Finite Group Databasebeta

← Group #10828581

Character table — Group #10828581

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order122222223444466666662244444412121212121212121212121222444444446666661212121212121212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-111-1-111111111111111-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-1-1-111-1-111
χ1211111111111111111111-1-111-1-111111111111111-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-111111-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-11111-1-111-1-1-1-111
χ17222222222-2-2-2-222222222222-2-2-2-22222-2-2-2-2-2-2-2-200-20020000220000-2-2-2-2000022000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-222-2-2-2-2-2-2-2-2222200200-2000022000022-2-20000-2-2000000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-22222-2-2-2-2-2-2-2-200200-20000-2-2000022220000-2-2000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-2222200-20020000-2-20000-2-222000022000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-22-2-22-2-2-2-2-1-11111-1-1-1-11111-1-1111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-1111122-2-2-2-222-2-2-1-1-1-1-1-111-1-1111111-1-1-1-111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-11111-2-2-222-2-2-222-1-1111111-1-1-1-1-1-1111111-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-22211-1-1-1-111111111111111-1-1-1-10000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-222-222-2-21111111111-1-1-1-111-1-1-1-111110000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-11111222222-2-2-2-211-1-1-1-1-1-111-1-1-1-1-1-1111111110000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-11111-2-22-2-222222111111-1-1111111-1-1-1-1-1-1-1-1-1-10000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-11111111100-20020000-1-1−i3−i3i3i31111−i3−i3i3i3-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-11111111100-20020000-1-1i3i3−i3−i31111i3i3−i3−i3-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-22211111111-1-1-1-100200-20000-1-1−i3−i3i3i3-1-111i3i3−i3−i311−i3−i3i3i3i3i3−i3−i30000000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-22211111111-1-1-1-100200-20000-1-1i3i3−i3−i3-1-111−i3−i3i3i311i3i3−i3−i3−i3−i3i3i30000000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-11111111100200-2000011−i3−i3i3i3-1-1-1-1i3i3−i3−i311i3i3−i3−i3−i3−i3i3i30000000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-11111111100200-2000011i3i3−i3−i3-1-1-1-1−i3−i3i3i311−i3−i3i3i3i3i3−i3−i30000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-100-2002000011−i3−i3i3i311-1-1−i3−i3i3i3-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-100-2002000011i3i3−i3−i311-1-1i3i3−i3−i3-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ372-2-222-2-22222-2-2-2-2-2-22222-2002-200000022-2-200000002-20002-22-20000002-22-22-20000002-22-20000000000000000
χ382-2-222-2-22222-2-2-2-2-2-22222-2002-200000022-2-20000000-22000-222-20000002-2-22-22000000-22-220000000000000000
χ392-2-222-2-22222-2-2-2-2-2-2222-2200-2200000022-2-200000002-2000-22-22000000-222-22-2000000-22-220000000000000000
χ402-2-222-2-22222-2-2-2-2-2-2222-2200-2200000022-2-20000000-220002-2-22000000-22-22-220000002-22-20000000000000000
