Finite Group Databasebeta

← Group #69413

Character table — Group #69413

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
χ911111-1-1-1-1-11-111-1-11111111-1-1-1-1-1-11-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111-1-1-1-1-11-111-1-11111111-1-1-1-1-1-11-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111-1-1-1-1-11-111-1-11111111-1-1-1-1-1-11-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1211111-1-1-1-1-11-111-1-11111111-1-1-1-1-1-11-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1311111-1-1-1-1-11-111-1-11111111-1-1-1-1-1-11-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111-1-1-1-1-11-111-1-11111111-1-1-1-1-1-11-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111-1-1-1-1-11-111-1-11111111-1-1-1-1-1-11-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111-1-1-1-1-11-111-1-11111111-1-1-1-1-1-11-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
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
χ2122222-2-2-2-2-22-222-2-2-1-1-1-1-1-1-1111111-11122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ2222222-2-2-2-2-22-222-2-2-1-1-1-1-1-1-1111111-11122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ2322222-2-2-2-2-22-222-2-2-1-1-1-1-1-1-1111111-111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ2422222-2-2-2-2-22-222-2-2-1-1-1-1-1-1-1111111-111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ252222-2222-2-2-2-2-2-22-22222-2-2-22222-2-2-2-2-2000000000000000000000000000000000000000000002-22-20000
χ262222-2222-2-2-2-2-2-22-22222-2-2-22222-2-2-2-2-200000000000000000000000000000000000000000000-22-220000
χ272222-2-2-2-222-22-2-2-222222-2-2-2-2-2-2-222-222000000000000000000000000000000000000000000002i−2i−2i2i0000
χ282222-2-2-2-222-22-2-2-222222-2-2-2-2-2-2-222-22200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ2922-2-2222-222-2-22-2-2-222-2-222-222-2-222-2-2-20000000000000000000000000000000000002-22-2000000000000
χ3022-2-2222-222-2-22-2-2-222-2-222-222-2-222-2-2-2000000000000000000000000000000000000-22-22000000000000
χ3122-2-22-2-22-2-2-222-22222-2-222-2-2-222-2-2-2220000000000000000000000000000000000002-2-22000000000000
χ3222-2-22-2-22-2-2-222-22222-2-222-2-2-222-2-2-222000000000000000000000000000000000000-222-2000000000000
χ3322-2-2-222-2-2-222-22-2222-2-2-2-2222-2-2-2-222200002-22-200000000000022-2-222-2-2000000000000000000000000
χ3422-2-2-222-2-2-222-22-2222-2-2-2-2222-2-2-2-22220000-22-22000000000000-2-222-2-222000000000000000000000000
χ3522-2-2-222-2-2-222-22-22-1-11111-1-1-11111-1-1-100002-22-20000−i3−i3i3i3−i3−i3i3i3-1-111-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ3622-2-2-222-2-2-222-22-22-1-11111-1-1-11111-1-1-100002-22-20000i3i3−i3−i3i3i3−i3−i3-1-111-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ3722-2-2-222-2-2-222-22-22-1-11111-1-1-11111-1-1-10000-22-220000−i3−i3i3i3−i3−i3i3i311-1-111-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ3822-2-2-222-2-2-222-22-22-1-11111-1-1-11111-1-1-10000-22-220000i3i3−i3−i3i3i3−i3−i311-1-111-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ3922-2-2-2-2-22222-2-222-222-2-2-2-22-2-222222-2-200002i−2i−2i2i0000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ4022-2-2-2-2-22222-2-222-222-2-2-2-22-2-222222-2-20000−2i2i2i−2i000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ4122-2-2-2-2-22222-2-222-2-1-11111-111-1-1-1-1-11100002i−2i−2i2i0000−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i33−3−3−3−3330000000000000000
χ4222-2-2-2-2-22222-2-222-2-1-11111-111-1-1-1-1-11100002i−2i−2i2i0000i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i−3−33333−3−30000000000000000
χ4322-2-2-2-2-22222-2-222-2-1-11111-111-1-1-1-1-1110000−2i2i2i−2i0000−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii−3−33333−3−30000000000000000
χ4422-2-2-2-2-22222-2-222-2-1-11111-111-1-1-1-1-1110000−2i2i2i−2i0000i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii33−3−3−3−3330000000000000000
χ452-22-222-222-22-2-2-2-222-22-22-2-22-22-22-222-200000000000000000000000000000000000000002i−2i2i−2i00000000
χ462-22-222-222-22-2-2-2-222-22-22-2-22-22-22-222-20000000000000000000000000000000000000000−2i2i−2i2i00000000
χ472-22-22-22-2-2222-2-22-22-22-22-2-2-22-22-222-2200000000000000000000000000000000000000002i−2i−2i2i00000000
χ482-22-22-22-2-2222-2-22-22-22-22-2-2-22-22-222-220000000000000000000000000000000000000000−2i2i2i−2i00000000
