Finite Group Databasebeta

← Group #10712384

Character table — Group #10712384

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222222222444444444444444444444444488888888888888888888888888888888242424242424242448484848
order1222234444688121266688888881212122424242424242424242424242244446666888812121212121212122424242424242424242416161616161616162288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111
χ9111-1-1111-1-11-1-1-1-11-1-11-1ii−i−i11-11iiii−i−i−i−i11-1-11-11-1i−i11-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1-1ii−i−i11-1-11-1i−i
χ10111-1-1111-1-11-1-1-1-11-1-11-1ii−i−i11-11iiii−i−i−i−i11-1-11-11-1i−i11-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1-1−i−iii-1-111-11−ii
χ11111-1-1111-1-11-1-1-1-11-1-11-1ii−i−i11-11iiii−i−i−i−i11-1-1-11-11i−i-1-111−i−iii-1-111ii−i−i−i−i−i−iiiii1-1ii−i−i11-1-1-11−ii
χ12111-1-1111-1-11-1-1-1-11-1-11-1ii−i−i11-11iiii−i−i−i−i11-1-1-11-11i−i-1-111−i−iii-1-111ii−i−i−i−i−i−iiiii1-1−i−iii-1-1111-1i−i
χ13111-1-1111-1-11-1-1-1-11-1-11-1−i−iii11-11−i−i−i−iiiii11-1-11-11-1−ii11-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1-1ii−i−i-1-111-11i−i
χ14111-1-1111-1-11-1-1-1-11-1-11-1−i−iii11-11−i−i−i−iiiii11-1-11-11-1−ii11-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1-1−i−iii11-1-11-1−ii
χ15111-1-1111-1-11-1-1-1-11-1-11-1−i−iii11-11−i−i−i−iiiii11-1-1-11-11−ii-1-111ii−i−i-1-111−i−iiiiiii−i−i−i−i1-1ii−i−i-1-1111-1−ii
χ16111-1-1111-1-11-1-1-1-11-1-11-1−i−iii11-11−i−i−i−iiiii11-1-1-11-11−ii-1-111ii−i−i-1-111−i−iiiiiii−i−i−i−i1-1−i−iii11-1-1-11i−i
χ1722222222222-2-222222-2-22222-222222222222-2-2-2-20000-2-2000000000000-2-2-2-200000000-2-2000000000000
χ1822222222222-2-222222-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2000022000000000000222200000000-2-2000000000000
χ19222222-2-2-2-2200-2-2222002i−2i2i−2i0-2-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000−i2i2−i2i22−22−20000
χ20222222-2-2-2-2200-2-2222002i−2i2i−2i0-2-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000i2−i2i2−i2−22−220000
χ21222222-2-2-2-2200-2-222200−2i2i−2i2i0-2-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000−i2i2−i2i2−22−220000
χ22222222-2-2-2-2200-2-222200−2i2i−2i2i0-2-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000i2−i2i2−i22−22−20000
χ2322222-12222-122-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2422222-12222-122-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-2-2-2-21111-1-1-1-111111111-1-1000000000000
χ2522222-12222-122-1-1-1-1-122-2-2-2-22-1-1-111111111-1-1-1-12222-2-2-1-1-1-1-2-2-2-2-1-1-1-1111111111111-1-1000000000000
χ2622222-12222-122-1-1-1-1-122-2-2-2-22-1-1-111111111-1-1-1-1-2-2-2-2-2-21111222211111111-1-1-1-1-1-1-1-1-1-1000000000000
χ2722222-12222-1-2-2-1-1-1-1-1-2-22222-2-1-1-1-1-1-1-1-1-1-1-111110000-2-2−i3i3−i3i30000−i3i3−i3i31111−i3−i3i3i3−i3−i3i3i311000000000000
χ2822222-12222-1-2-2-1-1-1-1-1-2-22222-2-1-1-1-1-1-1-1-1-1-1-111110000-2-2i3−i3i3−i30000i3−i3i3−i31111i3i3−i3−i3i3i3−i3−i311000000000000
χ2922222-12222-1-2-2-1-1-1-1-1-2-2-2-2-2-2-2-1-1-1111111111111000022−i3i3−i3i30000−i3i3−i3i3-1-1-1-1i3i3−i3−i3i3i3−i3−i311000000000000
χ3022222-12222-1-2-2-1-1-1-1-1-2-2-2-2-2-2-2-1-1-1111111111111000022i3−i3i3−i30000i3−i3i3−i3-1-1-1-1−i3−i3i3i3−i3−i3i3i311000000000000