χ412-2-222-2-222-2-222-2-2-2-22222-200-22000000-2-22200002-200002-2002-22-22-200-220000002-22-200000000000000000000
χ422-2-222-2-222-2-222-2-2-2-22222-200-22000000-2-2220000-220000-22002-2-22-2200-22000000-22-2200000000000000000000
χ432-2-222-2-222-2-222-2-2-2-2222-22002-2000000-2-22200002-20000-2200-222-22-2002-2000000-22-2200000000000000000000
χ442-2-222-2-222-2-222-2-2-2-2222-22002-2000000-2-2220000-2200002-200-22-22-22002-20000002-22-200000000000000000000
χ452-2-222-2-22-122-2-21111-1-1-12-2002-200−i3−i3i3i3-1-111−i3−i3i3i30002-20002-2-11−i3i3i3−i3−i3i3-11-11-11−i3i3−i3i3i3−i3-11-110000000000000000
χ462-2-222-2-22-122-2-21111-1-1-12-2002-200−i3−i3i3i3-1-111−i3−i3i3i3000-22000-22-11i3−i3−i3i3−i3i3-111-11-1−i3i3i3−i3−i3i31-11-10000000000000000
χ472-2-222-2-22-122-2-21111-1-1-12-2002-200i3i3−i3−i3-1-111i3i3−i3−i30002-20002-2-11i3−i3−i3i3i3−i3-11-11-11i3−i3i3−i3−i3i3-11-110000000000000000
χ482-2-222-2-22-122-2-21111-1-1-12-2002-200i3i3−i3−i3-1-111i3i3−i3−i3000-22000-22-11−i3i3i3−i3i3−i3-111-11-1i3−i3−i3i3i3−i31-11-10000000000000000
χ492-2-222-2-22-122-2-21111-1-1-1-2200-2200−i3−i3i3i3-1-111−i3−i3i3i30002-2000-221-1i3−i3−i3i3i3−i31-1-11-11i3−i3−i3i3i3−i31-11-10000000000000000
χ502-2-222-2-22-122-2-21111-1-1-1-2200-2200−i3−i3i3i3-1-111−i3−i3i3i3000-220002-21-1−i3i3i3−i3i3−i31-11-11-1i3−i3i3−i3−i3i3-11-110000000000000000
χ512-2-222-2-22-122-2-21111-1-1-1-2200-2200i3i3−i3−i3-1-111i3i3−i3−i30002-2000-221-1−i3i3i3−i3−i3i31-1-11-11−i3i3i3−i3−i3i31-11-10000000000000000
χ522-2-222-2-22-122-2-21111-1-1-1-2200-2200i3i3−i3−i3-1-111i3i3−i3−i3000-220002-21-1i3−i3−i3i3−i3i31-11-11-1−i3i3−i3i3i3−i3-11-110000000000000000
χ532-2-222-2-22-1-2-2221111-1-1-12-200-2200−i3−i3i3i311-1-1i3i3−i3−i32-200002-200-11-11-11i3−i31-1−i3i3i3−i3−i3i3-11-11−i3i3i3−i30000000000000000
χ542-2-222-2-22-1-2-2221111-1-1-12-200-2200−i3−i3i3i311-1-1i3i3−i3−i3-220000-2200-111-11-1i3−i31-1i3−i3−i3i3−i3i31-11-1i3−i3−i3i30000000000000000
χ552-2-222-2-22-1-2-2221111-1-1-12-200-2200i3i3−i3−i311-1-1−i3−i3i3i32-200002-200-11-11-11−i3i31-1i3−i3−i3i3i3−i3-11-11i3−i3−i3i30000000000000000
χ562-2-222-2-22-1-2-2221111-1-1-12-200-2200i3i3−i3−i311-1-1−i3−i3i3i3-220000-2200-111-11-1−i3i31-1−i3i3i3−i3i3−i31-11-1−i3i3i3−i30000000000000000
χ572-2-222-2-22-1-2-2221111-1-1-1-22002-200−i3−i3i3i311-1-1i3i3−i3−i32-20000-22001-1-11-11−i3i3-11i3−i3−i3i3i3−i31-11-1−i3i3i3−i30000000000000000
χ582-2-222-2-22-1-2-2221111-1-1-1-22002-200−i3−i3i3i311-1-1i3i3−i3−i3-2200002-2001-11-11-1−i3i3-11−i3i3i3−i3i3−i3-11-11i3−i3−i3i30000000000000000
χ592-2-222-2-22-1-2-2221111-1-1-1-22002-200i3i3−i3−i311-1-1−i3−i3i3i32-20000-22001-1-11-11i3−i3-11−i3i3i3−i3−i3i31-11-1i3−i3−i3i30000000000000000
χ602-2-222-2-22-1-2-2221111-1-1-1-22002-200i3i3−i3−i311-1-1−i3−i3i3i3-2200002-2001-11-11-1i3−i3-11i3−i3−i3i3−i3i3-11-11−i3i3i3−i30000000000000000
χ612-2-2-2222-222-22-222-2-2-22-2002i−2i002i−2i2i−2i2i−2i2-22-22i−2i2i−2i0000000000000000000000000000000000002-2002i−2i00000000
χ622-2-2-2222-222-22-222-2-2-22-2002i−2i002i−2i2i−2i2i−2i2-22-22i−2i2i−2i000000000000000000000000000000000000-2200−2i2i00000000
