Finite Group Databasebeta

← Group #69867

Character table — Group #69867

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222222222222222224444444444444444444444444444444444121212121212121224242424
order1222444422344444466612121212121212121212121244668888888812121212121224242424242424242424242424242424444444442244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ611111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ711111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11-1-1-1ii−i−iii−i−i1111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ101111-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11-1-1-1ii−i−iii−i−i1111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ111111-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11-1-1-1−i−iii−i−iii1111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ121111-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11-1-1-1−i−iii−i−iii1111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ131111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-1-11-1-1ii−i−i−i−iii11-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-1-11-1-1ii−i−i−i−iii11-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-1-11-1-1−i−iiiii−i−i11-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-1-11-1-1−i−iiiii−i−i11-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ182222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111000000000000
χ192222222222-1-2-2-2-222-1-1-111111111-1-1-1-1-2-2-1-12222-2-2-2-2-1-11111-1-1-1-1-1-1-1-111111111000000000000
χ202222222222-1-2-2-2-222-1-1-111111111-1-1-1-1-2-2-1-1-2-2-2-22222-1-1111111111111-1-1-1-1-1-1-1-1000000000000
χ2122222222-2-222222-2-2222222222222222-2-2-2-200000000-2-2-2-2-2-20000000000000000000000000000
χ2222222222-2-22-2-2-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-200000000-2-222220000000000000000000000000000
χ2322222222-2-2-12222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ2422222222-2-2-12222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ2522222222-2-2-1-2-2-2-2-2-2-1-1-111111111-1-1-1-122110000000011-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000
χ2622222222-2-2-1-2-2-2-2-2-2-1-1-111111111-1-1-1-122110000000011-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000
χ272222-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-2-222200000000-2-2-2-2220000000000000000000000000000
χ282222-2-2-2-2222-2-222-2-2222-2-2-2-22222-2-2-2-22-22200000000-2-222-2-20000000000000000000000000000
χ292222-2-2-2-222-122-2-2-2-2-1-1-1-1-1-1-111111111-22-1-1000000001111-1-133−3−3−3−33333−3−3−3−333000000000000
χ302222-2-2-2-222-122-2-2-2-2-1-1-1-1-1-1-111111111-22-1-1000000001111-1-1−3−33333−3−3−3−33333−3−3000000000000
χ312222-2-2-2-222-1-2-222-2-2-1-1-11111-1-1-1-111112-2-1-10000000011-1-11133−3−3−3−333−3−33333−3−3000000000000
χ322222-2-2-2-222-1-2-222-2-2-1-1-11111-1-1-1-111112-2-1-10000000011-1-111−3−33333−3−333−3−3−3−333000000000000
χ332222-2-2-2-2-2-2-122-2-222-1-1-1-1-1-1-1111111112-2112i2i−2i−2i2i2i−2i−2i-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii000000000000
χ342222-2-2-2-2-2-2-122-2-222-1-1-1-1-1-1-1111111112-211−2i−2i2i2i−2i−2i2i2i-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i000000000000
χ352222-2-2-2-2-2-2-1-2-22222-1-1-11111-1-1-1-11111-22112i2i−2i−2i−2i−2i2i2i-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ362222-2-2-2-2-2-2-1-2-22222-1-1-11111-1-1-1-11111-2211−2i−2i2i2i2i2i−2i−2i-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ3722-2-22i2i−2i−2i0022-22i−2i002-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ3822-2-22i2i−2i−2i0022-22i−2i002-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ3922-2-22i2i−2i−2i002-22−2i2i002-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ4022-2-22i2i−2i−2i002-22−2i2i002-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ4122-2-2−2i−2i2i2i0022-2−2i2i002-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ4222-2-2−2i−2i2i2i0022-2−2i2i002-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ4322-2-2−2i−2i2i2i002-222i−2i002-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ4422-2-2−2i−2i2i2i002-222i−2i002-2-2-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ452-2-222-22-22-2200002-2-22-2000000002-22-2002-200002i−2i2i−2i2-20000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ462-2-222-22-22-2200002-2-22-2000000002-22-2002-20000−2i2i−2i2i2-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ472-2-222-22-22-2-100002-21-113−33−33−33−3-11-1100-1100002i−2i2i−2i-113−33−3−i3i3−i3i3−i3i3−i3i3−ii−ii−ii−ii000000000000
