Finite Group Databasebeta

← Group #10828626

Character table — Group #10828626

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order122222222234444666444444666666121212121212121212121212224444444466661212121212121212121212121212121212124444444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-1-11-11-111-1-111-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-1-11-11-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-11-11-1-111-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-11-11-1-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1
χ911111-1-1-1-1111111111-1-1111111-1-1-1-11111111111111-11-1-1-1-11-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-11-1
χ1011111-1-1-1-1111111111-1-1111111-1-1-1-11111111111111-11-1-1-1-11-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-11-11
χ1111111-1-1-1-1111111111-1-1111111-1-1-1-1111111111111-11-11-1-11-11-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-11-11
χ1211111-1-1-1-1111111111-1-1111111-1-1-1-1111111111111-11-11-1-11-11-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1111-11-1
χ1311111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1111-1-11
χ1411111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-111-1
χ1511111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-111-1
χ1611111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-11-1-11
χ1722222222222-2-2-2-2222-2-222-2-2222222-2-2-2-22222-2-2-2-200002-2000000000000-2-2000022-2-200000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-222222222-2-2-2-2-2-2-2-222220000-22000000000000-2-20000-2-22200000000000000000000
χ192222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-211111111-1-11111-1-1-1-111110000000000000000
χ212222222222-12222-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111112-22-2-2-22-22-2-1-111-1-111-1-1-1-1111111-1-1110000000000000000
χ222222222222-12222-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-22-22-2-2-22-2211-1-111-1-1-1-111-1-1111111-1-10000000000000000
χ232222222222-1-2-2-2-2-1-1-1-2-222-2-2-1-1-1-1-1-11111-1-1-1-1111100002-20000−i3i3−i3i3−i3i3−i3i311−i3i3−i3i3-1-111−i3i3−i3i30000000000000000
χ242222222222-1-2-2-2-2-1-1-1-2-222-2-2-1-1-1-1-1-11111-1-1-1-1111100002-20000i3−i3i3−i3i3−i3i3−i311i3−i3i3−i3-1-111i3−i3i3−i30000000000000000
χ252222222222-1-2-2-2-2-1-1-1-2-2-2-222-1-1-1-1-1-111111111-1-1-1-10000-220000−i3i3i3−i3−i3i3i3−i311−i3i3i3−i311-1-1−i3i3i3−i30000000000000000
χ262222222222-1-2-2-2-2-1-1-1-2-2-2-222-1-1-1-1-1-111111111-1-1-1-10000-220000i3−i3−i3i3i3−i3−i3i311i3−i3−i3i311-1-1i3−i3−i3i30000000000000000
χ2722222-2-2-2-222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-20000-22000000000000220000-2-22200000000000000000000
χ2822222-2-2-2-222-2-2-2-222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200002-200000000000022000022-2-200000000000000000000
χ2922222-2-2-2-22-12222-1-1-1-2-22222-1-11111-1-1-1-1-1-1-1-1-1-1-1-12-22-2-2-2-22-22-1-11111-1-111-1-111111111-1-10000000000000000
χ3022222-2-2-2-22-12222-1-1-1-2-22222-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-22-22-2-22-22-211-1-1-1-1111111-1-11111-1-1110000000000000000
χ3122222-2-2-2-22-12222-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-111111111222222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-111110000000000000000
χ3222222-2-2-2-22-12222-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-111111111-2-2-2-22222221111-1-1-1-1111111-1-1-1-1-1-1-1-10000000000000000
χ3322222-2-2-2-22-1-2-2-2-2-1-1-12222-2-2-1-111111111-1-1-1-111110000-220000−i3i3i3−i3i3−i3−i3i3-1-1−i3i3i3−i311-1-1i3−i3−i3i30000000000000000
