Finite Group Databasebeta

← Group #10712391

Character table — Group #10712391

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222222222444444444444444444444444488888888888888888888888888888888242424242424242448484848
order12222344446668844446688812121212121212121212121224242424222244446666666688121212121212121224242424242416161616161616162444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ9111-1-111-11-11-1-111ii−i−i1-11-1-11-1iiii−i−i−i−i1-111-1-111-1-1ii−i−i1111-1-1-1-1i−iiiii−i−i−i−i1-1ii−i−i11-1-1ii−i−i1-1i−i
χ10111-1-111-11-11-1-111ii−i−i1-11-1-11-1iiii−i−i−i−i1-111-1-111-1-1ii−i−i1111-1-1-1-1i−iiiii−i−i−i−i1-1ii−i−i-1-111−i−iii-11−ii
χ11111-1-111-11-11-1-111ii−i−i1-11-1-11-1iiii−i−i−i−i1-111-1-1-1-111−i−iii-1-1-1-11111i−i−i−i−i−iiiii1-1ii−i−i11-1-1ii−i−i-11−ii
χ12111-1-111-11-11-1-111ii−i−i1-11-1-11-1iiii−i−i−i−i1-111-1-1-1-111−i−iii-1-1-1-11111i−i−i−i−i−iiiii1-1ii−i−i-1-111−i−iii1-1i−i
χ13111-1-111-11-11-1-111−i−iii1-11-1-11-1−i−i−i−iiiii1-111-1-111-1-1−i−iii1111-1-1-1-1−ii−i−i−i−iiiii1-1−i−iii11-1-1−i−iii1-1−ii
χ14111-1-111-11-11-1-111−i−iii1-11-1-11-1−i−i−i−iiiii1-111-1-111-1-1−i−iii1111-1-1-1-1−ii−i−i−i−iiiii1-1−i−iii-1-111ii−i−i-11i−i
χ15111-1-111-11-11-1-111−i−iii1-11-1-11-1−i−i−i−iiiii1-111-1-1-1-111ii−i−i-1-1-1-11111−iiiiii−i−i−i−i1-1−i−iii11-1-1−i−iii-11i−i
χ16111-1-111-11-11-1-111−i−iii1-11-1-11-1−i−i−i−iiiii1-111-1-1-1-111ii−i−i-1-1-1-11111−iiiiii−i−i−i−i1-1−i−iii-1-111ii−i−i1-1−ii
χ172222222222222-2-2222222-2-2-2222222222222-2-2-2-20000000000000000-2-200000000-2-2-2-2-2-2000000000000
χ182222222222222-2-2-2-2-2-222-2-2-222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002200000000-2-22222000000000000
χ19222222-2-2-2-2222002-22-222000-2-222-2-222-2-2-2-20000000000000000000000000000000000002−22−22−22−20000
χ20222222-2-2-2-2222002-22-222000-2-222-2-222-2-2-2-2000000000000000000000000000000000000−22−22−22−220000
χ21222222-2-2-2-222200-22-2222000-2-2-2-222-2-222-2-20000000000000000000000000000000000002−22−2−22−220000
χ22222222-2-2-2-222200-22-2222000-2-2-2-222-2-222-2-2000000000000000000000000000000000000−22−222−22−20000
χ2322222-12222-1-1-1222222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2422222-12222-1-1-1222222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111112211111111-1-1-1-1-1-1000000000000
χ2522222-12222-1-1-122-2-2-2-2-1-1222-1-111111111-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-1-11111000000000000
χ2622222-12222-1-1-122-2-2-2-2-1-1222-1-111111111-1-1-1-1-1-1-2-2-2-2222211111111-2-2-1-1-1-1-1-1-1-1-1-11111000000000000
χ2722222-12222-1-1-1-2-22222-1-1-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3-2-2−i3−i3i3i3−i3−i3i3i3111111000000000000
χ2822222-12222-1-1-1-2-22222-1-1-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3-2-2i3i3−i3−i3i3i3−i3−i3111111000000000000
χ2922222-12222-1-1-1-2-2-2-2-2-2-1-1-2-2-2-1-111111111-1-1111100000000−i3−i3i3i3−i3−i3i3i322i3i3−i3−i3i3i3−i3−i311-1-1-1-1000000000000
χ3022222-12222-1-1-1-2-2-2-2-2-2-1-1-2-2-2-1-111111111-1-1111100000000i3i3−i3−i3i3i3−i3−i322−i3−i3i3i3−i3−i3i3i311-1-1-1-1000000000000
χ31222-2-222-22-22-2-2-2-22i2i−2i−2i2-2-2222-22i2i2i2i−2i−2i−2i−2i2-2-2-2220000000000000000−2i2i00000000-22−2i−2i2i2i000000000000