χ482-2-222-22-22-2-100002-21-113−33−33−33−3-11-1100-110000−2i2i−2i2i-113−33−3i3−i3i3−i3i3−i3i3−i3i−ii−ii−ii−i000000000000
χ492-2-222-22-22-2-100002-21-11−33−33−33−33-11-1100-1100002i−2i2i−2i-11−33−33i3−i3i3−i3i3−i3i3−i3−ii−ii−ii−ii000000000000
χ502-2-222-22-22-2-100002-21-11−33−33−33−33-11-1100-110000−2i2i−2i2i-11−33−33−i3i3−i3i3−i3i3−i3i3i−ii−ii−ii−i000000000000
χ512-2-222-22-2-2220000-22-22-2000000002-22-200-222-22-20000-2200002-2-222-2-2200000000000000000000
χ522-2-222-22-2-2220000-22-22-2000000002-22-200-22-22-220000-220000-222-2-222-200000000000000000000
χ532-2-222-22-2-22-10000-221-113−33−33−33−3-11-11001-12-22-200001-1−33−33-111-1-111-13−3−333−3−33000000000000
χ542-2-222-22-2-22-10000-221-113−33−33−33−3-11-11001-1-22-2200001-1−33−331-1-111-1-11−333−3−333−3000000000000
χ552-2-222-22-2-22-10000-221-11−33−33−33−33-11-11001-12-22-200001-13−33−3-111-1-111-1−333−3−333−3000000000000
χ562-2-222-22-2-22-10000-221-11−33−33−33−33-11-11001-1-22-2200001-13−33−31-1-111-1-113−3−333−3−33000000000000
χ572-2-22-22-222-220000-22-22-200000000-22-22002-22i−2i−2i2i0000-2200002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ582-2-22-22-222-220000-22-22-200000000-22-22002-2−2i2i2i−2i0000-220000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ592-2-22-22-222-2-10000-221-113−33−3−33−331-11-100-112i−2i−2i2i00001-1−333−3−iii−ii−i−iii3−i3−i3i3−i3i3i3−i3000000000000
χ602-2-22-22-222-2-10000-221-113−33−3−33−331-11-100-11−2i2i2i−2i00001-1−333−3i−i−ii−iii−i−i3i3i3−i3i3−i3−i3i3000000000000
χ612-2-22-22-222-2-10000-221-11−33−333−33−31-11-100-112i−2i−2i2i00001-13−3−33−iii−ii−i−ii−i3i3i3−i3i3−i3−i3i3000000000000
χ622-2-22-22-222-2-10000-221-11−33−333−33−31-11-100-11−2i2i2i−2i00001-13−3−33i−i−ii−iii−ii3−i3−i3i3−i3i3i3−i3000000000000
χ632-2-22-22-22-22200002-2-22-200000000-22-2200-2200002-2-222-20000000000002-22-2-22-22000000000000
χ642-2-22-22-22-22200002-2-22-200000000-22-2200-220000-222-22-2000000000000-22-222-22-2000000000000
χ652-2-22-22-22-22-100002-21-113−33−3−33−331-11-1001-100002-2-22-113−3−33−33−333−33−3-11-111-11-1000000000000
χ662-2-22-22-22-22-100002-21-113−33−3−33−331-11-1001-10000-222-2-113−3−333−33−3−33−331-11-1-11-11000000000000
χ672-2-22-22-22-22-100002-21-11−33−333−33−31-11-1001-100002-2-22-11−333−33−33−3−33−33-11-111-11-1000000000000
χ682-2-22-22-22-22-100002-21-11−33−333−33−31-11-1001-10000-222-2-11−333−3−33−333−33−31-11-1-11-11000000000000
χ6944-4-44i4i−4i−4i00-24-44i−4i00-222-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000
χ7044-4-44i4i−4i−4i00-2-44−4i4i00-22222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000
χ7144-4-4−4i−4i4i4i00-24-4−4i4i00-222-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000
χ7244-4-4−4i−4i4i4i00-2-444i−4i00-22222-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000
χ734-44-44i−4i−4i4i004000000-4-44000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ744-44-44i−4i−4i4i00-200000022-223−23−23232i3−2i3−2i32i3−2i2i2i−2i0000000000000000000000000000000000000000000000
χ754-44-44i−4i−4i4i00-200000022-2−232323−23−2i32i32i3−2i3−2i2i2i−2i0000000000000000000000000000000000000000000000
χ764-44-4−4i4i4i−4i004000000-4-4400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ774-44-4−4i4i4i−4i00-200000022-223−23−2323−2i32i32i3−2i32i−2i−2i2i0000000000000000000000000000000000000000000000
χ784-44-4−4i4i4i−4i00-200000022-2−232323−232i3−2i3−2i32i32i−2i−2i2i0000000000000000000000000000000000000000000000

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