χ632-2-2-2222-222-22-222-2-2-22-200−2i2i00−2i2i−2i2i−2i2i2-22-2−2i2i−2i2i0000000000000000000000000000000000002-200−2i2i00000000
χ642-2-2-2222-222-22-222-2-2-22-200−2i2i00−2i2i−2i2i−2i2i2-22-2−2i2i−2i2i000000000000000000000000000000000000-22002i−2i00000000
χ652-2-2-2222-22-22-2222-2-2-22-2002i−2i00−2i2i2i−2i2i−2i-22-22−2i2i−2i2i00000000000000000000000000000000002-2002i−2i0000000000
χ662-2-2-2222-22-22-2222-2-2-22-2002i−2i00−2i2i2i−2i2i−2i-22-22−2i2i−2i2i0000000000000000000000000000000000-2200−2i2i0000000000
χ672-2-2-2222-22-22-2222-2-2-22-200−2i2i002i−2i−2i2i−2i2i-22-222i−2i2i−2i00000000000000000000000000000000002-200−2i2i0000000000
χ682-2-2-2222-22-22-2222-2-2-22-200−2i2i002i−2i−2i2i−2i2i-22-222i−2i2i−2i0000000000000000000000000000000000-22002i−2i0000000000
χ69444-44-4-4-444-4-44-4-444-44-40000000000004-4-44000000000000000000000000000000000000000000000000000000
χ70444-44-4-4-44-444-4-4-444-44-4000000000000-444-4000000000000000000000000000000000000000000000000000000
χ71444-44-4-4-4-24-4-4422-2-22-220000000023−23−2323-222-223−23−232300000000000000000000000000000000000000000000000000
χ72444-44-4-4-4-24-4-4422-2-22-2200000000−232323−23-222-2−232323−2300000000000000000000000000000000000000000000000000
χ73444-44-4-4-4-2-444-422-2-22-220000000023−23−23232-2-22−232323−2300000000000000000000000000000000000000000000000000
χ74444-44-4-4-4-2-444-422-2-22-2200000000−232323−232-2-2223−23−232300000000000000000000000000000000000000000000000000
χ7544-44-44-4-4400004-44-44-4-40000000000000000000000000000000000000000000000000000000000000022−22000000
χ7644-44-44-4-4400004-44-44-4-400000000000000000000000000000000000000000000000000000000000000−2222000000
χ7744-4-4-4-44440000-444-4-4-440000000000000000000000000000000000000000000000000000000000000000000022−22
χ7844-4-4-4-44440000-444-4-4-4400000000000000000000000000000000000000000000000000000000000000000000−2222
χ794-444-4-44-440000-44-444-4-4000000000000000000000000000000000000000000000000000000000000000022−220000
χ804-444-4-44-440000-44-444-4-40000000000000000000000000000000000000000000000000000000000000000−22220000
χ814-44-4-44-44400004-4-44-4-4400000000000000000000000000000000000000000000000000000000000000000022−2200
χ824-44-4-44-44400004-4-44-4-44000000000000000000000000000000000000000000000000000000000000000000−222200
χ834-4-4-4444-4-24-44-4-2-2222-22004i−4i004i−4i−2i2i−2i2i-22-22−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ844-4-4-4444-4-24-44-4-2-2222-2200−4i4i00−4i4i2i−2i2i−2i-22-222i−2i2i−2i00000000000000000000000000000000000000000000000000
χ854-4-4-4444-4-2-44-44-2-2222-22004i−4i00−4i4i−2i2i−2i2i2-22-22i−2i2i−2i00000000000000000000000000000000000000000000000000
χ864-4-4-4444-4-2-44-44-2-2222-2200−4i4i004i−4i2i−2i2i−2i2-22-2−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ8788-88-88-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-8-888-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-888-8-88-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-88-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000000000

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