χ32222-2-222-22-22-2-2-2-2−2i−2i2i2i2-2-2222-2−2i−2i−2i−2i2i2i2i2i2-2-2-22200000000000000002i−2i00000000-222i2i−2i−2i000000000000
χ33222-2-22-22-222-2-2002i−2i−2i2i2-2000-222i2i−2i−2i−2i−2i2i2i-220000000000000000000000000000000000002−2−22i2−i2−i2i20000
χ34222-2-22-22-222-2-2002i−2i−2i2i2-2000-222i2i−2i−2i−2i−2i2i2i-22000000000000000000000000000000000000−222−2−i2i2i2−i20000
χ35222-2-22-22-222-2-200−2i2i2i−2i2-2000-22−2i−2i2i2i2i2i−2i−2i-220000000000000000000000000000000000002−2−22−i2i2i2−i20000
χ36222-2-22-22-222-2-200−2i2i2i−2i2-2000-22−2i−2i2i2i2i2i−2i−2i-22000000000000000000000000000000000000−222−2i2−i2−i2i20000
χ37222-2-2-12-22-2-111222i2i−2i−2i-112-2-2-11−i−i−i−iiiii-11-1-11122-2-22i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii-11−i−iii000000000000
χ38222-2-2-12-22-2-111222i2i−2i−2i-112-2-2-11−i−i−i−iiiii-11-1-111-2-222−2i−2i2i2i1111-1-1-1-12i−2iiiii−i−i−i−i-11−i−iii000000000000
χ39222-2-2-12-22-2-11122−2i−2i2i2i-112-2-2-11iiii−i−i−i−i-11-1-11122-2-2−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i-11ii−i−i000000000000
χ40222-2-2-12-22-2-11122−2i−2i2i2i-112-2-2-11iiii−i−i−i−i-11-1-111-2-2222i2i−2i−2i1111-1-1-1-1−2i2i−i−i−i−iiiii-11ii−i−i000000000000
χ41222-2-2-12-22-2-111-2-22i2i−2i−2i-11-222-11−i−i−i−iiiii-1111-1-100000000−i3−i3i3i3i3i3−i3−i3−2i2i33−3−3−3−3331-1ii−i−i000000000000
χ42222-2-2-12-22-2-111-2-22i2i−2i−2i-11-222-11−i−i−i−iiiii-1111-1-100000000i3i3−i3−i3−i3−i3i3i3−2i2i−3−33333−3−31-1ii−i−i000000000000
χ43222-2-2-12-22-2-111-2-2−2i−2i2i2i-11-222-11iiii−i−i−i−i-1111-1-100000000−i3−i3i3i3i3i3−i3−i32i−2i−3−33333−3−31-1−i−iii000000000000
χ44222-2-2-12-22-2-111-2-2−2i−2i2i2i-11-222-11iiii−i−i−i−i-1111-1-100000000i3i3−i3−i3−i3−i3i3i32i−2i33−3−3−3−3331-1−i−iii000000000000
χ4522-22-22-2-222222220000-2-2-22-2-2-2000000002222222-22-200002-22-22-22-20000000000-2-20000000000000000
χ4622-22-22-2-222222220000-2-2-22-2-2-200000000222222-22-220000-22-22-22-220000000000-2-20000000000000000
χ4722-22-22-2-222222-2-20000-2-22-22-2-20000000022-2-2-2-200002-22-200000000002-22-22-22-2220000000000000000
χ4822-22-22-2-222222-2-20000-2-22-22-2-20000000022-2-2-2-20000-22-220000000000-22-22-22-22220000000000000000
χ4922-22-2-1-2-222-1-1-122000011-22-211−i3i3−i3i3−i3i3−i3i3-1-1-1-1-1-12-22-20000-11-11-11-1100−i3i3i3−i3−i3i3i3−i311−i3i3−i3i3000000000000
χ5022-22-2-1-2-222-1-1-122000011-22-211−i3i3−i3i3−i3i3−i3i3-1-1-1-1-1-1-22-2200001-11-11-11-100i3−i3−i3i3i3−i3−i3i311−i3i3−i3i3000000000000
χ5122-22-2-1-2-222-1-1-122000011-22-211i3−i3i3−i3i3−i3i3−i3-1-1-1-1-1-12-22-20000-11-11-11-1100i3−i3−i3i3i3−i3−i3i311i3−i3i3−i3000000000000
χ5222-22-2-1-2-222-1-1-122000011-22-211i3−i3i3−i3i3−i3i3−i3-1-1-1-1-1-1-22-2200001-11-11-11-100−i3i3i3−i3−i3i3i3−i311i3−i3i3−i3000000000000
χ5322-22-2-1-2-222-1-1-1-2-20000112-2211−i3i3−i3i3−i3i3−i3i3-1-1111100002-22-2−i3i3i3−i3−i3i3i3−i300-11-11-11-11-1-1i3−i3i3−i3000000000000
χ5422-22-2-1-2-222-1-1-1-2-20000112-2211−i3i3−i3i3−i3i3−i3i3-1-111110000-22-22i3−i3−i3i3i3−i3−i3i3001-11-11-11-1-1-1i3−i3i3−i3000000000000
χ5522-22-2-1-2-222-1-1-1-2-20000112-2211i3−i3i3−i3i3−i3i3−i3-1-1111100002-22-2i3−i3−i3i3i3−i3−i3i300-11-11-11-11-1-1−i3i3−i3i3000000000000
χ5622-22-2-1-2-222-1-1-1-2-20000112-2211i3−i3i3−i3i3−i3i3−i3-1-111110000-22-22−i3i3i3−i3−i3i3i3−i3001-11-11-11-1-1-1−i3i3−i3i3000000000000
