-1i3i3−i3−i3−i3−i3i3i300000000
χ25222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i322-2-20000-1-111-1-111i3i3−i3−i3−i3−i3i3i300000000
χ26222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-2-222000011-1-111-1-1−i3−i3i3i3i3i3−i3−i300000000
χ27222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111122000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i300002i2i−2i−2i33−3−3−3−333−i−iii−i−iii00000000
χ28222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111122000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000−2i−2i2i2i−3−33333−3−3ii−i−iii−i−i00000000
χ29222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111122000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i300002i2i−2i−2i−3−33333−3−3−i−iii−i−iii00000000
χ30222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111122000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000−2i−2i2i2i33−3−3−3−333ii−i−iii−i−i00000000
χ312222-2-22-22-2222-2-2-2-2-2-22222222-2-2-2-22-20000000022-2-222-2-20000000000000000000000000000000000000000020-20000
χ322222-2-22-22-2222-2-2-2-2-2-22222222-2-2-2-22-20000000022-2-222-2-200000000000000000000000000000000000000000-2020000
χ332222-2-22-22-22-2-222-2-2-2-2222-2-2-2-22222-220000000022-2-2-2-22200000000000000000000000000000000000000000000002-2
χ342222-2-22-22-22-2-222-2-2-2-2222-2-2-2-22222-220000000022-2-2-2-2220000000000000000000000000000000000000000000000-22
χ352222-2-2-22-22222-2-2-2-2-2-22222222-2-2-2-2-2200000000-2-222-2-222000000000000000000000000000000000000000020-200000
χ362222-2-2-22-22222-2-2-2-2-2-22222222-2-2-2-2-2200000000-2-222-2-2220000000000000000000000000000000000000000-20200000
χ372222-2-2-22-222-2-222-2-2-2-2222-2-2-2-222222-200000000-2-22222-2-2000000000000000000000000000000000000000000002-200
χ382222-2-2-22-222-2-222-2-2-2-2222-2-2-2-222222-200000000-2-22222-2-200000000000000000000000000000000000000000000-2200
χ392-2-222-222-2-22000022-2-22-2-200000000002i2i−2i−2i00002-22-200002i2i−2i−2i2i2i−2i−2i000000002−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ402-2-222-222-2-22000022-2-22-2-200000000002i2i−2i−2i00002-22-200002i2i−2i−2i2i2i−2i−2i00000000−22−22i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000
χ412-2-222-222-2-22000022-2-22-2-20000000000−2i−2i2i2i00002-22-20000−2i−2i2i2i−2i−2i2i2i000000002−22−2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ422-2-222-222-2-22000022-2-22-2-20000000000−2i−2i2i2i00002-22-20000−2i−2i2i2i−2i−2i2i2i00000000−22−22−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000
χ432-2-222-222-2-2-10000-1-111-11133−3−333−3−3002i2i−2i−2i0000-11-113−33−3−i−iii−i−iii−i3−i3i3i3−i3−i3i3i32−22−2−i2i2−i2i2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000
χ442-2-222-222-2-2-10000-1-111-11133−3−333−3−3002i2i−2i−2i0000-11-113−33−3−i−iii−i−iii−i3−i3i3i3−i3−i3i3i3−22−22i2−i2i2−i2−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000
χ452-2-222-222-2-2-10000-1-111-11133−3−333−3−300−2i−2i2i2i0000-11-113−33−3ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i32−22−2i2−i2i2−i2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000
χ462-2-222-222-2-2-10000-1-111-11133−3−333−3−300−2i−2i2i2i0000-11-113−33−3ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i3−22−22−i2i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000
χ472-2-222-222-2-2-10000-1-111-111−3−333−3−333002i2i−2i−2i0000-11-11−33−33−i−iii−i−iiii3i3−i3−i3i3i3−i3−i32−22−2−i2i2−i2i2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000
χ482-2-222-222-2-2-10000-1-111-111−3−333−3−333002i2i−2i−2i0000-11-11−33−33−i−iii−i−iiii3i3−i3−i3i3i3−i3−i3−22−22i2−i2i2−i2−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000
χ492-2-222-222-2-2-10000-1-111-111−3−333−3−33300−2i−2i2i2i0000-11-11−33−33ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i32−22−2i2−i2i2−i2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000
χ502-2-222-222-2-2-10000-1-111-111−3−333−3−33300−2i−2i2i2i0000-11-11−33−33ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i3−22−22−i2i2−i2i2−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000
χ512-2-222-2-2-2222000022-2-22-2-20000000000000022-2-2-22-2200000000000022-2-2-2-2222−2−222−2−222−2−222−2−222−2−222−2−2200000000
χ522-2-222-2-2-2222000022-2-22-2-20000000000000022-2-2-22-2200000000000022-2-2-2-222−222−2−222−2−222−2−222−2−222−2−222−200000000
χ532-2-222-2-2-2222000022-2-22-2-200000000000000-2-222-22-22000000000000-2-22222-2-22−2−22−222−22−2−222−2−22−222−2−222−200000000
χ542-2-222-2-2-2222000022-2-22-2-200000000000000-2-222-22-22000000000000-2-22222-2-2−222−22−2−22−222−2−222−22−2−222−2−2200000000
χ552-2-222-2-2-222-10000-1-111-11133−3−333−3−300000022-2-21-11-1−33−3333−3−3−3−333-1-11111-1-12−2−222−2−22ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ562-2-222-2-2-222-10000-1-111-11133−3−333−3−300000022-2-21-11-1−33−3333−3−3−3−333-1-11111-1-1−222−2−222−2−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ572-2-222-2-2-222-10000-1-111-11133−3−333−3−3000000-2-2221-11-1−33−33−3−33333−3−311-1-1-1-1112−2−22−222−2ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ582-2-222-2-2-222-10000-1-111-11133−3−333−3−3000000-2-2221-11-1−33−33−3−33333−3−311-1-1-1-111−222−22−2−22−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ592-2-222-2-2-222-10000-1-111-111−3−333−3−33300000022-2-21-11-13−33−3−3−33333−3−3-1-11111-1-12−2−222−2−22ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ602-2-222-2-2-222-10000-1-111-111−3−333−3−33300000022-2-21-11-13−33−3−3−33333−3−3-1-11111-1-1−222−2−222−2−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ612-2-222-2-2-222-10000-1-111-111−3−333−3−333000000-2-2221-11-13−33−333−3−3−3−33311-1-1-1-1112−2−22−222−2ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ622-2-222-2-2-222-10000-1-111-111−3−333−3−333000000-2-2221-11-13−33−333−3−3−3−33311-1-1-1-111−222−22−2−22−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
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χ964-4-44-44-444-4-2000022-2-2-222−23−2323232323−23−2300000000002-2-2223−23−2323000000000000000000000000000000000000000000000000

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