Finite Group Databasebeta

← Group #69868

Character table — Group #69868

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222222222222222224444444444444444444444444444444444121212121212121224242424
order1222444422344444466612121212121212121212121244668888888812121212121224242424242424242424242424242424444444444444
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
χ51111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-11-1-1-1ii−i−iii−i−i1111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-11-1-1-1ii−i−iii−i−i1111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-11-1-1-1−i−iii−i−iii1111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-11-1-1-1−i−iii−i−iii1111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-11-1-1ii−i−i−i−iii11-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-11-1-1ii−i−i−i−iii11-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-11-1-1−i−iiiii−i−i11-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-11-1-1−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
χ192222222222-122-2-2-2-2-1-1-111111111-1-1-1-1-2-2-1-12222-2-2-2-2-1-11111-1-1-1-1-1-1-1-111111111000000000000
χ202222222222-122-2-2-2-2-1-1-111111111-1-1-1-1-2-2-1-1-2-2-2-22222-1-1111111111111-1-1-1-1-1-1-1-1000000000000
χ2122222222-2-22-2-22222222222222222222-2-2-2-200000000-2-2-2-2-2-20000000000000000000000000000
χ2222222222-2-22-2-2-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-200000000-2-222220000000000000000000000000000
χ2322222222-2-2-1-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ2422222222-2-2-1-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111i3i3−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
χ272222-2-2-2-2222-2-222-2-22222222-2-2-2-2-2-2-2-2-222200000000-2-2-2-2220000000000000000000000000000
χ282222-2-2-2-2222-2-2-2-222222-2-2-2-22222-2-2-2-22-22200000000-2-222-2-20000000000000000000000000000
χ292222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-111111111-22-1-1000000001111-1-133−3−3−3−33333−3−3−3−333000000000000
χ302222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-111111111-22-1-1000000001111-1-1−3−33333−3−3−3−33333−3−3000000000000
χ312222-2-2-2-222-1-2-2-2-222-1-1-11111-1-1-1-111112-2-1-10000000011-1-11133−3−3−3−333−3−33333−3−3000000000000
χ322222-2-2-2-222-1-2-2-2-222-1-1-11111-1-1-1-111112-2-1-10000000011-1-111−3−33333−3−333−3−3−3−333000000000000
χ332222-2-2-2-2-2-2-12222-2-2-1-1-1-1-1-1-1111111112-2112i2i−2i−2i2i2i−2i−2i-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii000000000000
χ342222-2-2-2-2-2-2-12222-2-2-1-1-1-1-1-1-1111111112-211−2i−2i2i2i−2i−2i2i2i-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i000000000000
χ352222-2-2-2-2-2-2-122-2-222-1-1-11111-1-1-1-11111-22112i2i−2i−2i−2i−2i2i2i-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ362222-2-2-2-2-2-2-122-2-222-1-1-11111-1-1-1-11111-2211−2i−2i2i2i2i2i−2i−2i-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ3722-2-222-2-22-222-200002-2-20000000022-2-2002-200002-22-22-20000000000002-22-22-22-2000000000000
χ3822-2-222-2-22-222-200002-2-20000000022-2-2002-20000-22-222-2000000000000-22-22-22-22000000000000
χ3922-2-222-2-22-2-12-20000-11133−3−333−3−3-1-11100-1100002-22-2-113−33−33−33−33−33−3-11-11-11-11000000000000
χ4022-2-222-2-22-2-12-20000-11133−3−333−3−3-1-11100-110000-22-22-113−33−3−33−33−33−331-11-11-11-1000000000000
χ4122-2-222-2-22-2-12-20000-111−3−333−3−333-1-11100-1100002-22-2-11−33−33−33−33−33−33-11-11-11-11000000000000
χ4222-2-222-2-22-2-12-20000-111−3−333−3−333-1-11100-110000-22-22-11−33−333−33−33−33−31-11-11-11-1000000000000
