Finite Group Databasebeta

← Group #72248708

Character table — Group #72248708

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size111122222222222222222244444444444444444444444444888888161616161616161616161616161616161616161616161616161616161616161616161616242424242424242424242424242424244848484848484848
order122222222222222222366622222222666666666666666666666666444444444444121212121212121212121212121212121212121212121212222244444444444424444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i11-1-1ii−i−i
χ1011111111-1-1-111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii-1-111−i−iii
χ1111111111-1-1-111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1ii−i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-111-1-1iiii−i−i−i−i-1-111−i−iii
χ1211111111-1-1-111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1ii−i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111-1-111−i−i−i−iiiii11-1-1ii−i−i
χ1311111111-1-1-111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii11-1-1−i−iii
χ1411111111-1-1-111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i-1-111ii−i−i
χ1511111111-1-1-111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−iii-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-111-1-1−i−i−i−iiiii-1-111ii−i−i
χ1611111111-1-1-111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−iii-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111-1-111iiii−i−i−i−i11-1-1−i−iii
χ17222222222222222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ18222222222222222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000000000000000
χ19222222222222222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111000000000000000000000000
χ20222222222222222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1000000000000000000000000
χ212222222222-2-2-2-2-2-2-2-222222-2-2-222-2222222222-2-2-2-2-2-222-2-22-2-2-22-22i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ222222222222-2-2-2-2-2-2-2-222222-2-2-222-2222222222-2-2-2-2-2-222-2-22-2-2-22-2−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ232222222222-2-2-2-2-2-2-2-2-1-1-1-12-2-2-222-22-1-1-1-1-1-1-1-1111111-1-111-1111-112i−2i2i−2i00000000−i−iii−i−iii33−3−333−3−3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ242222222222-2-2-2-2-2-2-2-2-1-1-1-12-2-2-222-22-1-1-1-1-1-1-1-1111111-1-111-1111-112i−2i2i−2i00000000−i−iii−i−iii−3−333−3−333i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ252222222222-2-2-2-2-2-2-2-2-1-1-1-12-2-2-222-22-1-1-1-1-1-1-1-1111111-1-111-1111-11−2i2i−2i2i00000000ii−i−iii−i−i33−3−333−3−3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ262222222222-2-2-2-2-2-2-2-2-1-1-1-12-2-2-222-22-1-1-1-1-1-1-1-1111111-1-111-1111-11−2i2i−2i2i00000000ii−i−iii−i−i−3−333−3−333−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ2722222222-2-22-2-22222222222-2-2-2-2-22-22222-2-2-2-22222-2-2-2-2222-2-2-2-222-2-220000000022-2-2-2-2220000000000000000000000000000000000000000
χ2822222222-2-22-2-22222222222-2-2-2-2-22-22222-2-2-2-22222-2-2-2-2222-2-2-2-22-222-200000000-2-22222-2-20000000000000000000000000000000000000000
χ2922222222-2-22-2-222222-1-1-1-12-2-2-2-2-22-2-1-1-1-11111-1-1-1-11111-1-1-11111-12-2-2200000000-1-11111-1-133−3−3−3−333−3−33333−3−3000000000000000000000000
χ3022222222-2-22-2-222222-1-1-1-12-2-2-2-2-22-2-1-1-1-11111-1-1-1-11111-1-1-11111-12-2-2200000000-1-11111-1-1−3−33333−3−333−3−3−3−333000000000000000000000000