χ492-22-2-22-22-22-2222-2-22-22-2-2222-22-2-22-2-22000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ502-22-2-22-22-22-2222-2-22-22-2-2222-22-2-22-2-2200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ512-22-2-22-22-22-2222-2-2-11-111-1-1-11-111-111-1000000002i−2i2i−2i3−33−33−33−3−i3i3−i3i3−i3i3−i3i3−ii−ii−ii−ii0000000000000000
χ522-22-2-22-22-22-2222-2-2-11-111-1-1-11-111-111-1000000002i−2i2i−2i−33−33−33−33i3−i3i3−i3i3−i3i3−i3−ii−ii−ii−ii0000000000000000
χ532-22-2-22-22-22-2222-2-2-11-111-1-1-11-111-111-100000000−2i2i−2i2i3−33−33−33−3i3−i3i3−i3i3−i3i3−i3i−ii−ii−ii−i0000000000000000
χ542-22-2-22-22-22-2222-2-2-11-111-1-1-11-111-111-100000000−2i2i−2i2i−33−33−33−33−i3i3−i3i3−i3i3−i3i3i−ii−ii−ii−i0000000000000000
χ552-22-2-2-22-22-2-2-222222-22-2-222-22-222-2-22-2000000002-2-2200000000000000002-22-2-22-220000000000000000
χ562-22-2-2-22-22-2-2-222222-22-2-222-22-222-2-22-200000000-222-20000000000000000-22-222-22-20000000000000000
χ572-22-2-2-22-22-2-2-22222-11-111-1-11-11-1-111-11000000002-2-223−33−3−33−33−33−333−33−3-11-111-11-10000000000000000
χ582-22-2-2-22-22-2-2-22222-11-111-1-11-11-1-111-11000000002-2-22−33−333−33−33−33−3−33−33-11-111-11-10000000000000000
χ592-22-2-2-22-22-2-2-22222-11-111-1-11-11-1-111-1100000000-222-23−33−3−33−333−33−3−33−331-11-1-11-110000000000000000
χ602-22-2-2-22-22-2-2-22222-11-111-1-11-11-1-111-1100000000-222-2−33−333−33−3−33−333−33−31-11-1-11-110000000000000000
χ612-2-2222-2-22-2-22-222-22-2-222-222-2-222-2-2-222i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ622-2-2222-2-22-2-22-222-22-2-222-222-2-222-2-2-22−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ632-2-2222-2-22-2-22-222-2-111-1-11-1-111-1-1111-12i−2i2i−2i00000000−iii−i−iii−i−i3i3i3−i3−i3i3i3−i33−3−333−3−330000000000000000
χ642-2-2222-2-22-2-22-222-2-111-1-11-1-111-1-1111-12i−2i2i−2i00000000−iii−i−iii−ii3−i3−i3i3i3−i3−i3i3−333−3−333−30000000000000000
χ652-2-2222-2-22-2-22-222-2-111-1-11-1-111-1-1111-1−2i2i−2i2i00000000i−i−iii−i−ii−i3i3i3−i3−i3i3i3−i3−333−3−333−30000000000000000
χ662-2-2222-2-22-2-22-222-2-111-1-11-1-111-1-1111-1−2i2i−2i2i00000000i−i−iii−i−iii3−i3−i3i3i3−i3−i3i33−3−333−3−330000000000000000
χ672-2-222-222-22-2-2-22-222-2-222-22-222-2-22-22-22i−2i−2i2i000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ682-2-222-222-22-2-2-22-222-2-222-22-222-2-22-22-2−2i2i2i−2i00000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ692-2-222-222-22-2-2-22-22-111-1-11-11-1-111-11-112i−2i−2i2i00000000−iii−ii−i−ii3−3−33−333−3i3−i3−i3i3−i3i3i3−i30000000000000000
χ702-2-222-222-22-2-2-22-22-111-1-11-11-1-111-11-112i−2i−2i2i00000000−iii−ii−i−ii−333−33−3−33−i3i3i3−i3i3−i3−i3i30000000000000000
χ712-2-222-222-22-2-2-22-22-111-1-11-11-1-111-11-11−2i2i2i−2i00000000i−i−ii−iii−i3−3−33−333−3−i3i3i3−i3i3−i3−i3i30000000000000000
χ722-2-222-222-22-2-2-22-22-111-1-11-11-1-111-11-11−2i2i2i−2i00000000i−i−ii−iii−i−333−33−3−33i3−i3−i3i3−i3i3i3−i30000000000000000
χ732-2-22-22-2-2-222-22-2222-2-22-22-22-2-22-2222-20000000000000000000000000000000000000000000000002-22-2
χ742-2-22-22-2-2-222-22-2222-2-22-22-22-2-22-2222-2000000000000000000000000000000000000000000000000-22-22
χ752-2-22-2-2222-2222-2-2-22-2-22-22-2-222-22-22-220000000000000000000000000000000000000000000000002i−2i−2i2i
χ762-2-22-2-2222-2222-2-2-22-2-22-22-2-222-22-22-22000000000000000000000000000000000000000000000000−2i2i2i−2i
χ774444-4444-4-4-4-4-4-44-4-2-2-2-2222-2-2-2-2222220000000000000000000000000000000000000000000000000000
χ784444-4-4-4-444-44-4-4-44-2-2-2-22222222-2-22-2-20000000000000000000000000000000000000000000000000000
χ7944-4-4444-444-4-44-4-4-4-2-222-2-22-2-222-2-22220000000000000000000000000000000000000000000000000000
χ8044-4-44-4-44-4-4-444-444-2-222-2-2222-2-2222-2-20000000000000000000000000000000000000000000000000000
χ814-44-444-444-44-4-4-4-44-22-22-222-22-22-22-2-220000000000000000000000000000000000000000000000000000
χ824-44-44-44-4-4444-4-44-4-22-22-2222-22-22-2-22-20000000000000000000000000000000000000000000000000000
χ834-4-44-44-4-4-444-44-444-222-22-22-222-22-2-2-220000000000000000000000000000000000000000000000000000
χ844-4-44-4-4444-4444-4-4-4-222-22-222-2-22-22-22-20000000000000000000000000000000000000000000000000000

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