Finite Group Databasebeta

← Group #10712398

Character table — Group #10712398

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222222222444444444444444444444444488888888888888888888888888888888242424242424242448484848
order1222234444666884444668881212121212121212121212122424242444444444881212121212121212121212121212121224242424242416161616161616162444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1
χ9111-1-111-11-1-1-1111ii−i−i1-11-1-1iiii−i−i−i−i1-11-111-1-111-1-1ii−i−ii−iiiii−i−i−i−i1111-1-1-1-11-1ii−i−i11-1-1ii−i−i1-1i−i
χ10111-1-111-11-1-1-1111ii−i−i1-11-1-1iiii−i−i−i−i1-11-111-1-111-1-1ii−i−ii−iiiii−i−i−i−i1111-1-1-1-11-1ii−i−i-1-111−i−iii-11−ii
χ11111-1-111-11-1-1-1111ii−i−i1-11-1-1iiii−i−i−i−i1-11-111-1-1-1-111−i−iiii−i−i−i−i−iiiii-1-1-1-111111-1ii−i−i11-1-1ii−i−i-11−ii
χ12111-1-111-11-1-1-1111ii−i−i1-11-1-1iiii−i−i−i−i1-11-111-1-1-1-111−i−iiii−i−i−i−i−iiiii-1-1-1-111111-1ii−i−i-1-111−i−iii1-1i−i
χ13111-1-111-11-1-1-1111−i−iii1-11-1-1−i−i−i−iiiii1-11-111-1-111-1-1−i−iii−ii−i−i−i−iiiii1111-1-1-1-11-1−i−iii11-1-1−i−iii1-1−ii
χ14111-1-111-11-1-1-1111−i−iii1-11-1-1−i−i−i−iiiii1-11-111-1-111-1-1−i−iii−ii−i−i−i−iiiii1111-1-1-1-11-1−i−iii-1-111ii−i−i-11i−i
χ15111-1-111-11-1-1-1111−i−iii1-11-1-1−i−i−i−iiiii1-11-111-1-1-1-111ii−i−i−iiiiii−i−i−i−i-1-1-1-111111-1−i−iii11-1-1−i−iii-11i−i
χ16111-1-111-11-1-1-1111−i−iii1-11-1-1−i−i−i−iiiii1-11-111-1-1-1-111ii−i−i−iiiiii−i−i−i−i-1-1-1-111111-1−i−iii-1-111ii−i−i1-1−ii
χ172222222222222-2-2222222-2-2-2222222222222-2-2-2-200000000-2-20000000000000000-2-2-2-2-2-2000000000000
χ182222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000220000000000000000-2-22222000000000000
χ19222222-2-2-2-2222002-22-22200022-2-222-2-2-2-2-2-20000000000000000000000000000000000002−22−22−22−20000
χ20222222-2-2-2-2222002-22-22200022-2-222-2-2-2-2-2-2000000000000000000000000000000000000−22−22−22−220000
χ21222222-2-2-2-222200-22-2222000-2-222-2-222-2-2-2-20000000000000000000000000000000000002−22−2−22−220000
χ22222222-2-2-2-222200-22-2222000-2-222-2-222-2-2-2-2000000000000000000000000000000000000−22−222−22−20000
χ2322222-12222-1-1-1222222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2422222-12222-1-1-1222222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2221111111111111111-1-1-1-1-1-1000000000000
χ2522222-12222-1-1-122-2-2-2-2-1-122211111111-1-1-1-1-1-1-1-12222-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1-1-11111000000000000
χ2622222-12222-1-1-122-2-2-2-2-1-122211111111-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-1-1-1-1-1-1-1-111111111-1-11111000000000000
χ2722222-12222-1-1-1-2-22222-1-1-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111100000000-2-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3111111000000000000
χ2822222-12222-1-1-1-2-22222-1-1-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111100000000-2-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3111111000000000000
χ2922222-12222-1-1-1-2-2-2-2-2-2-1-1-2-2-211111111-1-1-1-111110000000022−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311-1-1-1-1000000000000
χ3022222-12222-1-1-1-2-2-2-2-2-2-1-1-2-2-211111111-1-1-1-111110000000022i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311-1-1-1-1000000000000
χ31222-2-222-22-2-2-22-2-22i2i−2i−2i2-2-2222i2i2i2i−2i−2i−2i−2i2-22-2-2-22200000000−2i2i0000000000000000-22−2i−2i2i2i000000000000