χ3122222222-2-22-2-222222-1-1-1-12-2-2-2-2-22-2-1-1-1-11111-1-1-1-11111-1-1-11111-1-222-20000000011-1-1-1-11133−3−3−3−33333−3−3−3−333000000000000000000000000
χ3222222222-2-22-2-222222-1-1-1-12-2-2-2-2-22-2-1-1-1-11111-1-1-1-11111-1-1-11111-1-222-20000000011-1-1-1-111−3−33333−3−3−3−33333−3−3000000000000000000000000
χ3322222222-2-2-222-2-2-2-2-2-1-1-1-12222-2-2-2-2-1-1-1-111111111-1-11111-1-1-1-1112i2i−2i−2i22-2-22i2i−2i−2i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii000000000000000000000000
χ3422222222-2-2-222-2-2-2-2-2-1-1-1-12222-2-2-2-2-1-1-1-111111111-1-11111-1-1-1-1112i2i−2i−2i-2-222−2i−2i2i2i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ3522222222-2-2-222-2-2-2-2-2-1-1-1-12222-2-2-2-2-1-1-1-111111111-1-11111-1-1-1-111−2i−2i2i2i22-2-2−2i−2i2i2iiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i000000000000000000000000
χ3622222222-2-2-222-2-2-2-2-2-1-1-1-12222-2-2-2-2-1-1-1-111111111-1-11111-1-1-1-111−2i−2i2i2i-2-2222i2i−2i−2iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii000000000000000000000000
χ37222222-2-22222222-2-222222-22-2-22-2-2-222-2-222-2-222-2-222-2-222-22-2-22-20000000000000000000000000000000000002222-2-2-2-20000000000000000
χ38222222-2-22222222-2-222222-22-2-22-2-2-222-2-222-2-222-2-222-2-222-22-2-22-2000000000000000000000000000000000000-2-2-2-222220000000000000000
χ39222222-2-222-2-2-2-2-222-22222-2-2222-22-222-2-222-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ40222222-2-222-2-2-2-2-222-22222-2-2222-22-222-2-222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ41222222-2-2-2-22-2-222-2-222222-2-222-22-2222-2-2-2-22222-2-2-2-22222-2-222-2-20000000000000000000000000000000000000000000022-2-2-2-22200000000
χ42222222-2-2-2-22-2-222-2-222222-2-222-22-2222-2-2-2-22222-2-2-2-22222-2-222-2-200000000000000000000000000000000000000000000-2-22222-2-200000000
χ43222222-2-2-2-2-222-2-222-22222-22-2-2-222222-2-2-2-222-2-2222222-2-2-22-2-2-2200000000000000000000000000000000000022-2-2-2-2220000000000000000
χ44222222-2-2-2-2-222-2-222-22222-22-2-2-222222-2-2-2-222-2-2222222-2-2-22-2-2-22000000000000000000000000000000000000-2-22222-2-20000000000000000
χ452222-2-22222222-2-2-2-222222-2-22-2-2-222-2-22222-2-222-2-22222-2-2-2-22-2-2200000000000000000000000000000000000000000000000000002-22-20000
χ462222-2-22222222-2-2-2-222222-2-22-2-2-222-2-22222-2-222-2-22222-2-2-2-22-2-220000000000000000000000000000000000000000000000000000-22-220000
χ472222-2-22222-2-2-22222-22222-22-22-2-2-22-2-22222-2-2-2-222-2-22222-22-22-2-2000000000000000000000000000000000000000000000000000000002-22-2
χ482222-2-22222-2-2-22222-22222-22-22-2-2-22-2-22222-2-2-2-222-2-22222-22-22-2-200000000000000000000000000000000000000000000000000000000-22-22
χ492222-2-222-2-22-2-2-2-2-2-222222-22-22222-2-2-222-2-22222-2-2-2-2-2-2-2-2-22-2222000000000000000000000000000000000000000000000000000000002i−2i−2i2i
χ502222-2-222-2-22-2-2-2-2-2-222222-22-22222-2-2-222-2-22222-2-2-2-2-2-2-2-2-22-222200000000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ512222-2-222-2-2-2222222-22222-2-22-222-2-2-2-222-2-222-2-22222-2-222-2-22-22-200000000000000000000000000000000000000000000000000002-2-220000
χ522222-2-222-2-2-2222222-22222-2-22-222-2-2-2-222-2-222-2-22222-2-222-2-22-22-20000000000000000000000000000000000000000000000000000-222-20000
