Finite Group Databasebeta

← Group #69421

Character table — Group #69421

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111111111111222222222222222244444444444444444444444444444444444412121212121212121212121212121212
order122222222222222236666666666666664444444444441212121212121212121212121212121212121212121212124444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-11-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i11-1-1
χ10111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-11-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii−i−iii-1-111
χ11111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-11-1-1ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i−i−iii-1-111
χ12111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-11-1-1ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iiiii−i−i11-1-1
χ13111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-11-1-1−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1−i−iiiii−i−i-1-111
χ14111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-11-1-1−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i−i−iii11-1-1
χ15111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-11-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii11-1-1
χ16111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-11-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−iii−i−i-1-111
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ21222222-2-2-2-2-2-22-2-22-1-1-1-1-1-1-1111111-1112i2i−2i−2i2i2i−2i−2i22-2-2−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111110000000000000000
χ22222222-2-2-2-2-2-22-2-22-1-1-1-1-1-1-1111111-1112i2i−2i−2i−2i−2i2i2i-2-222−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-10000000000000000
χ23222222-2-2-2-2-2-22-2-22-1-1-1-1-1-1-1111111-111−2i−2i2i2i2i2i−2i−2i-2-222iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-10000000000000000
χ24222222-2-2-2-2-2-22-2-22-1-1-1-1-1-1-1111111-111−2i−2i2i2i−2i−2i2i2i22-2-2iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111110000000000000000
χ252222-2-2222-22-2-2-2-2-22222-2-2-2222-2-2-2-22-200002-22-200000000000022-2-222-2-2000000000000000000000000
χ262222-2-2222-22-2-2-2-2-22222-2-2-2222-2-2-2-22-20000-22-22000000000000-2-222-2-222000000000000000000000000
χ272222-2-2222-22-2-2-2-2-2-1-1-1-1111-1-1-11111-1100002-22-2000033−3−333−3−3-1-111-1-11133−3−333−3−30000000000000000
χ282222-2-2222-22-2-2-2-2-2-1-1-1-1111-1-1-11111-1100002-22-20000−3−333−3−333-1-111-1-111−3−333−3−3330000000000000000
χ292222-2-2222-22-2-2-2-2-2-1-1-1-1111-1-1-11111-110000-22-22000033−3−333−3−311-1-111-1-1−3−333−3−3330000000000000000
χ302222-2-2222-22-2-2-2-2-2-1-1-1-1111-1-1-11111-110000-22-220000−3−333−3−33311-1-111-1-133−3−333−3−30000000000000000
χ312222-2-2-2-2-22-22-222-22222-2-2-2-2-2-2222-2-2200002i−2i−2i2i0000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ322222-2-2-2-2-22-22-222-22222-2-2-2-2-2-2222-2-220000−2i2i2i−2i000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ332222-2-2-2-2-22-22-222-2-1-1-1-1111111-1-1-111-100002i−2i−2i2i0000−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i−3−33333−3−30000000000000000
χ342222-2-2-2-2-22-22-222-2-1-1-1-1111111-1-1-111-100002i−2i−2i2i0000i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i33−3−3−3−3330000000000000000
χ352222-2-2-2-2-22-22-222-2-1-1-1-1111111-1-1-111-10000−2i2i2i−2i0000−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii33−3−3−3−3330000000000000000
χ362222-2-2-2-2-22-22-222-2-1-1-1-1111111-1-1-111-10000−2i2i2i−2i0000i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii−3−33333−3−30000000000000000
χ3722-2-22222-22-2-2-22-2-222-2-222-222-222-2-2-2-2000000000000000000000000000000000000000000002-22-20000
χ3822-2-22222-22-2-2-22-2-222-2-222-222-222-2-2-2-200000000000000000000000000000000000000000000-22-220000
χ3922-2-222-2-22-222-2-22-222-2-222-2-2-22-2-22-222000000000000000000000000000000000000000000002i−2i−2i2i0000
χ4022-2-222-2-22-222-2-22-222-2-222-2-2-22-2-22-22200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ4122-2-2-2-222-2-2-222-22222-2-2-2-2222-2-2-222-220000000000000000000000000000000000002-22-2000000000000
χ4222-2-2-2-222-2-2-222-22222-2-2-2-2222-2-2-222-22000000000000000000000000000000000000-22-22000000000000
χ4322-2-2-2-2-2-2222-222-2222-2-2-2-22-2-2222-222-20000000000000000000000000000000000002-2-22000000000000
χ4422-2-2-2-2-2-2222-222-2222-2-2-2-22-2-2222-222-2000000000000000000000000000000000000-222-2000000000000
χ452-22-22-22-222-22-2-2-222-22-22-2-22-222-2-22-2200000000000000000000000000000000000000002i−2i2i−2i00000000