χ3422222-2-2-2-22-1-2-2-2-2-1-1-12222-2-2-1-111111111-1-1-1-111110000-220000i3−i3−i3i3−i3i3i3−i3-1-1i3−i3−i3i311-1-1−i3i3i3−i30000000000000000
χ3522222-2-2-2-22-1-2-2-2-2-1-1-122-2-222-1-1111111111111-1-1-1-100002-20000−i3i3−i3i3i3−i3i3−i3-1-1−i3i3−i3i3-1-111i3−i3i3−i30000000000000000
χ3622222-2-2-2-22-1-2-2-2-2-1-1-122-2-222-1-1111111111111-1-1-1-100002-20000i3−i3i3−i3−i3i3−i3i3-1-1i3−i3i3−i3-1-111−i3i3−i3i30000000000000000
χ372222-222-2-2-2222-2-22222-20000-2-222-2-222-2-200000000020-200020-2002200-2-22-200-2-2000000220000000000000000
χ382222-222-2-2-2222-2-22222-20000-2-222-2-222-2-2000000000-202000-20200-2-200222-20022000000-2-20000000000000000
χ392222-222-2-2-22-2-222222-220000-2-222-2-2-2-2220000000020-200020-202200-2-200-22-2-200000022000000000000000000
χ402222-222-2-2-22-2-222222-220000-2-222-2-2-2-22200000000-202000-2020-2-2002200-2222000000-2-2000000000000000000
χ412222-222-2-2-2-122-2-2-1-1-12-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i3020-200020-2−i3i3-1-1i3−i311-11i3−i311−i3i3−i3i3−i3i3-1-10000000000000000
χ422222-222-2-2-2-122-2-2-1-1-12-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i30-202000-202i3−i311−i3i3-1-1-11−i3i3-1-1−i3i3−i3i3i3−i3110000000000000000
χ432222-222-2-2-2-122-2-2-1-1-12-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i3020-200020-2i3−i3-1-1−i3i311-11−i3i311i3−i3i3−i3i3−i3-1-10000000000000000
χ442222-222-2-2-2-122-2-2-1-1-12-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i30-202000-202−i3i311i3−i3-1-1-11i3−i3-1-1i3−i3i3−i3−i3i3110000000000000000
χ452222-222-2-2-2-1-2-222-1-1-1-22000011-1-11111-1-1−i3−i3i3i3i3i3−i3−i320-200020-20-1-1−i3i311i3−i31-111i3−i3−i3i3i3−i3-1-1−i3i30000000000000000
χ462222-222-2-2-2-1-2-222-1-1-1-22000011-1-11111-1-1−i3−i3i3i3i3i3−i3−i3-202000-202011i3−i3-1-1−i3i31-1-1-1−i3i3−i3i3i3−i311i3−i30000000000000000
χ472222-222-2-2-2-1-2-222-1-1-1-22000011-1-11111-1-1i3i3−i3−i3−i3−i3i3i320-200020-20-1-1i3−i311−i3i31-111−i3i3i3−i3−i3i3-1-1i3−i30000000000000000
χ482222-222-2-2-2-1-2-222-1-1-1-22000011-1-11111-1-1i3i3−i3−i3−i3−i3i3i3-202000-202011−i3i3-1-1i3−i31-1-1-1i3−i3i3−i3−i3i311−i3i30000000000000000
χ492222-2-2-222-2222-2-2222-220000-2-2-2-22222-2-200000000020-2000-20200220022-2200-2-2000000-2-20000000000000000
χ502222-2-2-222-2222-2-2222-220000-2-2-2-22222-2-2000000000-20200020-200-2-200-2-2-220022000000220000000000000000
χ512222-2-2-222-22-2-2222222-20000-2-2-2-222-2-2220000000020-2000-2020220022002-2-2-2000000-2-2000000000000000000
χ522222-2-2-222-22-2-2222222-20000-2-2-2-222-2-22200000000-20200020-20-2-200-2-2002-22200000022000000000000000000
χ532222-2-2-222-2-122-2-2-1-1-1-2200001111-1-1-1-111−i3−i3i3i3−i3−i3i3i3020-2000-202i3−i3-1-1i3−i3-1-11-1−i3i311i3−i3i3−i3−i3i3110000000000000000
χ542222-2-2-222-2-122-2-2-1-1-1-2200001111-1-1-1-111−i3−i3i3i3−i3−i3i3i30-20200020-2−i3i311−i3i3111-1i3−i3-1-1i3−i3i3−i3i3−i3-1-10000000000000000
χ552222-2-2-222-2-122-2-2-1-1-1-2200001111-1-1-1-111i3i3−i3−i3i3i3−i3−i3020-2000-202−i3i3-1-1−i3i3-1-11-1i3−i311−i3i3−i3i3i3−i3110000000000000000
χ562222-2-2-222-2-122-2-2-1-1-1-2200001111-1-1-1-111i3i3−i3−i3i3i3−i3−i30-20200020-2i3−i311i3−i3111-1−i3i3-1-1−i3i3−i3i3−i3i3-1-10000000000000000
χ572222-2-2-222-2-1-2-222-1-1-12-200001111-1-111-1-1−i3−i3i3i3i3i3−i3−i320-2000-2020-1-1i3−i3-1-1i3−i3-1111−i3i3i3−i3−i3i311−i3i30000000000000000
χ582222-2-2-222-2-1-2-222-1-1-12-200001111-1-111-1-1−i3−i3i3i3i3i3−i3−i3-20200020-2011−i3i311−i3i3-11-1-1i3−i3i3−i3−i3i3-1-1i3−i30000000000000000