χ532222-2-2-2-222222-2-222222222-2-22-22-2-2-2-2-2-22222222222-2-2-2-22-2-22-2-200002-22-20000000000002-22-22-22-200000000000000000000000000000000
χ542222-2-2-2-222222-2-222222222-2-22-22-2-2-2-2-2-22222222222-2-2-2-22-2-22-2-20000-22-22000000000000-22-22-22-2200000000000000000000000000000000
χ552222-2-2-2-222222-2-2222-1-1-1-12-2-22-22-2-21111-1-1-1-1-1-1-1-1-1-11111-111-11100002-22-200003−33−33−33−3-11-11-11-113−33−33−33−3000000000000000000000000
χ562222-2-2-2-222222-2-2222-1-1-1-12-2-22-22-2-21111-1-1-1-1-1-1-1-1-1-11111-111-11100002-22-20000−33−33−33−33-11-11-11-11−33−33−33−33000000000000000000000000
χ572222-2-2-2-222222-2-2222-1-1-1-12-2-22-22-2-21111-1-1-1-1-1-1-1-1-1-11111-111-1110000-22-2200003−33−33−33−31-11-11-11-1−33−33−33−33000000000000000000000000
χ582222-2-2-2-222222-2-2222-1-1-1-12-2-22-22-2-21111-1-1-1-1-1-1-1-1-1-11111-111-1110000-22-220000−33−33−33−331-11-11-11-13−33−33−33−3000000000000000000000000
χ592222-2-2-2-222-2-2-222-2-2-22222222-2-222-2-2-2-2-22222-2-2-2-2-2-2-2-222222-2-22000000002i−2i2i−2i00000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ602222-2-2-2-222-2-2-222-2-2-22222222-2-222-2-2-2-2-22222-2-2-2-2-2-2-2-222222-2-2200000000−2i2i−2i2i0000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ612222-2-2-2-222-2-2-222-2-2-2-1-1-1-1222-2-222-21111-1-1-1-111111111-1-1-1-1-111-1000000002i−2i2i−2i−i3i3i3−i3−i3i3i3−i3−333−3−333−3−iii−i−iii−i000000000000000000000000
χ622222-2-2-2-222-2-2-222-2-2-2-1-1-1-1222-2-222-21111-1-1-1-111111111-1-1-1-1-111-1000000002i−2i2i−2ii3−i3−i3i3i3−i3−i3i33−3−333−3−33−iii−i−iii−i000000000000000000000000
χ632222-2-2-2-222-2-2-222-2-2-2-1-1-1-1222-2-222-21111-1-1-1-111111111-1-1-1-1-111-100000000−2i2i−2i2i−i3i3i3−i3−i3i3i3−i33−3−333−3−33i−i−iii−i−ii000000000000000000000000
χ642222-2-2-2-222-2-2-222-2-2-2-1-1-1-1222-2-222-21111-1-1-1-111111111-1-1-1-1-111-100000000−2i2i−2i2ii3−i3−i3i3i3−i3−i3i3−333−3−333−3i−i−iii−i−ii000000000000000000000000
χ652222-2-2-2-2-2-22-2-2-2-22222222222-22-2-22-2-2-2-2-2-2-2-22222-2-222-2-2222-22-2000000002-2-2200000000000000002-2-22-222-2000000000000000000000000
χ662222-2-2-2-2-2-22-2-2-2-22222222222-22-2-22-2-2-2-2-2-2-2-22222-2-222-2-2222-22-200000000-222-20000000000000000-222-22-2-22000000000000000000000000
χ672222-2-2-2-2-2-22-2-2-2-2222-1-1-1-1222-22-2-2211111111-1-1-1-111-1-111-1-1-11-11000000002-2-223−3−33−333−33−3−33−333−3-111-11-1-11000000000000000000000000
χ682222-2-2-2-2-2-22-2-2-2-2222-1-1-1-1222-22-2-2211111111-1-1-1-111-1-111-1-1-11-11000000002-2-22−333−33−3−33−333−33−3−33-111-11-1-11000000000000000000000000
χ692222-2-2-2-2-2-22-2-2-2-2222-1-1-1-1222-22-2-2211111111-1-1-1-111-1-111-1-1-11-1100000000-222-23−3−33−333−3−333−33−3−331-1-11-111-1000000000000000000000000
χ702222-2-2-2-2-2-22-2-2-2-2222-1-1-1-1222-22-2-2211111111-1-1-1-111-1-111-1-1-11-1100000000-222-2−333−33−3−333−3−33−333−31-1-11-111-1000000000000000000000000
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χ722222-2-2-2-2-2-2-22222-2-2-222222-2-222-222-2-2-2-2-2-2-2-2-2-2-2-22222222-2-22220000-222-2000000000000-22-222-22-200000000000000000000000000000000
χ732222-2-2-2-2-2-2-22222-2-2-2-1-1-1-12-2-222-222111111111111-1-1-1-1-1-1-111-1-1-100002-2-220000−i3i3−i3i3i3−i3i3−i3-11-111-11-1−i3i3−i3i3i3−i3i3−i3000000000000000000000000
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χ8644-4-400004-444-40000-444-4-40000000000004-4004-4004-4000000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ8744-4-400004-4-4-440000444-4-40000000000004-400-4400-440000000000000000000000000000000000000000000000000000002-2-222-2-2200000000
