Finite Group Databasebeta

← Group #117145

Character table — Group #117145

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888888888888888888882222444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91-1-1111-1-111-1-111111-1-1-1-1-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1i−iii−i−ii−i11-1-1
χ101-1-1111-1-111-1-111111-1-1-1-1-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−ii−i−iii−ii-1-111
χ111-1-1111-1-111-1-111111-1-1-1-1-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−iiii−i−i−ii-1-111
χ121-1-1111-1-111-1-111111-1-1-1-1-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111i−i−i−iiii−i11-1-1
χ131-1-1111-1-111-1-111111-1-1-1-1-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-1111111-1-1i−i−i−iiii−i-1-111
χ141-1-1111-1-111-1-111111-1-1-1-1-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111-1-111−iiii−i−i−ii11-1-1
χ151-1-1111-1-111-1-111111-1-1-1-1-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-111-1-1−ii−i−iii−ii11-1-1
χ161-1-1111-1-111-1-111111-1-1-1-1-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-1-1-111i−iii−i−ii−i-1-111
χ1722222222222222-2-2-222-2-2-2-2-2-2-2-2-22-22-2000000000000000000000000000000000000000000002i−2i2i−2i
χ1822222222222222-2-2-222-2-2-2-2-2-2-2-2-22-22-200000000000000000000000000000000000000000000−2i2i−2i2i
χ19222222222222-2-222-2-2-2-2-2-2-2-2-222-2-22-22000000000000000000000000000000002-22-2000000000000
χ20222222222222-2-222-2-2-2-2-2-2-2-2-222-2-22-2200000000000000000000000000000000-22-22000000000000
χ21222222222222-2-2-2-22-2-2222222-2-22-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ22222222222222-2-2-2-22-2-2222222-2-22-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ2322222222-2-2-2-22222-22222-2-22222-2-2-2-2-2000000000000000000000000000000000000220000-2-20000
χ2422222222-2-2-2-22222-22222-2-22222-2-2-2-2-2000000000000000000000000000000000000-2-20000220000
χ2522222222-2-2-2-222-2-2222-2-222-2-2-2-22-22-222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2622222222-2-2-2-222-2-2222-2-222-2-2-2-22-22-22-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2222-2-2-2-222-2-22222-22-2000000000000000022-2-222-2-2000000000000000000000000
χ2822222222-2-2-2-2-2-2222-2-2-2-222-2-22222-22-20000000000000000-2-222-2-222000000000000000000000000
χ2922222222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-22222000000000000000000000000000000000000002-22-2000000
χ3022222222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2222200000000000000000000000000000000000000-22-22000000
χ312222-2-2-2-22-22-20000-2002-22-22-20020000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2002-2002-20000000000000000
χ322222-2-2-2-22-22-20000-2002-22-22-20020000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i200-2200-220000000000000000
χ332222-2-2-2-22-22-20000-2002-22-22-20020000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i200-2200-220000000000000000
χ342222-2-2-2-22-22-20000-2002-22-22-20020000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i2002-2002-20000000000000000
χ352222-2-2-2-2-22-220000-200-222-2-220020000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2i2−i2−i2i22-2002-2000000000000000000
χ362222-2-2-2-2-22-220000-200-222-2-220020000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2−i2i2i2−i2-2200-22000000000000000000
χ372222-2-2-2-2-22-220000-200-222-2-220020000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2i2−i2−i2i2-2200-22000000000000000000
χ382222-2-2-2-2-22-220000-200-222-2-220020000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2−i2i2i2−i22-2002-2000000000000000000
χ392-2-2222-2-222-2-222-2-2-2-2-22222-2-222-22-2-22000000000000000000000000000000000000000000002i−2i−2i2i
χ402-2-2222-2-222-2-222-2-2-2-2-22222-2-222-22-2-2200000000000000000000000000000000000000000000−2i2i2i−2i
χ412-2-2222-2-222-2-2-2-222-2222222-2-2-2-2-2-222-2000000000000000000000000000000002-2-22000000000000
χ422-2-2222-2-222-2-2-2-222-2222222-2-2-2-2-2-222-200000000000000000000000000000000-222-2000000000000