χ31222-2-2222-2-2222-2-22-2-2-222i2i−2i−2i-22-222i2i2i2i−2i−2i−2i−2i-2-2220000−2i2i000000000000−2i−2i2i2i00000000-22000000000000
χ32222-2-2222-2-2222-2-22-2-2-22−2i−2i2i2i-22-22−2i−2i−2i−2i2i2i2i2i-2-22200002i−2i0000000000002i2i−2i−2i00000000-22000000000000
χ33222-2-22-2-222200222-2-2002-2-220-22-222-2-2-2-2220000000000000000000000000000000000002−2−22−222−20000
χ34222-2-22-2-222200222-2-2002-2-220-22-222-2-2-2-222000000000000000000000000000000000000−222−22−2−220000
χ35222-2-22-2-222200222-2-200-222-20-22-2-2-22222-2-20000000000000000000000000000000000002−2−222−2−220000
χ36222-2-22-2-222200222-2-200-222-20-22-2-2-22222-2-2000000000000000000000000000000000000−222−2−222−20000
χ37222-2-2-122-2-2-12211-111-222i2i−2i−2i-2-11-1−i−i−i−iiiii11-1-10000−2i2i−i3i3i3−i30000−i3i3i3−i3ii−i−i33−3−3−3−3331-1000000000000
χ38222-2-2-122-2-2-12211-111-222i2i−2i−2i-2-11-1−i−i−i−iiiii11-1-10000−2i2ii3−i3−i3i30000i3−i3−i3i3ii−i−i−3−33333−3−31-1000000000000
χ39222-2-2-122-2-2-12211-111-22−2i−2i2i2i-2-11-1iiii−i−i−i−i11-1-100002i−2i−i3i3i3−i30000−i3i3i3−i3−i−iii−3−33333−3−31-1000000000000
χ40222-2-2-122-2-2-12211-111-22−2i−2i2i2i-2-11-1iiii−i−i−i−i11-1-100002i−2ii3−i3−i3i30000i3−i3−i3i3−i−iii33−3−3−3−3331-1000000000000
χ41222-2-2-122-2-2-1-2-211-1112-22i2i−2i−2i2-11-1−i−i−i−iiiii-1-1112-22-22i−2i-1-1112i2i−2i−2i-1-111−i−iii−i−i−i−iiiii-11000000000000
χ42222-2-2-122-2-2-1-2-211-1112-22i2i−2i−2i2-11-1−i−i−i−iiiii-1-111-22-222i−2i11-1-1−2i−2i2i2i11-1-1−i−iiiiiii−i−i−i−i-11000000000000
χ43222-2-2-122-2-2-1-2-211-1112-2−2i−2i2i2i2-11-1iiii−i−i−i−i-1-1112-22-2−2i2i-1-111−2i−2i2i2i-1-111ii−i−iiiii−i−i−i−i-11000000000000
χ44222-2-2-122-2-2-1-2-211-1112-2−2i−2i2i2i2-11-1iiii−i−i−i−i-1-111-22-22−2i2i11-1-12i2i−2i−2i11-1-1ii−i−i−i−i−i−iiiii-11000000000000
χ4522-22-22-22-22222-2-2-22-2-2-200002-22200000000-2-22222-2-20022220000-2-2-2-20000000000002-2000000000000
χ4622-22-22-22-22222-2-2-22-2-2-200002-22200000000-2-222-2-22200-2-2-2-2000022220000000000002-2000000000000
χ4722-22-22-22-222-2-2-2-2-22-2220000-2-2220000000022-2-200000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i-22000000000000
χ4822-22-22-22-222-2-2-2-2-22-2220000-2-2220000000022-2-20000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i-22000000000000
χ4922-22-2-1-22-22-122111-11-2-2000021-1-13−33−33−33−311-1-122-2-200-1-1-1-1000011113−33−33−3−333−3−33-11000000000000
χ5022-22-2-1-22-22-122111-11-2-2000021-1-13−33−33−33−311-1-1-2-2220011110000-1-1-1-13−33−3−333−3−333−3-11000000000000
χ5122-22-2-1-22-22-122111-11-2-2000021-1-1−33−33−33−3311-1-122-2-200-1-1-1-100001111−33−33−333−3−333−3-11000000000000
χ5222-22-2-1-22-22-122111-11-2-2000021-1-1−33−33−33−3311-1-1-2-2220011110000-1-1-1-1−33−333−3−333−3−33-11000000000000
χ5322-22-2-1-22-22-1-2-2111-11220000-21-1-13−33−33−33−3-1-111000000−i3i3−i3i32i−2i2i−2ii3−i3i3−i3−33−33−ii−ii−ii−ii1-1000000000000
χ5422-22-2-1-22-22-1-2-2111-11220000-21-1-13−33−33−33−3-1-111000000i3−i3i3−i3−2i2i−2i2i−i3i3−i3i3−33−33i−ii−ii−ii−i1-1000000000000
χ5522-22-2-1-22-22-1-2-2111-11220000-21-1-1−33−33−33−33-1-111000000−i3i3−i3i3−2i2i−2i2ii3−i3i3−i33−33−3i−ii−ii−ii−i1-1000000000000
χ5622-22-2-1-22-22-1-2-2111-11220000-21-1-1−33−33−33−33-1-111000000i3−i3i3−i32i−2i2i−2i−i3i3−i3i33−33−3−ii−ii−ii−ii1-1000000000000
χ5722-2-222-222-222222-2-222-20000-2-2-2200000000222200000000002-2-22000000002-22-2-22-22-2-2000000000000