χ592222-2-2-222-2-1-2-222-1-1-12-200001111-1-111-1-1i3i3−i3−i3−i3−i3i3i320-2000-2020-1-1−i3i3-1-1−i3i3-1111i3−i3−i3i3i3−i311i3−i30000000000000000
χ602222-2-2-222-2-1-2-222-1-1-12-200001111-1-111-1-1i3i3−i3−i3−i3−i3i3i3-20200020-2011i3−i311i3−i3-11-1-1−i3i3−i3i3i3−i3-1-1−i3i30000000000000000
χ6122-2-2-20000222-22-2-22-2002i−2i2i−2i2-200002-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000022-2-2002i−2i0000
χ6222-2-2-20000222-22-2-22-2002i−2i2i−2i2-200002-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000-2-22200−2i2i0000
χ6322-2-2-20000222-22-2-22-200−2i2i−2i2i2-200002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000022-2-200−2i2i0000
χ6422-2-2-20000222-22-2-22-200−2i2i−2i2i2-200002-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000-2-222002i−2i0000
χ6522-2-2-2000022-22-22-22-2002i−2i−2i2i2-20000-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000022-2-200002i−2i000000
χ6622-2-2-2000022-22-22-22-2002i−2i−2i2i2-20000-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000-2-2220000−2i2i000000
χ6722-2-2-2000022-22-22-22-200−2i2i2i−2i2-20000-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000022-2-20000−2i2i000000
χ6822-2-2-2000022-22-22-22-200−2i2i2i−2i2-20000-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000-2-22200002i−2i000000
χ6944-4-440000-444-4-44-44-4000000-4400004-4-4400000000000000000000000000000000000000000000000000000000
χ7044-4-440000-44-444-4-44-4000000-440000-444-400000000000000000000000000000000000000000000000000000000
χ7144-4-440000-4-24-4-442-220000002-20000-222-223−23−232323−23−2323000000000000000000000000000000000000000000000000
χ7244-4-440000-4-24-4-442-220000002-20000-222-2−232323−23−232323−23000000000000000000000000000000000000000000000000
χ7344-4-440000-4-2-444-42-220000002-200002-2-2223−23−2323−232323−23000000000000000000000000000000000000000000000000
χ7444-4-440000-4-2-444-42-220000002-200002-2-22−232323−2323−23−2323000000000000000000000000000000000000000000000000
χ7544-4-4-400004-24-44-42-22004i−4i4i−4i-220000-22-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ7644-4-4-400004-24-44-42-2200−4i4i−4i4i-220000-22-222i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ7744-4-4-400004-2-44-442-22004i−4i−4i4i-2200002-22-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ7844-4-4-400004-2-44-442-2200−4i4i4i−4i-2200002-22-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ794-44-404-400040000-4-44000000004-400000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ804-44-404-400040000-4-44000000004-40000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ814-44-40-4400040000-4-4400000000-4400000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ824-44-40-4400040000-4-4400000000-440000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ834-4-440004-40400004-4-400000000004-4000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ844-4-440004-40400004-4-400000000004-400000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ854-4-44000-440400004-4-40000000000-44000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ864-4-44000-440400004-4-40000000000-4400000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ878-88-808-8000-4000044-400000000-4400000000000000000000000000000000000000000000000000000000000000
χ888-88-80-88000-4000044-4000000004-400000000000000000000000000000000000000000000000000000000000000
χ898-8-880008-80-40000-4440000000000-44000000000000000000000000000000000000000000000000000000000000
χ908-8-88000-880-40000-44400000000004-4000000000000000000000000000000000000000000000000000000000000

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