Finite Group Databasebeta

← Group #10816046

Character table — Group #10816046

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222222222222222222224444444444444444444444444444444444444444888888888888888888881212121212121212242424242424242424242424
order122222344446668888888812121212242424242424242422444444444466888812121212121212121212242424242424242424242424668888121212121212242424242424242422444444222244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111111111-1-111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111
χ7111111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-1
χ8111111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ911111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-111
χ1011111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ1111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111
χ1211111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1
χ1311111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1
χ1411111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-111
χ1511111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1
χ1611111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-111
χ171-11-1-1111-11-1-1-11ii−i−iii−i−i11-1-1iiii−i−i−i−i1-1i−i1-1i−i11-1-1-11i−ii−i11111-1-1-1-1-1ii−i−iiiii−i−i−i−i1-11-1i−iii−i−i1-111-1-1ii−i−i1-1i−i1-1i−i1-11-1i−ii−i1-1i−i
χ181-11-1-1111-11-1-1-11ii−i−iii−i−i11-1-1iiii−i−i−i−i1-1i−i1-1i−i11-1-1-11i−ii−i11111-1-1-1-1-1ii−i−iiiii−i−i−i−i1-11-1i−iii−i−i1-111-1-1ii−i−i-11−ii-11−ii-11-11−ii−ii-11−ii
χ191-11-1-1111-11-1-1-11ii−i−iii−i−i11-1-1iiii−i−i−i−i-11−ii-11−ii11-1-1-11i−ii−i11111-1-1-1-1-1ii−i−iiiii−i−i−i−i-11-11−ii−i−iii-11-1-111−i−iii1-1i−i1-1i−i-11-11−ii−ii1-1i−i
χ201-11-1-1111-11-1-1-11ii−i−iii−i−i11-1-1iiii−i−i−i−i-11−ii-11−ii11-1-1-11i−ii−i11111-1-1-1-1-1ii−i−iiiii−i−i−i−i-11-11−ii−i−iii-11-1-111−i−iii-11−ii-11−ii1-11-1i−ii−i-11−ii
χ211-11-1-1111-11-1-1-11ii−i−i−i−iii11-1-1iiii−i−i−i−i1-1−ii1-1−ii-1-111-11i−i−ii1-1-1-1-11111-1ii−i−i−i−i−i−iiiii1-1-11i−i−i−iii1-1-1-111ii−i−i1-1i−i1-1i−i1-1-11i−i−ii-11−ii
χ221-11-1-1111-11-1-1-11ii−i−i−i−iii11-1-1iiii−i−i−i−i1-1−ii1-1−ii-1-111-11i−i−ii1-1-1-1-11111-1ii−i−i−i−i−i−iiiii1-1-11i−i−i−iii1-1-1-111ii−i−i-11−ii-11−ii-111-1−iii−i1-1i−i
χ231-11-1-1111-11-1-1-11ii−i−i−i−iii11-1-1iiii−i−i−i−i-11i−i-11i−i-1-111-11i−i−ii1-1-1-1-11111-1ii−i−i−i−i−i−iiiii-111-1−iiii−i−i-1111-1-1−i−iii1-1i−i1-1i−i-111-1−iii−i-11−ii
χ241-11-1-1111-11-1-1-11ii−i−i−i−iii11-1-1iiii−i−i−i−i-11i−i-11i−i-1-111-11i−i−ii1-1-1-1-11111-1ii−i−i−i−i−i−iiiii-111-1−iiii−i−i-1111-1-1−i−iii-11−ii-11−ii1-1-11i−i−ii1-1i−i
χ251-11-1-1111-11-1-1-11−i−iiiii−i−i11-1-1−i−i−i−iiiii1-1i−i1-1i−i-1-111-11−iii−i1-1-1-1-11111-1−i−iiiiiii−i−i−i−i1-1-11−iiii−i−i1-1-1-111−i−iii1-1−ii1-1−ii1-1-11−iii−i-11i−i
χ261-11-1-1111-11-1-1-11−i−iiiii−i−i11-1-1−i−i−i−iiiii1-1i−i1-1i−i-1-111-11−iii−i1-1-1-1-11111-1−i−iiiiiii−i−i−i−i1-1-11−iiii−i−i1-1-1-111−i−iii-11i−i-11i−i-111-1i−i−ii1-1−ii
χ271-11-1-1111-11-1-1-11−i−iiiii−i−i11-1-1−i−i−i−iiiii-11−ii-11−ii-1-111-11−iii−i1-1-1-1-11111-1−i−iiiiiii−i−i−i−i-111-1i−i−i−iii-1111-1-1ii−i−i1-1−ii1-1−ii-111-1i−i−ii-11i−i
χ281-11-1-1111-11-1-1-11−i−iiiii−i−i11-1-1−i−i−i−iiiii-11−ii-11−ii-1-111-11−iii−i1-1-1-1-11111-1−i−iiiiiii−i−i−i−i-111-1i−i−i−iii-1111-1-1ii−i−i-11i−i-11i−i1-1-11−iii−i1-1−ii
