Finite Group Databasebeta

← Group #10713263

Character table — Group #10713263

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222222222444444448888888888888888161616161616161616161616242424242424242448484848
order1222223444466612121212668888121244881212121224242424242424244488121212122424242416161616161616164444
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
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-111-11-1111-1-1-1-1-1-11-11-111i−ii−iii−i−iii−i−i11-1-11-1i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ101111-1-111-11-1111-1-1-1-1-1-11-11-111i−ii−iii−i−iii−i−i11-1-11-1i−i11-1-1ii−i−i-1-111−i−iii-11−ii
χ111111-1-111-11-1111-1-1-1-1-1-11-11-111i−ii−iii−i−iii−i−i11-1-1-11−ii-1-111−i−iii11-1-1ii−i−i-11−ii
χ121111-1-111-11-1111-1-1-1-1-1-11-11-111i−ii−iii−i−iii−i−i11-1-1-11−ii-1-111−i−iii-1-111−i−iii1-1i−i
χ131111-1-111-11-1111-1-1-1-1-1-11-11-111−ii−ii−i−iii−i−iii11-1-11-1−ii11-1-1−i−iii11-1-1−i−iii1-1−ii
χ141111-1-111-11-1111-1-1-1-1-1-11-11-111−ii−ii−i−iii−i−iii11-1-11-1−ii11-1-1−i−iii-1-111ii−i−i-11i−i
χ151111-1-111-11-1111-1-1-1-1-1-11-11-111−ii−ii−i−iii−i−iii11-1-1-11i−i-1-111ii−i−i11-1-1−i−iii-11i−i
χ161111-1-111-11-1111-1-1-1-1-1-11-11-111−ii−ii−i−iii−i−iii11-1-1-11i−i-1-111ii−i−i-1-111ii−i−i1-1−ii
χ1722222222222222222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2000000000000000000000000
χ19222222-12222-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ20222222-12222-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ21222222-12222-1-1-1-1-1-1-1-1-12222-1-1-2-2-2-211111111-1-1-1-122-2-2-1-1-1-11111000000000000
χ22222222-12222-1-1-1-1-1-1-1-1-12222-1-1-2-2-2-211111111-1-1-1-1-2-2221111-1-1-1-1000000000000
χ23222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-1-1-1-1111111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ24222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-1-1-1-1111111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ25222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2221111-1-1-1-111110000−i3i3−i3i3i3−i3i3−i3000000000000
χ26222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2221111-1-1-1-111110000i3−i3i3−i3−i3i3−i3i3000000000000
χ272222-2-222-22-2222-2-2-2-2-2-2-22-22222i−2i−2i2i2i2i−2i−2i−2i−2i2i2i-2-222000000000000000000000000
χ282222-2-222-22-2222-2-2-2-2-2-2-22-2222−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i-2-222000000000000000000000000
χ292222-2-2-12-22-2-1-1-11111112-22-2-1-12i−2i2i−2i−i−iii−i−iii-1-1112-22i−2i-1-111−i−iii000000000000
χ302222-2-2-12-22-2-1-1-11111112-22-2-1-12i−2i2i−2i−i−iii−i−iii-1-111-22−2i2i11-1-1ii−i−i000000000000
χ312222-2-2-12-22-2-1-1-11111112-22-2-1-1−2i2i−2i2iii−i−iii−i−i-1-1112-2−2i2i-1-111ii−i−i000000000000
χ322222-2-2-12-22-2-1-1-11111112-22-2-1-1−2i2i−2i2iii−i−iii−i−i-1-111-222i−2i11-1-1−i−iii000000000000
χ332222-2-2-12-22-2-1-1-1111111-22-22-1-12i−2i−2i2i−i−iiiii−i−i11-1-10000−i3i3i3−i33−3−33000000000000
χ342222-2-2-12-22-2-1-1-1111111-22-22-1-12i−2i−2i2i−i−iiiii−i−i11-1-10000i3−i3−i3i3−333−3000000000000
χ352222-2-2-12-22-2-1-1-1111111-22-22-1-1−2i2i2i−2iii−i−i−i−iii11-1-10000−i3i3i3−i3−333−3000000000000
χ362222-2-2-12-22-2-1-1-1111111-22-22-1-1−2i2i2i−2iii−i−i−i−iii11-1-10000i3−i3−i3i33−3−33000000000000
χ3722-2-22-22-222-22-2-222-2-22-22-2-22-220000000000002-22-200000000000000002-22-20000
χ3822-2-22-22-222-22-2-222-2-22-22-2-22-220000000000002-22-20000000000000000-22-220000
χ3922-2-22-22-222-22-2-222-2-22-2-222-2-22000000000000-22-220000000000002-22-200000000
χ4022-2-22-22-222-22-2-222-2-22-2-222-2-22000000000000-22-22000000000000-22-2200000000
χ4122-2-2-222-2-2222-2-2-2-222-2222-2-2-220000000000002-2-2200000000000000002i−2i−2i2i0000
χ4222-2-2-222-2-2222-2-2-2-222-2222-2-2-220000000000002-2-220000000000000000−2i2i2i−2i0000
χ4322-2-2-222-2-2222-2-2-2-222-22-2-222-22000000000000-222-20000000000002-2-2200000000
χ4422-2-2-222-2-2222-2-2-2-222-22-2-222-22000000000000-222-2000000000000-222-200000000
χ454444444-4-4-4-4444-4-4-4-4440000-4-40000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-22222-2-20000220000000023−2323−230000000000000000000000000000
χ47444444-2-4-4-4-4-2-2-22222-2-200002200000000−2323−23230000000000000000000000000000
χ484444-4-44-44-444444444-4-40000-4-40000000000000000000000000000000000000000
χ494444-4-4-2-44-44-2-2-2-2-2-2-22200002200000000−2i32i32i3−2i30000000000000000000000000000
χ504444-4-4-2-44-44-2-2-2-2-2-2-222000022000000002i3−2i3−2i32i30000000000000000000000000000
χ5144-4-44-444-4-444-4-4-4-4444-400004-40000000000000000000000000000000000000000
χ5244-4-44-4-24-4-44-22222-2-2-220000-22000023−2323−2300000000000000000000000000000000
χ5344-4-44-4-24-4-44-22222-2-2-220000-220000−2323−232300000000000000000000000000000000
χ5444-4-44-4-2-444-4-222-2-222-224-4-442-2000000000000-22-22000000000000000000000000
χ5544-4-44-4-2-444-4-222-2-222-22-444-42-20000000000002-22-2000000000000000000000000
χ5644-4-4-44444-4-44-4-444-4-4-4400004-40000000000000000000000000000000000000000
χ5744-4-4-44-244-4-4-222-2-2222-20000-220000−2i32i32i3−2i300000000000000000000000000000000
χ5844-4-4-44-244-4-4-222-2-2222-20000-2200002i3−2i3−2i32i300000000000000000000000000000000
χ5944-4-4-44-2-4-444-22222-2-22-244-4-42-2000000000000-222-2000000000000000000000000
χ6044-4-4-44-2-4-444-22222-2-22-2-4-4442-20000000000002-2-22000000000000000000000000
χ618-88-80080000-88-80000000000000000000000000000000000000000000000000000
χ628-88-800-400004-4443−4343−43000000000000000000000000000000000000000000000000
χ638-88-800-400004-44−4343−4343000000000000000000000000000000000000000000000000
χ648-8-880080000-8-880000000000000000000000000000000000000000000000000000
χ658-8-8800-4000044-443−43−4343000000000000000000000000000000000000000000000000
χ668-8-8800-4000044-4−434343−43000000000000000000000000000000000000000000000000

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