Finite Group Databasebeta

← Group #106930

Character table — Group #106930

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444422224444444444888888884444888888888888888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ911111111-1-1-1-1111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ1011111111-1-1-1-1111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1iiii−i−i−i−i11-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111-1-111
χ1111111111-1-1-1-1111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1−i−i−i−iiiii11-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111
χ1211111111-1-1-1-1111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ1311111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-1-11111-11111-1iiii−i−i−i−i-1-111iiii−i−i−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111
χ1411111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-1-11111-11111-1iiii−i−i−i−i-1-111−i−i−i−iiiiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ1511111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-1-11111-11111-1−i−i−i−iiiii-1-111iiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ1611111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-1-11111-11111-1−i−i−i−iiiii-1-111−i−i−i−iiiii−i−iiiiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111
χ171-1-1-1111-111-1-111-1111-1-1-1-11-111-1-111-1-1-111-1-11ii−i−iii−i−i1-11-111-1-111-1-1i−ii−iii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−i
χ181-1-1-1111-111-1-111-1111-1-1-1-11-111-1-111-1-1-111-1-11ii−i−iii−i−i1-11-1-1-111-1-111i−ii−iii−i−iii−i−i-1-111-1-111−ii−ii−ii−ii
χ191-1-1-1111-111-1-111-1111-1-1-1-11-111-1-111-1-1-111-1-11−i−iii−i−iii1-11-111-1-111-1-1−ii−ii−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii
χ201-1-1-1111-111-1-111-1111-1-1-1-11-111-1-111-1-1-111-1-11−i−iii−i−iii1-11-1-1-111-1-111−ii−ii−i−iii−i−iii-1-111-1-111i−ii−ii−ii−i
χ211-1-1-1111-111-1-111-1111-1-1-1-11-1-1-11111-1-1-1-1-1111ii−i−iii−i−i-11-1111-1-111-1-1i−ii−i−i−iii−i−iii-1-111-1-111i−ii−i−ii−ii
χ221-1-1-1111-111-1-111-1111-1-1-1-11-1-1-11111-1-1-1-1-1111ii−i−iii−i−i-11-11-1-111-1-111i−ii−i−i−iii−i−iii11-1-111-1-1−ii−iii−ii−i
χ231-1-1-1111-111-1-111-1111-1-1-1-11-1-1-11111-1-1-1-1-1111−i−iii−i−iii-11-1111-1-111-1-1−ii−iiii−i−iii−i−i-1-111-1-111−ii−iii−ii−i
χ241-1-1-1111-111-1-111-1111-1-1-1-11-1-1-11111-1-1-1-1-1111−i−iii−i−iii-11-11-1-111-1-111−ii−iiii−i−iii−i−i11-1-111-1-1i−ii−i−ii−ii
χ251-1-1-1111-1-1-11111-1-1-1-1111-1-1111-1-111-1-11-1-111-111-1-1-1-1111-1-11ii−i−i−i−iii1-1-1111-1-1-1-111ii−i−i−i−iii−iii−i−iii−i
χ261-1-1-1111-1-1-11111-1-1-1-1111-1-1111-1-111-1-11-1-111-111-1-1-1-1111-1-11−i−iiiii−i−i1-1-1111-1-1-1-111−i−iiiii−i−ii−i−iii−i−ii
χ271-1-1-1111-1-1-11111-1-1-1-1111-1-1111-1-111-1-11-1-111-1-1-11111-1-11-1-11ii−i−i−i−iii-111-1-1-11111-1-1ii−i−i−i−iiii−i−iii−i−ii
χ281-1-1-1111-1-1-11111-1-1-1-1111-1-1111-1-111-1-11-1-111-1-1-11111-1-11-1-11−i−iiiii−i−i-111-1-1-11111-1-1−i−iiiii−i−i−iii−i−iii−i
χ291-1-1-1111-1-1-11111-1-1-1-1111-1-11-1-11111-1-1111-1-1-111-1-1-1-111-111-1ii−i−i−i−iii1-1-11-1-11111-1-1−i−iiiii−i−i−iii−ii−i−ii
