Finite Group Databasebeta

← Group #10826860

Character table — Group #10826860

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order122222222234444666444444666666121212121212121212121212224444444466661212121212121212121212121212121212124444444422228888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-111-1-1-1-11-111-1-11111-1-1-1-111-1-1-1-111-1-111111111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-111-1-1-1-11-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1
χ911111-1-1-1-1111111111-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-11-1
χ1011111-1-1-1-1111111111-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-11
χ1111111-1-1-1-1111111111-1-1111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-11
χ1211111-1-1-1-1111111111-1-1111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-11-1
χ1311111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-111111-111-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1111-1-11
χ1411111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-111111-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-111-1
χ1511111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-11-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-111-1
χ1611111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-11-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-11-1-11
χ1722222222222-2-2-2-2222-2-222-2-2222222-2-2-2-22222-2-2-2-20000002-200000000000000-2-222-2-200000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-222222222-2-2-2-2-2-2-2-22222000000-2200000000000000-2-2-2-22200000000000000000000
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
χ202222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2111111111111-1-1-1-1-1-111110000000000000000
χ212222222222-12222-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111112-222-2-2-2-22-2-1-111-1-1-1-11111-1-11111-1-1110000000000000000
χ222222222222-12222-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-22-2-222-2-2-2211-1-11111-1-1-1-1-1-1111111-1-10000000000000000
χ232222222222-1-2-2-2-2-1-1-1-2-222-2-2-1-1-1-1-1-11111-1-1-1-111110000002-200−i3i3−i3i3−i3−i3i3i3−i3−i3i3i311-1-111−i3i3−i3i30000000000000000
χ242222222222-1-2-2-2-2-1-1-1-2-222-2-2-1-1-1-1-1-11111-1-1-1-111110000002-200i3−i3i3−i3i3i3−i3−i3i3i3−i3−i311-1-111i3−i3i3−i30000000000000000
χ252222222222-1-2-2-2-2-1-1-1-2-2-2-222-1-1-1-1-1-111111111-1-1-1-1000000-2200−i3i3i3−i3−i3−i3i3i3i3i3−i3−i31111-1-1−i3i3i3−i30000000000000000
χ262222222222-1-2-2-2-2-1-1-1-2-2-2-222-1-1-1-1-1-111111111-1-1-1-1000000-2200i3−i3−i3i3i3i3−i3−i3−i3−i3i3i31111-1-1i3−i3−i3i30000000000000000
χ2722222-2-2-2-222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-2000000-220000000000000022-2-22200000000000000000000
χ2822222-2-2-2-222-2-2-2-222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222220000002-2000000000000002222-2-200000000000000000000
χ2922222-2-2-2-22-12222-1-1-1-2-22222-1-11111-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-222-1-1-1-111111111111111-1-1-1-10000000000000000
χ3022222-2-2-2-22-12222-1-1-1-2-22222-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-1-1-1-1-111111111110000000000000000
χ3122222-2-2-2-22-12222-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-1111111112-2-2-222222-2-1-1111111-1-1-1-111-1-1-1-1-1-1110000000000000000
χ3222222-2-2-2-22-12222-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-111111111-2222-2-222-2211-1-1-1-1-1-1111111-1-1-1-111-1-10000000000000000