χ8844-4-400004-4-4-440000444-4-40000000000004-400-4400-44000000000000000000000000000000000000000000000000000000-222-2-222-200000000
χ8944-4-40000-444-440000-444-4-4000000000000-44004-400-440000000000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ9044-4-40000-444-440000-444-4-4000000000000-44004-400-44000000000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ9144-4-40000-44-44-40000444-4-4000000000000-4400-44004-40000000000000000000000000000000000000000000000000000002-22-2-22-2200000000
χ9244-4-40000-44-44-40000444-4-4000000000000-4400-44004-4000000000000000000000000000000000000000000000000000000-22-222-22-200000000
χ934-4-44004-4000004-44-404-44-400000000004-40000004-400004-40000000000000000000000000000000000000000002-22-22-22-20000000000000000
χ944-4-44004-4000004-44-404-44-400000000004-40000004-400004-4000000000000000000000000000000000000000000-22-22-22-220000000000000000
χ954-4-44004-400000-44-4404-44-400000000004-4000000-440000-440000000000000000000000000000000000000000002-2-222-2-220000000000000000
χ964-4-44004-400000-44-4404-44-400000000004-4000000-440000-44000000000000000000000000000000000000000000-222-2-222-20000000000000000
χ974-4-4400-44000004-4-4404-44-40000000000-44000000-4400004-40000000000000000000000000000000000000000002-22-2-22-220000000000000000
χ984-4-4400-44000004-4-4404-44-40000000000-44000000-4400004-4000000000000000000000000000000000000000000-22-222-22-20000000000000000
χ994-4-4400-4400000-444-404-44-40000000000-440000004-40000-440000000000000000000000000000000000000000002-2-22-222-20000000000000000
χ1004-4-4400-4400000-444-404-44-40000000000-440000004-40000-44000000000000000000000000000000000000000000-222-22-2-220000000000000000
χ10188-8-800008-888-80000-8-4-444000000000000-4400-4400-440000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-800008-8-8-8800008-4-444000000000000-44004-4004-40000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-80000-888-880000-8-4-4440000000000004-400-44004-40000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-80000-88-88-800008-4-4440000000000004-4004-400-440000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-80000000000008-8-88000000008-80000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-88-8000000000000-444-400000000-440000−4i34i3000000−4i34i300000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-88-8000000000000-444-400000000-4400004i3−4i30000004i3−4i300000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-880000000000008-8-8800000000-880000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-88000000000000-444-4000000004-40000−4i34i30000004i3−4i300000000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-88000000000000-444-4000000004-400004i3−4i3000000−4i34i300000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88008-8000008-88-80-44-440000000000-44000000-440000-44000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88008-800000-88-880-44-440000000000-440000004-400004-4000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-8800-88000008-8-880-44-4400000000004-40000004-40000-44000000000000000000000000000000000000000000000000000000000000000000
χ1148-8-8800-8800000-888-80-44-4400000000004-4000000-4400004-4000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).