χ4322-2-222-2-2-222-2200002-2-20000000022-2-200-222i−2i2i−2i0000-2200002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ4422-2-222-2-2-222-2200002-2-20000000022-2-200-22−2i2i−2i2i0000-220000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ4522-2-222-2-2-22-1-220000-11133−3−333−3−3-1-111001-12i−2i2i−2i00001-1−33−33−iii−i−iii−i−i3i3i3−i3−i3i3i3−i3000000000000
χ4622-2-222-2-2-22-1-220000-11133−3−333−3−3-1-111001-1−2i2i−2i2i00001-1−33−33i−i−iii−i−iii3−i3−i3i3i3−i3−i3i3000000000000
χ4722-2-222-2-2-22-1-220000-111−3−333−3−333-1-111001-12i−2i2i−2i00001-13−33−3−iii−i−iii−ii3−i3−i3i3i3−i3−i3i3000000000000
χ4822-2-222-2-2-22-1-220000-111−3−333−3−333-1-111001-1−2i2i−2i2i00001-13−33−3i−i−iii−i−ii−i3i3i3−i3−i3i3i3−i3000000000000
χ4922-2-2-2-2222-22-2200002-2-200000000-2-222002-22-2-220000-2200002-2-22-222-200000000000000000000
χ5022-2-2-2-2222-22-2200002-2-200000000-2-222002-2-222-20000-220000-222-22-2-2200000000000000000000
χ5122-2-2-2-2222-2-1-220000-11133−3−3−3−33311-1-100-112-2-2200001-1−333−3-111-11-1-11−333−33−3−33000000000000
χ5222-2-2-2-2222-2-1-220000-11133−3−3−3−33311-1-100-11-222-200001-1−333−31-1-11-111-13−3−33−333−3000000000000
χ5322-2-2-2-2222-2-1-220000-111−3−33333−3−311-1-100-112-2-2200001-13−3−33-111-11-1-113−3−33−333−3000000000000
χ5422-2-2-2-2222-2-1-220000-111−3−33333−3−311-1-100-11-222-200001-13−3−331-1-11-111-1−333−33−3−33000000000000
χ5522-2-2-2-222-2222-200002-2-200000000-2-22200-2200002i−2i−2i2i2-20000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ5622-2-2-2-222-2222-200002-2-200000000-2-22200-220000−2i2i2i−2i2-2000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ5722-2-2-2-222-22-12-20000-11133−3−3−3−33311-1-1001-100002i−2i−2i2i-113−3−33i3−i3i3−i3−i3i3−i3i3−ii−iii−ii−i000000000000
χ5822-2-2-2-222-22-12-20000-11133−3−3−3−33311-1-1001-10000−2i2i2i−2i-113−3−33−i3i3−i3i3i3−i3i3−i3i−ii−i−ii−ii000000000000
χ5922-2-2-2-222-22-12-20000-111−3−33333−3−311-1-1001-100002i−2i−2i2i-11−333−3−i3i3−i3i3i3−i3i3−i3−ii−iii−ii−i000000000000
χ6022-2-2-2-222-22-12-20000-111−3−33333−3−311-1-1001-10000−2i2i2i−2i-11−333−3i3−i3i3−i3−i3i3−i3i3i−ii−i−ii−ii000000000000
χ612-22-22i−2i2i−2i002002-22i−2i-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ622-22-22i−2i2i−2i002002-22i−2i-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ632-22-22i−2i2i−2i00200-22−2i2i-22-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ642-22-22i−2i2i−2i00200-22−2i2i-22-2-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ652-22-2−2i2i−2i2i002002-2−2i2i-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ662-22-2−2i2i−2i2i002002-2−2i2i-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ672-22-2−2i2i−2i2i00200-222i−2i-22-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ682-22-2−2i2i−2i2i00200-222i−2i-22-2-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ694-44-44i−4i4i−4i00-2004-44i−4i2-22-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ704-44-44i−4i4i−4i00-200-44−4i4i2-222-22-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ714-44-4−4i4i−4i4i00-2004-4−4i4i2-22-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ724-44-4−4i4i−4i4i00-200-444i−4i2-222-22-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ734-4-444i−4i−4i4i004000000-4-44000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ744-4-444i−4i−4i4i00-200000022-223−23−23232i3−2i3−2i32i3−2i2i2i−2i0000000000000000000000000000000000000000000000
χ754-4-444i−4i−4i4i00-200000022-2−232323−23−2i32i32i3−2i3−2i2i2i−2i0000000000000000000000000000000000000000000000
χ764-4-44−4i4i4i−4i004000000-4-4400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ774-4-44−4i4i4i−4i00-200000022-223−23−2323−2i32i32i3−2i32i−2i−2i2i0000000000000000000000000000000000000000000000
χ784-4-44−4i4i4i−4i00-200000022-2−232323−232i3−2i3−2i32i32i−2i−2i2i0000000000000000000000000000000000000000000000

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