χ3322222-2-2-2-22-1-2-2-2-2-1-1-12222-2-2-1-111111111-1-1-1-11111000000-2200−i3i3−i3i3i3i3−i3−i3i3i3−i3−i3-1-111-1-1−i3i3−i3i30000000000000000
χ3422222-2-2-2-22-1-2-2-2-2-1-1-12222-2-2-1-111111111-1-1-1-11111000000-2200i3−i3i3−i3−i3−i3i3i3−i3−i3i3i3-1-111-1-1i3−i3i3−i30000000000000000
χ3522222-2-2-2-22-1-2-2-2-2-1-1-122-2-222-1-1111111111111-1-1-1-10000002-200−i3i3i3−i3i3i3−i3−i3−i3−i3i3i3-1-1-1-111−i3i3i3−i30000000000000000
χ3622222-2-2-2-22-1-2-2-2-2-1-1-122-2-222-1-1111111111111-1-1-1-10000002-200i3−i3−i3i3−i3−i3i3i3i3i3−i3−i3-1-1-1-111i3−i3−i3i30000000000000000
χ372222-222-2-2-2222-2-22222-20000-2-222-2-222-2-20000000002002-2000-2002200002-22-22-2000000-2-20000000000000000
χ382222-222-2-2-2222-2-22222-20000-2-222-2-222-2-2000000000-200-22000200-2-20000-22-222-2000000220000000000000000
χ392222-222-2-2-22-2-222222-220000-2-222-2-2-2-22200000000202-20000-2022002-22-20000-220000-2-2000000000000000000
χ402222-222-2-2-22-2-222222-220000-2-222-2-2-2-22200000000-20-22000020-2-200-22-220000-22000022000000000000000000
χ412222-222-2-2-2-122-2-2-1-1-12-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i302002-2000-2−i3i3-1-1−i3i3i3−i3-11-11-11−i3i3−i3i3i3−i3110000000000000000
χ422222-222-2-2-2-122-2-2-1-1-12-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i30-200-220002i3−i311i3−i3−i3i31-11-1-11−i3i3−i3i3−i3i3-1-10000000000000000
χ432222-222-2-2-2-122-2-2-1-1-12-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i302002-2000-2i3−i3-1-1i3−i3−i3i3-11-11-11i3−i3i3−i3−i3i3110000000000000000
χ442222-222-2-2-2-122-2-2-1-1-12-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i30-200-220002−i3i311−i3i3i3−i31-11-1-11i3−i3i3−i3i3−i3-1-10000000000000000
χ452222-222-2-2-2-1-2-222-1-1-1-22000011-1-11111-1-1−i3−i3i3i3i3i3−i3−i3202-20000-20-1-1−i3i3-11-11−i3i3i3−i31-1−i3i3i3−i311i3−i30000000000000000
χ462222-222-2-2-2-1-2-222-1-1-1-22000011-1-11111-1-1−i3−i3i3i3i3i3−i3−i3-20-2200002011i3−i31-11-1i3−i3−i3i31-1−i3i3i3−i3-1-1−i3i30000000000000000
χ472222-222-2-2-2-1-2-222-1-1-1-22000011-1-11111-1-1i3i3−i3−i3−i3−i3i3i3202-20000-20-1-1i3−i3-11-11i3−i3−i3i31-1i3−i3−i3i311−i3i30000000000000000
χ482222-222-2-2-2-1-2-222-1-1-1-22000011-1-11111-1-1i3i3−i3−i3−i3−i3i3i3-20-2200002011−i3i31-11-1−i3i3i3−i31-1i3−i3−i3i3-1-1i3−i30000000000000000
χ492222-2-2-222-2222-2-2222-220000-2-2-2-22222-2-2000000000200-22000-200220000-22-22-22000000-2-20000000000000000
χ502222-2-2-222-2222-2-2222-220000-2-2-2-22222-2-2000000000-2002-2000200-2-200002-22-2-22000000220000000000000000
χ512222-2-2-222-22-2-2222222-20000-2-2-2-222-2-2220000000020-220000-202200-22-2200002-20000-2-2000000000000000000
χ522222-2-2-222-22-2-2222222-20000-2-2-2-222-2-22200000000-202-2000020-2-2002-22-200002-2000022000000000000000000
χ532222-2-2-222-2-122-2-2-1-1-1-2200001111-1-1-1-111−i3−i3i3i3−i3−i3i3i30200-22000-2−i3i3-1-1i3−i3−i3i31-11-11-1i3−i3i3−i3i3−i3110000000000000000
χ542222-2-2-222-2-122-2-2-1-1-1-2200001111-1-1-1-111−i3−i3i3i3−i3−i3i3i30-2002-20002i3−i311−i3i3i3−i3-11-111-1i3−i3i3−i3−i3i3-1-10000000000000000
χ552222-2-2-222-2-122-2-2-1-1-1-2200001111-1-1-1-111i3i3−i3−i3i3i3−i3−i30200-22000-2i3−i3-1-1−i3i3i3−i31-11-11-1−i3i3−i3i3−i3i3110000000000000000
χ562222-2-2-222-2-122-2-2-1-1-1-2200001111-1-1-1-111i3i3−i3−i3i3i3−i3−i30-2002-20002−i3i311i3−i3−i3i3-11-111-1−i3i3−i3i3i3−i3-1-10000000000000000
χ572222-2-2-222-2-1-2-222-1-1-12-200001111-1-111-1-1−i3−i3i3i3i3i3−i3−i320-220000-20-1-1−i3i31-11-1i3−i3−i3i3-11i3−i3−i3i311i3−i30000000000000000
χ582222-2-2-222-2-1-2-222-1-1-12-200001111-1-111-1-1−i3−i3i3i3i3i3−i3−i3-202-200002011i3−i3-11-11−i3i3i3−i3-11i3−i3−i3i3-1-1−i3i30000000000000000