χ32222-2-222-22-2-2-22-2-2−2i−2i2i2i2-2-222−2i−2i−2i−2i2i2i2i2i2-22-2-2-222000000002i−2i0000000000000000-222i2i−2i−2i000000000000
χ33222-2-22-22-22-2-22002i−2i−2i2i2-20002i2i−2i−2i−2i−2i2i2i-22-220000000000000000000000000000000000002−2−22i2−i2−i2i20000
χ34222-2-22-22-22-2-22002i−2i−2i2i2-20002i2i−2i−2i−2i−2i2i2i-22-22000000000000000000000000000000000000−222−2−i2i2i2−i20000
χ35222-2-22-22-22-2-2200−2i2i2i−2i2-2000−2i−2i2i2i2i2i−2i−2i-22-220000000000000000000000000000000000002−2−22−i2i2i2−i20000
χ36222-2-22-22-22-2-2200−2i2i2i−2i2-2000−2i−2i2i2i2i2i−2i−2i-22-22000000000000000000000000000000000000−222−2i2−i2−i2i20000
χ37222-2-2-12-22-211-1222i2i−2i−2i-112-2-2−i−i−i−iiiii-11-11-1-11122-2-22i2i−2i−2i2i−2i−i−i−i−iiiii-1-1-1-11111-11−i−iii000000000000
χ38222-2-2-12-22-211-1222i2i−2i−2i-112-2-2−i−i−i−iiiii-11-11-1-111-2-222−2i−2i2i2i2i−2iiiii−i−i−i−i1111-1-1-1-1-11−i−iii000000000000
χ39222-2-2-12-22-211-122−2i−2i2i2i-112-2-2iiii−i−i−i−i-11-11-1-11122-2-2−2i−2i2i2i−2i2iiiii−i−i−i−i-1-1-1-11111-11ii−i−i000000000000
χ40222-2-2-12-22-211-122−2i−2i2i2i-112-2-2iiii−i−i−i−i-11-11-1-111-2-2222i2i−2i−2i−2i2i−i−i−i−iiiii1111-1-1-1-1-11ii−i−i000000000000
χ41222-2-2-12-22-211-1-2-22i2i−2i−2i-11-222−i−i−i−iiiii-11-1111-1-100000000−2i2i33−3−3−3−333−i3−i3i3i3i3i3−i3−i31-1ii−i−i000000000000
χ42222-2-2-12-22-211-1-2-22i2i−2i−2i-11-222−i−i−i−iiiii-11-1111-1-100000000−2i2i−3−33333−3−3i3i3−i3−i3−i3−i3i3i31-1ii−i−i000000000000
χ43222-2-2-12-22-211-1-2-2−2i−2i2i2i-11-222iiii−i−i−i−i-11-1111-1-1000000002i−2i33−3−3−3−333i3i3−i3−i3−i3−i3i3i31-1−i−iii000000000000
χ44222-2-2-12-22-211-1-2-2−2i−2i2i2i-11-222iiii−i−i−i−i-11-1111-1-1000000002i−2i−3−33333−3−3−i3−i3i3i3i3i3−i3−i31-1−i−iii000000000000
χ4522-22-22-2-222222220000-2-2-22-200000000-2-22222222-22-2000000000000002-22-22-22-2-2-20000000000000000
χ4622-22-22-2-222222220000-2-2-22-200000000-2-2222222-22-2200000000000000-22-22-22-22-2-20000000000000000
χ4722-22-22-2-222222-2-20000-2-22-2200000000-2-222-2-2-2-200002-22-2002-22-22-22-200000000220000000000000000
χ4822-22-22-2-222222-2-20000-2-22-2200000000-2-222-2-2-2-20000-22-2200-22-22-22-2200000000220000000000000000
χ4922-22-2-1-2-222-1-1-122000011-22-2−i3i3−i3i3−i3i3−i3i311-1-1-1-1-1-12-22-2000000−i3i3i3−i3−i3i3i3−i3-11-11-11-1111−i3i3−i3i3000000000000
χ5022-22-2-1-2-222-1-1-122000011-22-2−i3i3−i3i3−i3i3−i3i311-1-1-1-1-1-1-22-22000000i3−i3−i3i3i3−i3−i3i31-11-11-11-111−i3i3−i3i3000000000000
χ5122-22-2-1-2-222-1-1-122000011-22-2i3−i3i3−i3i3−i3i3−i311-1-1-1-1-1-12-22-2000000i3−i3−i3i3i3−i3−i3i3-11-11-11-1111i3−i3i3−i3000000000000
χ5222-22-2-1-2-222-1-1-122000011-22-2i3−i3i3−i3i3−i3i3−i311-1-1-1-1-1-1-22-22000000−i3i3i3−i3−i3i3i3−i31-11-11-11-111i3−i3i3−i3000000000000
χ5322-22-2-1-2-222-1-1-1-2-20000112-22−i3i3−i3i3−i3i3−i3i311-1-1111100002-22-200-11-11-11-11−i3i3i3−i3−i3i3i3−i3-1-1i3−i3i3−i3000000000000
χ5422-22-2-1-2-222-1-1-1-2-20000112-22−i3i3−i3i3−i3i3−i3i311-1-111110000-22-22001-11-11-11-1i3−i3−i3i3i3−i3−i3i3-1-1i3−i3i3−i3000000000000
χ5522-22-2-1-2-222-1-1-1-2-20000112-22i3−i3i3−i3i3−i3i3−i311-1-1111100002-22-200-11-11-11-11i3−i3−i3i3i3−i3−i3i3-1-1−i3i3−i3i3000000000000
χ5622-22-2-1-2-222-1-1-1-2-20000112-22i3−i3i3−i3i3−i3i3−i311-1-111110000-22-22001-11-11-11-1−i3i3i3−i3−i3i3i3−i3-1-1−i3i3−i3i3000000000000