χ301-1-1-1111-1-1-11111-1-1-1-1111-1-11-1-11111-1-1111-1-1-111-1-1-1-111-111-1−i−iiiii−i−i1-1-11-1-11111-1-1ii−i−i−i−iiii−i−ii−iii−i
χ311-1-1-1111-1-1-11111-1-1-1-1111-1-11-1-11111-1-1111-1-1-1-1-11111-1-1-111-1ii−i−i−i−iii-111-111-1-1-1-111−i−iiiii−i−ii−i−ii−iii−i
χ321-1-1-1111-1-1-11111-1-1-1-1111-1-11-1-11111-1-1111-1-1-1-1-11111-1-1-111-1−i−iiiii−i−i-111-111-1-1-1-111ii−i−i−i−iii−iii−ii−i−ii
χ3322222222222222222-22-2-22-222222-2-2-2-2-22222-200000000-2-2-2-2000000000000000000000000000000000000
χ3422222222222222222-22-2-22-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000
χ35222222222222-2-2-2-2-22-222-22-200002-22-2-20000-20000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ36222222222222-2-2-2-2-22-222-22-200002-22-2-20000-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-22-222000022i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-22-22200002−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i000000000000000000000000
χ3922222222-2-2-2-2222-2-22-22222-22222-2-2-2-22-2-2-2-2200000000-2-222000000000000000000000000000000000000
χ4022222222-2-2-2-2222-2-22-22222-2-2-2-2-2-2-2-2-22222220000000022-2-2000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2222222-2220000-22-22-20000-222222222000000000000-2-2-2-2000000000000000000000000
χ4222222222-2-2-2-2-2-2-2222222-2220000-22-22-20000-2-2-2-2-2-2-2-2-20000000000002222000000000000000000000000
χ4322222222-2-2-2-2-2-2-222-22-2-2-2-2200002-22-22000020000000000000000000000002-22-2-22-220000000000000000
χ4422222222-2-2-2-2-2-2-222-22-2-2-2-2200002-22-2200002000000000000000000000000-22-222-22-20000000000000000
χ45222-22-2-2-22-22-22-222-20200-20-22-22-2000002-22-200000000000002−22−22−22−20000000000002−22−22−22−200000000
χ46222-22-2-2-22-22-22-222-20200-20-22-22-2000002-22-20000000000000−22−22−22−22000000000000−22−22−22−2200000000
χ47222-22-2-2-22-22-22-222-20200-20-2-22-2200000-22-2200000000000002−22−22−22−2000000000000−22−22−22−2200000000
χ48222-22-2-2-22-22-22-222-20200-20-2-22-2200000-22-220000000000000−22−22−22−220000000000002−22−22−22−200000000
χ49222-22-2-2-2-22-222-22-220-200-2022-22-200000-22-220000000000000i2−i2i2−i2−i2i2−i2i2000000000000i2−i2i2−i2−i2i2−i2i200000000
χ50222-22-2-2-2-22-222-22-220-200-2022-22-200000-22-220000000000000−i2i2−i2i2i2−i2i2−i2000000000000−i2i2−i2i2i2−i2i2−i200000000
χ51222-22-2-2-2-22-222-22-220-200-202-22-22000002-22-20000000000000i2−i2i2−i2−i2i2−i2i2000000000000−i2i2−i2i2i2−i2i2−i200000000
χ52222-22-2-2-2-22-222-22-220-200-202-22-22000002-22-20000000000000−i2i2−i2i2i2−i2i2−i2000000000000i2−i2i2−i2−i2i2−i2i200000000
χ532-2-222-2-222-2-222-2-22-20-2002022-2-22000002-2-2200000000000002−2−222−2−220000000000002−2−222−2−2200000000
χ542-2-222-2-222-2-222-2-22-20-2002022-2-22000002-2-220000000000000−222−2−222−2000000000000−222−2−222−200000000
χ552-2-222-2-222-2-222-2-22-20-200202-222-200000-222-200000000000002−2−222−2−22000000000000−222−2−222−200000000
χ562-2-222-2-222-2-222-2-22-20-200202-222-200000-222-20000000000000−222−2−222−20000000000002−2−222−2−2200000000