χ291-11-1-1111-11-1-1-11−i−iii−i−iii11-1-1−i−i−i−iiiii1-1−ii1-1−ii11-1-1-11−ii−ii11111-1-1-1-1-1−i−iii−i−i−i−iiiii1-11-1−ii−i−iii1-111-1-1−i−iii1-1−ii1-1−ii1-11-1−ii−ii1-1−ii
χ301-11-1-1111-11-1-1-11−i−iii−i−iii11-1-1−i−i−i−iiiii1-1−ii1-1−ii11-1-1-11−ii−ii11111-1-1-1-1-1−i−iii−i−i−i−iiiii1-11-1−ii−i−iii1-111-1-1−i−iii-11i−i-11i−i-11-11i−ii−i-11i−i
χ311-11-1-1111-11-1-1-11−i−iii−i−iii11-1-1−i−i−i−iiiii-11i−i-11i−i11-1-1-11−ii−ii11111-1-1-1-1-1−i−iii−i−i−i−iiiii-11-11i−iii−i−i-11-1-111ii−i−i1-1−ii1-1−ii-11-11i−ii−i1-1−ii
χ321-11-1-1111-11-1-1-11−i−iii−i−iii11-1-1−i−i−i−iiiii-11i−i-11i−i11-1-1-11−ii−ii11111-1-1-1-1-1−i−iii−i−i−i−iiiii-11-11i−iii−i−i-11-1-111ii−i−i-11i−i-11i−i1-11-1−ii−ii-11i−i
χ33222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ34222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-2-2-2-21111111111111100000000000000000000
χ35222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-122-2-2-111111111-1-1-1-1-111111111-1-1-2-2221111-1-11111-1-1-1-100000000000000000000
χ36222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-2-1-122-2-2-111111111-1-1-1-1-1111111111122-2-2-1-1-1-111-1-1-1-1111100000000000000000000
χ37222222-12222-1-1-1-2-2-2-22222-1-1-1-11111111122222222-2-2-2-2-1-1-2-222-111111111-11111-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111100000000000000000000
χ38222222-12222-1-1-1-2-2-2-22222-1-1-1-111111111-2-2-2-2-2-2-2-2-2-2-2-2-1-1-2-222-111111111-11111-1-1-1-1-1-1-1-1112222111111-1-1-1-1-1-1-1-100000000000000000000
χ39222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111122-2-222-2-22222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111-1-122-2-21111-1-1-1-1-1-1111100000000000000000000
χ40222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111-2-222-2-2222222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111-2-222-1-1-1-1111111-1-1-1-100000000000000000000
χ412222-2-2222-2-222222220000222222222222000000000000-2-2-2-200-200000000-2-2-2-2-2000000000000000000000000000022-2-2-2-222000000000000
χ422222-2-2222-2-222222220000222222222222000000000000-2-2-2-200-200000000-2-2-2-2-20000000000000000000000000000-2-22222-2-2000000000000
χ432222-2-2222-2-2222-2-2-2-200002222-2-2-2-2-2-2-2-2000000000000-2-22200-200000000-2222200000000000000000000000000002222-2-2-2-2000000000000
χ442222-2-2222-2-2222-2-2-2-200002222-2-2-2-2-2-2-2-2000000000000-2-22200-200000000-222220000000000000000000000000000-2-2-2-22222000000000000
χ452222-2-22-2-22222200002222-2-2-2-20000000022-2-2-2-2220000-2-200-2-22000000002000022-2-222-2-22200002-22-2-2-20000000000000000000000000000
χ462222-2-22-2-22222200002222-2-2-2-200000000-2-22222-2-20000-2-200-2-22000000002000022-2-222-2-2-2-20000-22-22220000000000000000000000000000
χ472222-2-22-2-2222220000-2-2-2-2-2-2-2-2000000002222-2-2-2-20000-2-2002220000000020000-2-222-2-222220000-22-22-2-20000000000000000000000000000
χ482222-2-22-2-2222220000-2-2-2-2-2-2-2-200000000-2-2-2-222220000-2-2002220000000020000-2-222-2-222-2-200002-22-2220000000000000000000000000000
χ492222-2-2-1-2-222-1-1-100002222111133−3−333−3−322-2-2-2-22200001100-2-2-133−3−333−3−3-13−33−3-1-111-1-111-1-10000-11-11113−33−33−33−300000000000000000000
χ502222-2-2-1-2-222-1-1-100002222111133−3−333−3−3-2-22222-2-200001100-2-2-133−3−333−3−3-13−33−3-1-111-1-1111100001-11-1-1-1−33−33−33−3300000000000000000000