χ5722-2-222-222-2-2-22220000-22-2-2200000000-222-222-2-22-2-22000000000000002-22-2-22-22-220000000000000000
χ5822-2-222-222-2-2-22220000-22-2-2200000000-222-222-2-2-222-200000000000000-22-222-22-2-220000000000000000
χ5922-2-222-222-2-2-22-2-20000-2222-200000000-222-2-2-22200002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i000000002-20000000000000000
χ6022-2-222-222-2-2-22-2-20000-2222-200000000-222-2-2-2220000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i000000002-20000000000000000
χ6122-2-22-1-222-211-12200001-1-2-223−33−3−33−331-1-11-1-1112-2-220000003−3−33−333−3-11-111-11-11-13−3−33000000000000
χ6222-2-22-1-222-211-12200001-1-2-223−33−3−33−331-1-11-1-111-222-2000000−333−33−3−331-11-1-11-111-13−3−33000000000000
χ6322-2-22-1-222-211-12200001-1-2-22−33−333−33−31-1-11-1-1112-2-22000000−333−33−3−33-11-111-11-11-1−333−3000000000000
χ6422-2-22-1-222-211-12200001-1-2-22−33−333−33−31-1-11-1-111-222-20000003−3−33−333−31-11-1-11-111-1−333−3000000000000
χ6522-2-22-1-222-211-1-2-200001-122-23−33−3−33−331-1-1111-1-100002i−2i−2i2i00−ii−iii−ii−i−i3i3i3−i3i3−i3−i3i3-11−333−3000000000000
χ6622-2-22-1-222-211-1-2-200001-122-23−33−3−33−331-1-1111-1-10000−2i2i2i−2i00i−ii−i−ii−iii3−i3−i3i3−i3i3i3−i3-11−333−3000000000000
χ6722-2-22-1-222-211-1-2-200001-122-2−33−333−33−31-1-1111-1-100002i−2i−2i2i00−ii−iii−ii−ii3−i3−i3i3−i3i3i3−i3-113−3−33000000000000
χ6822-2-22-1-222-211-1-2-200001-122-2−33−333−33−31-1-1111-1-10000−2i2i2i−2i00i−ii−i−ii−ii−i3i3i3−i3i3−i3−i3i3-113−3−33000000000000
χ6944444-2-4-4-4-4-2-2-2004-44-4-2-2000-2-222-2-2222222000000000000000000000000000000000000000000000000
χ7044444-2-4-4-4-4-2-2-200-44-44-2-200022-2-222-2-22222000000000000000000000000000000000000000000000000
χ71444-4-4-2-44-4422-2004i−4i−4i4i-22000−2i−2i2i2i2i2i−2i−2i2-22-2000000000000000000000000000000000000000000000000
χ72444-4-4-2-44-4422-200−4i4i4i−4i-220002i2i−2i−2i−2i−2i2i2i2-22-2000000000000000000000000000000000000000000000000
χ7344-44-4444-4-4444000000-4-40000000000044-4-4000000000000000000000000000000000000000000000000
χ7444-44-4-244-4-4-2-2-200000022000−2i32i32i3−2i3−2i32i32i3−2i3-2-222000000000000000000000000000000000000000000000000
χ7544-44-4-244-4-4-2-2-2000000220002i3−2i3−2i32i32i3−2i3−2i32i3-2-222000000000000000000000000000000000000000000000000
χ7644-4-4444-4-44-4-44000000-44000000000004-4-44000000000000000000000000000000000000000000000000
χ7744-4-44-24-4-4422-20000002-200023−23−2323−232323−23-222-2000000000000000000000000000000000000000000000000
χ7844-4-44-24-4-4422-20000002-2000−232323−2323−23−2323-222-2000000000000000000000000000000000000000000000000
χ798-80008000000-842−4200000000000000000000042−420000000000000000000000000000000000000000000000
χ808-80008000000-8−4242000000000000000000000−42420000000000000000000000000000000000000000000000
χ818-8000-40000−4i34i3442−42000000000000000000000−22222i6−2i600000000000000000000000000000000000000000000
χ828-8000-40000−4i34i34−424200000000000000000000022−22−2i62i600000000000000000000000000000000000000000000
χ838-8000-400004i3−4i3442−42000000000000000000000−2222−2i62i600000000000000000000000000000000000000000000
χ848-8000-400004i3−4i34−424200000000000000000000022−222i6−2i600000000000000000000000000000000000000000000

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