χ572-2-222-2-22-222-22-2-2-22020020-22-2-2200000-222-20000000000000i2−i2−i2i2−i2i2i2−i2000000000000i2−i2−i2i2−i2i2i2−i200000000
χ582-2-222-2-22-222-22-2-2-22020020-22-2-2200000-222-20000000000000−i2i2i2−i2i2−i2−i2i2000000000000−i2i2i2−i2i2−i2−i2i200000000
χ592-2-222-2-22-222-22-2-2-22020020-2-222-2000002-2-220000000000000i2−i2−i2i2−i2i2i2−i2000000000000−i2i2i2−i2i2−i2−i2i200000000
χ602-2-222-2-22-222-22-2-2-22020020-2-222-2000002-2-220000000000000−i2i2i2−i2i2−i2−i2i2000000000000i2−i2−i2i2−i2i2i2−i200000000
χ612-2-2-2222-222-2-222-222-2-222-2-2-222-2-2-2-222222-2-2-200000000-22-22000000000000000000000000000000000000
χ622-2-2-2222-222-2-222-222-2-222-2-2-2-2-222-2-2222-2-222-2000000002-22-2000000000000000000000000000000000000
χ632-2-2-2222-222-2-2-2-22-2-222-2-222200002-2-2220000-20000000000000000000000002-2-222-2-220000000000000000
χ642-2-2-2222-222-2-2-2-22-2-222-2-222200002-2-2220000-2000000000000000000000000-222-2-222-20000000000000000
χ652-2-2-2222-222-2-2-2-22-2-2-22222-220000-222-2-20000222-2-2-2-222000000000000-222-2000000000000000000000000
χ662-2-2-2222-222-2-2-2-22-2-2-22222-220000-222-2-200002-2-22222-2-20000000000002-2-22000000000000000000000000
χ672-2-2-2222-2-2-22222-2-2-222-2-2-22222-2-2-2-222-2-2-222200000000-222-2000000000000000000000000000000000000
χ682-2-2-2222-2-2-22222-2-2-222-2-2-222-2-222-2-222-222-2-22000000002-2-22000000000000000000000000000000000000
χ692-2-2-2222-2-2-222-2-22222-2-2-222-20000-222-220000-22i2i−2i−2i2i2i−2i−2i000000000000−2i2i−2i2i000000000000000000000000
χ702-2-2-2222-2-2-222-2-22222-2-2-222-20000-222-220000-2−2i−2i2i2i−2i−2i2i2i0000000000002i−2i2i−2i000000000000000000000000
χ712-2-2-2222-2-2-222-2-2222-2-2222-2-200002-2-22-2000020000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ722-2-2-2222-2-2-222-2-2222-2-2222-2-200002-2-22-200002000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ73444-44-4-4-44-44-4-44-4-440-40040400000000000000000000000000000000000000000000000000000000000000
χ74444-44-4-4-4-44-44-44-44-4040040-400000000000000000000000000000000000000000000000000000000000000
χ7544-44-44-4-4000000000404-40-400000000000000022−2222−2222−2222−220000000000000000000000000000000000000000
χ7644-44-44-4-4000000000404-40-4000000000000000−2222−2222−2222−22220000000000000000000000000000000000000000
χ7744-44-44-4-4000000000-40-44040000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ7844-44-44-4-4000000000-40-4404000000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ794-44-4-44-4400000000040-440-40000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ804-44-4-44-4400000000040-440-4000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ814-44-4-44-44000000000-404-40400000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ824-44-4-44-44000000000-404-404000000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ834-4-444-4-444-4-44-444-440400-40-400000000000000000000000000000000000000000000000000000000000000
χ844-4-444-4-44-444-4-4444-40-400-40400000000000000000000000000000000000000000000000000000000000000
χ8588-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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