χ432-2-2222-2-222-2-2-2-2-2-2222-2-2-2-222222-2-22200000000000000000000000022-2-2-2-2220000000000000000
χ442-2-2222-2-222-2-2-2-2-2-2222-2-2-2-222222-2-222000000000000000000000000-2-22222-2-20000000000000000
χ452-2-2222-2-2-2-2222222-2-2-2-2-22222-2-2-2-2-2220000000000000000000000000000000000002i−2i0000−2i2i0000
χ462-2-2222-2-2-2-2222222-2-2-2-2-22222-2-2-2-2-222000000000000000000000000000000000000−2i2i00002i−2i0000
χ472-2-2222-2-2-2-22222-2-22-2-222-2-2-2-2222-222-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ482-2-2222-2-2-2-22222-2-22-2-222-2-2-2-2222-222-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ492-2-2222-2-2-2-222-2-22222222-2-2-2-2-2-222-2-2200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ502-2-2222-2-2-2-222-2-22222222-2-2-2-2-2-222-2-220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ512-2-2222-2-2-2-222-2-2-2-2-222-2-2222222-222-2-2000000000000000000000000000000000000002i−2i−2i2i000000
χ522-2-2222-2-2-2-222-2-2-2-2-222-2-2222222-222-2-200000000000000000000000000000000000000−2i2i2i−2i000000
χ532-2-22-2-2222-2-220000-200-22-222-2002000022−2−222−2−2−2−222−2−2222−22−2−22−22002-200-220000000000000000
χ542-2-22-2-2222-2-220000-200-22-222-2002000022−2−222−2−2−2−222−2−222−22−222−22−200-22002-20000000000000000
χ552-2-22-2-2222-2-220000-200-22-222-20020000−2−222−2−22222−2−222−2−22−22−2−22−2200-22002-20000000000000000
χ562-2-22-2-2222-2-220000-200-22-222-20020000−2−222−2−22222−2−222−2−2−22−222−22−2002-200-220000000000000000
χ572-2-22-2-222-222-20000-2002-2-22-22002000022−2−2−2−222−2−22222−2−22−2−22−222−22-200-22000000000000000000
χ582-2-22-2-222-222-20000-2002-2-22-22002000022−2−2−2−222−2−22222−2−2−222−22−2−22-22002-2000000000000000000
χ592-2-22-2-222-222-20000-2002-2-22-220020000−2−22222−2−222−2−2−2−2222−2−22−222−2-22002-2000000000000000000
χ602-2-22-2-222-222-20000-2002-2-22-220020000−2−22222−2−222−2−2−2−222−222−22−2−222-200-22000000000000000000
χ614444-4-4-4-44-44-40000400-44-44-4400-40000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-44-4400004004-4-444-400-40000000000000000000000000000000000000000000000000000
χ6344-4-44-44-40000004-40000000004-4000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ6444-4-44-44-40000004-40000000004-400000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ6544-4-44-44-4000000-44000000000-44000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6644-4-44-44-4000000-44000000000-4400000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6744-4-4-44-4400004-40004-40000000000000000022−22−2222000022−22−222200000000000000000000000000000000
χ6844-4-4-44-4400004-40004-400000000000000000−222222−220000−222222−2200000000000000000000000000000000
χ6944-4-4-44-440000-44000-44000000000000022−22−2222000022−22−2222000000000000000000000000000000000000
χ7044-4-4-44-440000-44000-440000000000000−222222−220000−222222−22000000000000000000000000000000000000
χ714-44-44-4-440000004-4000000000-44000002-22-22-22-2-22-22-22-2200000000000000000000000000000000
χ724-44-44-4-440000004-4000000000-4400000-22-22-22-222-22-22-22-200000000000000000000000000000000
χ734-44-44-4-44000000-440000000004-4000002-22-2-22-22-22-222-22-200000000000000000000000000000000
χ744-44-44-4-44000000-440000000004-400000-22-222-22-22-22-2-22-2200000000000000000000000000000000
χ754-44-4-444-400004-4000-44000000000000000002i2−2i2−2i22i20000−2i22i22i2−2i200000000000000000000000000000000
χ764-44-4-444-400004-4000-4400000000000000000−2i22i22i2−2i200002i2−2i2−2i22i200000000000000000000000000000000
χ774-44-4-444-40000-440004-400000000000002i2−2i2−2i22i20000−2i22i22i2−2i2000000000000000000000000000000000000
χ784-44-4-444-40000-440004-40000000000000−2i22i22i2−2i200002i2−2i2−2i22i2000000000000000000000000000000000000
χ794-4-44-4-4444-4-4400004004-44-4-4400-40000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-444-40000400-444-44-400-40000000000000000000000000000000000000000000000000000

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