χ5722-2-222-222-22-2-2220000-22-2-22-22000000002-222-2-22-2-2200002-22-2-22-220000000000-220000000000000000
χ5822-2-222-222-22-2-2220000-22-2-22-22000000002-222-2-2-222-20000-22-222-22-20000000000-220000000000000000
χ5922-2-222-222-22-2-2-2-20000-2222-2-22000000002-2-2-22200002i−2i−2i2i00000000002i−2i2i−2i−2i2i−2i2i2-20000000000000000
χ6022-2-222-222-22-2-2-2-20000-2222-2-22000000002-2-2-2220000−2i2i2i−2i0000000000−2i2i−2i2i2i−2i2i−2i2-20000000000000000
χ6122-2-22-1-222-2-1112200001-1-2-221-13−33−3−33−33-11-1-1112-2-220000-11-111-11-1003−3−33−333−31-13−3−33000000000000
χ6222-2-22-1-222-2-1112200001-1-2-221-13−33−3−33−33-11-1-111-222-200001-11-1-11-1100−333−33−3−331-13−3−33000000000000
χ6322-2-22-1-222-2-1112200001-1-2-221-1−33−333−33−3-11-1-1112-2-220000-11-111-11-100−333−33−3−331-1−333−3000000000000
χ6422-2-22-1-222-2-1112200001-1-2-221-1−33−333−33−3-11-1-111-222-200001-11-1-11-11003−3−33−333−31-1−333−3000000000000
χ6522-2-22-1-222-2-111-2-200001-122-21-13−33−3−33−33-1111-1-100002i−2i−2i2i−i3i3i3−i3i3−i3−i3i300−ii−iii−ii−i-11−333−3000000000000
χ6622-2-22-1-222-2-111-2-200001-122-21-13−33−3−33−33-1111-1-10000−2i2i2i−2ii3−i3−i3i3−i3i3i3−i300i−ii−i−ii−ii-11−333−3000000000000
χ6722-2-22-1-222-2-111-2-200001-122-21-1−33−333−33−3-1111-1-100002i−2i−2i2ii3−i3−i3i3−i3i3i3−i300−ii−iii−ii−i-113−3−33000000000000
χ6822-2-22-1-222-2-111-2-200001-122-21-1−33−333−33−3-1111-1-10000−2i2i2i−2i−i3i3i3−i3i3−i3−i3i300i−ii−i−ii−ii-113−3−33000000000000
χ6944444-2-4-4-4-4-2-2-2004-44-4-2-200022-2-222-2-22222000000000000000000000000000000000000000000000000
χ7044444-2-4-4-4-4-2-2-200-44-44-2-20002222-2-222-2-222000000000000000000000000000000000000000000000000
χ71444-4-4-2-44-44-222004i−4i−4i4i-220002-2−2i−2i2i2i2i2i−2i−2i2-2000000000000000000000000000000000000000000000000
χ72444-4-4-2-44-44-22200−4i4i4i−4i-220002-22i2i−2i−2i−2i−2i2i2i2-2000000000000000000000000000000000000000000000000
χ7344-44-4444-4-4444000000-4-40004400000000-4-4000000000000000000000000000000000000000000000000
χ7444-44-4-244-4-4-2-2-200000022000-2-2−2i32i32i3−2i3−2i32i32i3−2i322000000000000000000000000000000000000000000000000
χ7544-44-4-244-4-4-2-2-200000022000-2-22i3−2i3−2i32i32i3−2i3−2i32i322000000000000000000000000000000000000000000000000
χ7644-4-4444-4-444-4-4000000-440004-400000000-44000000000000000000000000000000000000000000000000
χ7744-4-44-24-4-44-2220000002-2000-2223−23−2323−232323−232-2000000000000000000000000000000000000000000000000
χ7844-4-44-24-4-44-2220000002-2000-22−232323−2323−23−23232-2000000000000000000000000000000000000000000000000
χ798-800080000-80042−4200000000000000000000042−420000000000000000000000000000000000000000000000
χ808-800080000-800−4242000000000000000000000−42420000000000000000000000000000000000000000000000
χ818-8000-400004−4i34i342−42000000000000000000000−22222i6−2i600000000000000000000000000000000000000000000
χ828-8000-400004−4i34i3−424200000000000000000000022−22−2i62i600000000000000000000000000000000000000000000
χ838-8000-4000044i3−4i342−42000000000000000000000−2222−2i62i600000000000000000000000000000000000000000000
χ848-8000-4000044i3−4i3−424200000000000000000000022−222i6−2i600000000000000000000000000000000000000000000

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