χ5822-2-222-222-222222-2-222-20000-2-2-220000000022220000000000-222-200000000-22-222-22-2-2-2000000000000
χ5922-2-222-222-22-2-222-2-22-2200002-2-2200000000-2-2-2-22-2-220022-2-20000-2-22200000000000022000000000000
χ6022-2-222-222-22-2-222-2-22-2200002-2-2200000000-2-2-2-2-222-200-2-222000022-2-200000000000022000000000000
χ6122-2-22-1-222-2-122-1-111-12-20000-211-1−i3i3−i3i3i3−i3i3−i3-1-1-1-1000000−i3i3i3−i32-2-22i3−i3−i3i3i3−i3−i3i3-11-111-11-111000000000000
χ6222-2-22-1-222-2-122-1-111-12-20000-211-1−i3i3−i3i3i3−i3i3−i3-1-1-1-1000000i3−i3−i3i3-222-2−i3i3i3−i3i3−i3−i3i31-11-1-11-1111000000000000
χ6322-2-22-1-222-2-122-1-111-12-20000-211-1i3−i3i3−i3−i3i3−i3i3-1-1-1-1000000−i3i3i3−i3-222-2i3−i3−i3i3−i3i3i3−i31-11-1-11-1111000000000000
χ6422-2-22-1-222-2-122-1-111-12-20000-211-1i3−i3i3−i3−i3i3−i3i3-1-1-1-1000000i3−i3−i3i32-2-22−i3i3i3−i3−i3i3i3−i3-11-111-11-111000000000000
χ6522-2-22-1-222-2-1-2-2-1-111-1-220000211-1−i3i3−i3i3i3−i3i3−i311112-2-2200-1-111000011-1-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3-1-1000000000000
χ6622-2-22-1-222-2-1-2-2-1-111-1-220000211-1−i3i3−i3i3i3−i3i3−i31111-222-20011-1-10000-1-111−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3-1-1000000000000
χ6722-2-22-1-222-2-1-2-2-1-111-1-220000211-1i3−i3i3−i3−i3i3−i3i311112-2-2200-1-111000011-1-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3-1-1000000000000
χ6822-2-22-1-222-2-1-2-2-1-111-1-220000211-1i3−i3i3−i3−i3i3−i3i31111-222-20011-1-10000-1-111i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3-1-1000000000000
χ6944444-2-4-4-4-4-20022-2-2-2004i−4i4i−4i0222−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ7044444-2-4-4-4-4-20022-2-2-200−4i4i−4i4i02222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ71444-4-4-2-4-444-200-2-2-222004-4-4402-22-2-22222-2-2000000000000000000000000000000000000000000000000
χ72444-4-4-2-4-444-200-2-2-22200-444-402-2222-2-2-2-222000000000000000000000000000000000000000000000000
χ7344-44-444-44-440044-44-400000004-4-400000000000000000000000000000000000000000000000000000000
χ7444-44-4-24-44-4-200-2-22-220000000-222−2i32i32i3−2i3−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ7544-44-4-24-44-4-200-2-22-220000000-2222i3−2i3−2i32i32i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ7644-4-4444-4-44400-4-4-4-44000000044-400000000000000000000000000000000000000000000000000000000
χ7744-4-44-24-4-44-2002222-20000000-2-2223−23−2323−232323−23000000000000000000000000000000000000000000000000
χ7844-4-44-24-4-44-2002222-20000000-2-22−232323−2323−23−2323000000000000000000000000000000000000000000000000
χ798-800080000-842−42000000000000000000000000042−4200000000000000000000000000000000000000000000
χ808-800080000-8−42420000000000000000000000000−424200000000000000000000000000000000000000000000
χ818-8000-40000442−4243−4300000000000000000000026−26−222200000000000000000000000000000000000000000000
χ828-8000-40000442−42−4343000000000000000000000−2626−222200000000000000000000000000000000000000000000
χ838-8000-400004−424243−43000000000000000000000−262622−2200000000000000000000000000000000000000000000
χ848-8000-400004−4242−434300000000000000000000026−2622−2200000000000000000000000000000000000000000000

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