χ592222-2-2-222-2-1-2-222-1-1-12-200001111-1-111-1-1i3i3−i3−i3−i3−i3i3i320-220000-20-1-1i3−i31-11-1−i3i3i3−i3-11−i3i3i3−i311−i3i30000000000000000
χ602222-2-2-222-2-1-2-222-1-1-12-200001111-1-111-1-1i3i3−i3−i3−i3−i3i3i3-202-200002011−i3i3-11-11i3−i3−i3i3-11−i3i3i3−i3-1-1i3−i30000000000000000
χ612-2-22-20000222-22-2-2-22002-22-22-200002-22-22-22-22-22-200000000000000000000000000000000000022-2-2002-20000
χ622-2-22-20000222-22-2-2-22002-22-22-200002-22-22-22-22-22-2000000000000000000000000000000000000-2-22200-220000
χ632-2-22-20000222-22-2-2-2200-22-222-200002-22-2-22-22-22-2200000000000000000000000000000000000022-2-200-220000
χ642-2-22-20000222-22-2-2-2200-22-222-200002-22-2-22-22-22-22000000000000000000000000000000000000-2-222002-20000
χ652-2-22-2000022-22-22-2-22002-2-222-20000-22-222-22-2-22-220000000000000000000000000000000022-2-200002-2000000
χ662-2-22-2000022-22-22-2-22002-2-222-20000-22-222-22-2-22-2200000000000000000000000000000000-2-2220000-22000000
χ672-2-22-2000022-22-22-2-2200-222-22-20000-22-22-22-222-22-20000000000000000000000000000000022-2-20000-22000000
χ682-2-22-2000022-22-22-2-2200-222-22-20000-22-22-22-222-22-200000000000000000000000000000000-2-22200002-2000000
χ6944-4-40004-40400004-4-400000000004-4000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ7044-4-40004-40400004-4-400000000004-400000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ7144-4-4000-440400004-4-40000000000-44000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ7244-4-4000-440400004-4-40000000000-4400000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ734-44-404-400040000-44-4000000004-400000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ744-44-404-400040000-44-4000000004-40000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ754-44-40-4400040000-44-400000000-4400000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ764-44-40-4400040000-44-400000000-440000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ774-4-4440000-444-4-44-4-44000000-4400004-4-4400000000000000000000000000000000000000000000000000000000
χ784-4-4440000-44-444-4-4-44000000-440000-444-400000000000000000000000000000000000000000000000000000000
χ794-4-4440000-4-24-4-4422-20000002-20000-222-2−2i32i32i3−2i3−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ804-4-4440000-4-24-4-4422-20000002-20000-222-22i3−2i3−2i32i32i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ814-4-4440000-4-2-444-422-20000002-200002-2-22−2i32i32i3−2i32i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ824-4-4440000-4-2-444-422-20000002-200002-2-222i3−2i3−2i32i3−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ834-4-44-400004-24-44-422-2004-44-4-220000-22-22-22-22-22-22000000000000000000000000000000000000000000000000
χ844-4-44-400004-24-44-422-200-44-44-220000-22-222-22-22-22-2000000000000000000000000000000000000000000000000
χ854-4-44-400004-2-44-4422-2004-4-44-2200002-22-2-22-222-22-2000000000000000000000000000000000000000000000000
χ864-4-44-400004-2-44-4422-200-444-4-2200002-22-22-22-2-22-22000000000000000000000000000000000000000000000000
χ8788-8-80008-80-40000-4440000000000-44000000000000000000000000000000000000000000000000000000000000
χ8888-8-8000-880-40000-44400000000004-4000000000000000000000000000000000000000000000000000000000000
χ898-88-808-8000-400004-4400000000-4400000000000000000000000000000000000000000000000000000000000000
χ908-88-80-88000-400004-44000000004-400000000000000000000000000000000000000000000000000000000000000

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