Finite Group Databasebeta

← Group #10713259

Character table — Group #10713259

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222222222444444448888888888888888161616161616161616161616242424242424242448484848
order12222234444666666688881212121244881212121224242424242424244444121212121212121216161616161616164488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ91111-1-111-11-11-1-11-1-111-11-11-11-1i−ii−iii−i−i11-1-1ii−i−i1-1i−iii−i−i11-1-111-1-1ii−i−i1-1i−i
χ101111-1-111-11-11-1-11-1-111-11-11-11-1i−ii−iii−i−i11-1-1ii−i−i1-1i−iii−i−i11-1-1-1-111−i−iii-11−ii
χ111111-1-111-11-11-1-11-1-111-11-11-11-1i−ii−iii−i−i11-1-1ii−i−i-11−ii−i−iii-1-11111-1-1ii−i−i-11−ii
χ121111-1-111-11-11-1-11-1-111-11-11-11-1i−ii−iii−i−i11-1-1ii−i−i-11−ii−i−iii-1-111-1-111−i−iii1-1i−i
χ131111-1-111-11-11-1-11-1-111-11-11-11-1−ii−ii−i−iii11-1-1−i−iii1-1−ii−i−iii11-1-111-1-1−i−iii1-1−ii
χ141111-1-111-11-11-1-11-1-111-11-11-11-1−ii−ii−i−iii11-1-1−i−iii1-1−ii−i−iii11-1-1-1-111ii−i−i-11i−i
χ151111-1-111-11-11-1-11-1-111-11-11-11-1−ii−ii−i−iii11-1-1−i−iii-11i−iii−i−i-1-11111-1-1−i−iii-11i−i
χ161111-1-111-11-11-1-11-1-111-11-11-11-1−ii−ii−i−iii11-1-1−i−iii-11i−iii−i−i-1-111-1-111ii−i−i1-1−ii
χ17222222222222222222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-2000000000000000000000000
χ18222222222222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000
χ19222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ20222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ21222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-1111122-2-21111-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-11111-2-222-1-1-1-11111000000000000
χ23222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-1-1-1-1111111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ24222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-1-1-1-1111111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ272222-2-222-22-22-2-22-2-22-22-222-22-22i−2i−2i2i2i2i−2i−2i-2-222−2i−2i2i2i000000000000000000000000
χ282222-2-222-22-22-2-22-2-22-22-222-22-2−2i2i2i−2i−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000
χ292222-2-2-12-22-2-111-111-12-22-2-11-112i−2i2i−2i−i−iii-1-111−i−iii2-22i−2i−i−iii-1-111000000000000
χ302222-2-2-12-22-2-111-111-12-22-2-11-112i−2i2i−2i−i−iii-1-111−i−iii-22−2i2iii−i−i11-1-1000000000000
χ312222-2-2-12-22-2-111-111-12-22-2-11-11−2i2i−2i2iii−i−i-1-111ii−i−i2-2−2i2iii−i−i-1-111000000000000
χ322222-2-2-12-22-2-111-111-12-22-2-11-11−2i2i−2i2iii−i−i-1-111ii−i−i-222i−2i−i−iii11-1-1000000000000
χ332222-2-2-12-22-2-111-111-1-22-22-11-112i−2i−2i2i−i−iii11-1-1ii−i−i00003−3−33−i3i3i3−i3000000000000
χ342222-2-2-12-22-2-111-111-1-22-22-11-112i−2i−2i2i−i−iii11-1-1ii−i−i0000−333−3i3−i3−i3i3000000000000
χ352222-2-2-12-22-2-111-111-1-22-22-11-11−2i2i2i−2iii−i−i11-1-1−i−iii00003−3−33i3−i3−i3i3000000000000
χ362222-2-2-12-22-2-111-111-1-22-22-11-11−2i2i2i−2iii−i−i11-1-1−i−iii0000−333−3−i3i3i3−i3000000000000
χ3722-2-22-22-222-2-2222-2-2-22-2-22-222-2000000002-22-2000000000000000000002-22-20000
χ3822-2-22-22-222-2-2222-2-2-22-2-22-222-2000000002-22-200000000000000000000-22-220000
χ3922-2-22-22-222-2-2222-2-2-2-222-2-222-200000000-22-2200000000000000002-22-200000000
χ4022-2-22-22-222-2-2222-2-2-2-222-2-222-200000000-22-220000000000000000-22-2200000000
χ4122-2-2-222-2-222-2-2-2222-222-2-2-2-222000000002-2-22000000000000000000002i−2i−2i2i0000
χ4222-2-2-222-2-222-2-2-2222-222-2-2-2-222000000002-2-2200000000000000000000−2i2i2i−2i0000
χ4322-2-2-222-2-222-2-2-2222-2-2-222-2-22200000000-222-200000000000000002-2-2200000000
χ4422-2-2-222-2-222-2-2-2222-2-2-222-2-22200000000-222-20000000000000000-222-200000000
χ454444444-4-4-4-444444440000-4-4-4-40000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-2-2-2-2000022220000−2i32i3−2i32i300000000000000000000000000000000
χ47444444-2-4-4-4-4-2-2-2-2-2-2-20000222200002i3−2i32i3−2i300000000000000000000000000000000
χ484444-4-44-44-444-4-44-4-440000-44-440000000000000000000000000000000000000000
χ494444-4-4-2-44-44-222-222-200002-22-2000023−23−232300000000000000000000000000000000
χ504444-4-4-2-44-44-222-222-200002-22-20000−232323−2300000000000000000000000000000000
χ5144-4-44-444-4-44-4444-4-4-400004-4-440000000000000000000000000000000000000000
χ5244-4-44-4-24-4-442-2-2-22220000-222-2000000000000−2i32i3−2i32i3000000000000000000000000
χ5344-4-44-4-24-4-442-2-2-22220000-222-20000000000002i3−2i32i3−2i3000000000000000000000000
χ5444-4-44-4-2-444-42-2-2-22224-4-442-2-2200000000-22-220000000000000000000000000000
χ5544-4-44-4-2-444-42-2-2-2222-444-42-2-22000000002-22-20000000000000000000000000000
χ5644-4-4-44444-4-4-4-4-4444-4000044-4-40000000000000000000000000000000000000000
χ5744-4-4-44-244-4-4222-2-2-220000-2-22200000000000023−23−2323000000000000000000000000
χ5844-4-4-44-244-4-4222-2-2-220000-2-222000000000000−232323−23000000000000000000000000
χ5944-4-4-44-2-4-444222-2-2-2244-4-422-2-200000000-222-20000000000000000000000000000
χ6044-4-4-44-2-4-444222-2-2-22-4-44422-2-2000000002-2-220000000000000000000000000000
χ618-88-80080000800-800-8000000000000000000000000000000000000000000000000
χ628-88-800-40000-4−4i34i34−4i34i34000000000000000000000000000000000000000000000000
χ638-88-800-40000-44i3−4i344i3−4i34000000000000000000000000000000000000000000000000
χ648-8-880080000-800-8008000000000000000000000000000000000000000000000000
χ658-8-8800-400004−4i34i344i3−4i3-4000000000000000000000000000000000000000000000000
χ668-8-8800-4000044i3−4i34−4i34i3-4000000000000000000000000000000000000000000000000

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