χ512222-2-2-1-2-222-1-1-1000022221111−3−333−3−33322-2-2-2-22200001100-2-2-1−3−333−3−333-1−33−33-1-111-1-111-1-10000-11-1111−33−33−33−3300000000000000000000
χ522222-2-2-1-2-222-1-1-1000022221111−3−333−3−333-2-22222-2-200001100-2-2-1−3−333−3−333-1−33−33-1-111-1-1111100001-11-1-1-13−33−33−33−300000000000000000000
χ532222-2-2-1-2-222-1-1-10000-2-2-2-2111133−3−333−3−32222-2-2-2-20000110022-1−3−333−3−333-13−33−311-1-111-1-1-1-100001-11-111−33−333−33−300000000000000000000
χ542222-2-2-1-2-222-1-1-10000-2-2-2-2111133−3−333−3−3-2-2-2-222220000110022-1−3−333−3−333-13−33−311-1-111-1-1110000-11-11-1-13−33−3−33−3300000000000000000000
χ552222-2-2-1-2-222-1-1-10000-2-2-2-21111−3−333−3−3332222-2-2-2-20000110022-133−3−333−3−3-1−33−3311-1-111-1-1-1-100001-11-1113−33−3−33−3300000000000000000000
χ562222-2-2-1-2-222-1-1-10000-2-2-2-21111−3−333−3−333-2-2-2-222220000110022-133−3−333−3−3-1−33−3311-1-111-1-1110000-11-11-1-1−33−333−33−300000000000000000000
χ572-22-22-222-2-22-2-222i2i−2i−2i000022-2-22i2i2i2i−2i−2i−2i−2i0000000000002-2−2i2i00-2000000002−2i−2i2i2i00000000000000000000000000002-2−2i2i-222i−2i000000000000
χ582-22-22-222-2-22-2-222i2i−2i−2i000022-2-22i2i2i2i−2i−2i−2i−2i0000000000002-2−2i2i00-2000000002−2i−2i2i2i0000000000000000000000000000-222i−2i2-2−2i2i000000000000
χ592-22-22-222-2-22-2-22−2i−2i2i2i000022-2-2−2i−2i−2i−2i2i2i2i2i0000000000002-22i−2i00-20000000022i2i−2i−2i00000000000000000000000000002-22i−2i-22−2i2i000000000000
χ602-22-22-222-2-22-2-22−2i−2i2i2i000022-2-2−2i−2i−2i−2i2i2i2i2i0000000000002-22i−2i00-20000000022i2i−2i−2i0000000000000000000000000000-22−2i2i2-22i−2i000000000000
χ612-22-22-22-222-2-2-2200002i2i−2i−2i-2-222000000002-2−2i2i-222i−2i00002-200−2i2i200000000-200002i2i−2i−2i−2i−2i2i2i2-200002i−2i−2i2i-220000000000000000000000000000
χ622-22-22-22-222-2-2-2200002i2i−2i−2i-2-22200000000-222i−2i2-2−2i2i00002-200−2i2i200000000-200002i2i−2i−2i−2i−2i2i2i-220000−2i2i2i−2i2-20000000000000000000000000000
χ632-22-22-22-222-2-2-220000−2i−2i2i2i-2-222000000002-22i−2i-22−2i2i00002-2002i−2i200000000-20000−2i−2i2i2i2i2i−2i−2i2-20000−2i2i2i−2i-220000000000000000000000000000
χ642-22-22-22-222-2-2-220000−2i−2i2i2i-2-22200000000-22−2i2i2-22i−2i00002-2002i−2i200000000-20000−2i−2i2i2i2i2i−2i−2i-2200002i−2i−2i2i2-20000000000000000000000000000
χ652-22-22-2-1-222-211-100002i2i−2i−2i11-1-1−i3−i3i3i3i3i3−i3−i32-2−2i2i-222i−2i0000-1100−2i2i-1−3−33333−3−31−i3i3i3−i3−i−iiiii−i−i-110000−iii−i1-1−333−3−i3i3i3−i300000000000000000000
χ662-22-22-2-1-222-211-100002i2i−2i−2i11-1-1−i3−i3i3i3i3i3−i3−i3-222i−2i2-2−2i2i0000-1100−2i2i-1−3−33333−3−31−i3i3i3−i3−i−iiiii−i−i1-10000i−i−ii-113−3−33i3−i3−i3i300000000000000000000
χ672-22-22-2-1-222-211-100002i2i−2i−2i11-1-1i3i3−i3−i3−i3−i3i3i32-2−2i2i-222i−2i0000-1100−2i2i-133−3−3−3−3331i3−i3−i3i3−i−iiiii−i−i-110000−iii−i1-13−3−33i3−i3−i3i300000000000000000000
χ682-22-22-2-1-222-211-100002i2i−2i−2i11-1-1i3i3−i3−i3−i3−i3i3i3-222i−2i2-2−2i2i0000-1100−2i2i-133−3−3−3−3331i3−i3−i3i3−i−iiiii−i−i1-10000i−i−ii-11−333−3−i3i3i3−i300000000000000000000
χ692-22-22-2-1-222-211-10000−2i−2i2i2i11-1-1−i3−i3i3i3i3i3−i3−i32-22i−2i-22−2i2i0000-11002i−2i-133−3−3−3−3331−i3i3i3−i3ii−i−i−i−iii-110000i−i−ii1-13−3−33−i3i3i3−i300000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.