χ462-22-22-22-222-22-2-2-222-22-22-2-22-222-2-22-220000000000000000000000000000000000000000−2i2i−2i2i00000000
χ472-22-22-2-22-2-22-2-22222-22-22-2-2-22-2-22222-200000000000000000000000000000000000000002-2-2200000000
χ482-22-22-2-22-2-22-2-22222-22-22-2-2-22-2-22222-20000000000000000000000000000000000000000-222-200000000
χ492-22-2-222-22-2-2-2222-22-22-2-2222-22-222-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ502-22-2-222-22-2-2-2222-22-22-2-2222-22-222-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ512-22-2-22-22-22222-2-2-22-22-2-222-22-22-2-2-2220000000000000000000000000000000000000000000000002i−2i−2i2i
χ522-22-2-22-22-22222-2-2-22-22-2-222-22-22-2-2-222000000000000000000000000000000000000000000000000−2i2i2i−2i
χ532-2-222-22-2-222-22-22-22-2-222-222-2-22-22-22-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ542-2-222-22-2-222-22-22-22-2-222-222-2-22-22-22-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ552-2-222-22-2-222-22-22-2-111-1-11-1-111-11-11-11000000002i−2i2i−2i3−33−33−33−3−i3i3−i3i3−i3i3−i3i3−ii−ii−ii−ii0000000000000000
χ562-2-222-22-2-222-22-22-2-111-1-11-1-111-11-11-11000000002i−2i2i−2i−33−33−33−33i3−i3i3−i3i3−i3i3−i3−ii−ii−ii−ii0000000000000000
χ572-2-222-22-2-222-22-22-2-111-1-11-1-111-11-11-1100000000−2i2i−2i2i3−33−33−33−3i3−i3i3−i3i3−i3i3−i3i−ii−ii−ii−i0000000000000000
χ582-2-222-22-2-222-22-22-2-111-1-11-1-111-11-11-1100000000−2i2i−2i2i−33−33−33−33−i3i3−i3i3−i3i3−i3i3i−ii−ii−ii−i0000000000000000
χ592-2-222-2-222-2-2222-2-22-2-222-22-222-22-2-2-22000000002i−2i−2i2i00000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ602-2-222-2-222-2-2222-2-22-2-222-22-222-22-2-2-2200000000−2i2i2i−2i0000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ612-2-222-2-222-2-2222-2-2-111-1-11-11-1-11-1111-1000000002i−2i−2i2i−i3i3−i3i3i3−i3i3−i3−33−333−33−3−ii−iii−ii−i0000000000000000
χ622-2-222-2-222-2-2222-2-2-111-1-11-11-1-11-1111-1000000002i−2i−2i2ii3−i3i3−i3−i3i3−i3i33−33−3−33−33−ii−iii−ii−i0000000000000000
χ632-2-222-2-222-2-2222-2-2-111-1-11-11-1-11-1111-100000000−2i2i2i−2i−i3i3−i3i3i3−i3i3−i33−33−3−33−33i−ii−i−ii−ii0000000000000000
χ642-2-222-2-222-2-2222-2-2-111-1-11-11-1-11-1111-100000000−2i2i2i−2ii3−i3i3−i3−i3i3−i3i3−33−333−33−3i−ii−i−ii−ii0000000000000000
χ652-2-22-222-2-2-222-22-222-2-22-22-22-2-2-22-22222-22-2000000002-2-222-2-2200000000000000000000000000000000
χ662-2-22-222-2-2-222-22-222-2-22-22-22-2-2-22-2222-22-2200000000-222-2-222-200000000000000000000000000000000
χ672-2-22-222-2-2-222-22-22-111-11-11-1111-11-1-1-12-22-200000000-111-1-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ682-2-22-222-2-2-222-22-22-111-11-11-1111-11-1-1-12-22-200000000-111-1-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ692-2-22-222-2-2-222-22-22-111-11-11-1111-11-1-1-1-22-22000000001-1-111-1-11−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ702-2-22-222-2-2-222-22-22-111-11-11-1111-11-1-1-1-22-22000000001-1-111-1-11i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ712-2-22-22-2222-2-2-2-2222-2-22-22-2-2222-222-2-22i−2i−2i2i000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ722-2-22-22-2222-2-2-2-2222-2-22-22-2-2222-222-2-2−2i2i2i−2i00000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ732-2-22-22-2222-2-2-2-222-111-11-111-1-1-11-1-1112i−2i−2i2i00000000−iii−ii−i−ii3−3−33−333−3−i3i3i3−i3i3−i3−i3i30000000000000000
χ742-2-22-22-2222-2-2-2-222-111-11-111-1-1-11-1-1112i−2i−2i2i00000000−iii−ii−i−ii−333−33−3−33i3−i3−i3i3−i3i3i3−i30000000000000000
χ752-2-22-22-2222-2-2-2-222-111-11-111-1-1-11-1-111−2i2i2i−2i00000000i−i−ii−iii−i3−3−33−333−3i3−i3−i3i3−i3i3i3−i30000000000000000
χ762-2-22-22-2222-2-2-2-222-111-11-111-1-1-11-1-111−2i2i2i−2i00000000i−i−ii−iii−i−333−33−3−33−i3i3i3−i3i3−i3−i3i30000000000000000
χ7744-4-44444-44-4-4-44-4-4-2-222-2-22-2-22-2-222220000000000000000000000000000000000000000000000000000
χ7844-4-444-4-44-444-4-44-4-2-222-2-2222-222-22-2-20000000000000000000000000000000000000000000000000000
χ7944-4-4-4-444-4-4-444-444-2-22222-2-2-2222-2-22-20000000000000000000000000000000000000000000000000000
χ8044-4-4-4-4-4-4444-444-44-2-22222-222-2-2-22-2-220000000000000000000000000000000000000000000000000000
χ814-44-44-44-444-44-4-4-44-22-22-222-22-2-222-22-20000000000000000000000000000000000000000000000000000
χ824-44-44-4-44-4-44-4-4444-22-22-2222-222-2-2-2-220000000000000000000000000000000000000000000000000000
χ834-44-4-444-44-4-4-4444-4-22-222-2-2-22-22-2-22220000000000000000000000000000000000000000000000000000
χ844-44-4-44-44-44444-4-4-4-22-222-2-22-22-2222-2-20000000000000000000000000000000000000000000000000000

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