Finite Group Databasebeta

← Group #106965

Character table — Group #106965

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222222222222444444444444444444444444444444444444444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ511111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1iiii−i−i−i−i-111-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ10111111111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1iiii−i−i−i−i-111-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ11111111111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1−i−i−i−iiiii-111-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ12111111111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1−i−i−i−iiiii-111-1-1−i−iii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ13111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111iiii−i−i−i−i-1-1-111ii−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ14111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111iiii−i−i−i−i-1-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ15111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111−i−i−i−iiiii-1-1-111−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ16111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111−i−i−i−iiiii-1-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ1711-1-11-1-1111-1-1111-1-1-11-111-1-11-11-1-111-1-111-1-1ii−i−iii−i−i11-11-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1i−ii−i1-11-1
χ1811-1-11-1-1111-1-1111-1-1-11-111-1-11-11-1-111-1-111-1-1ii−i−iii−i−i11-11-1i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111−ii−ii-11-11
χ1911-1-11-1-1111-1-1111-1-1-11-111-1-11-11-1-111-1-111-1-1−i−iii−i−iii11-11-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111i−ii−i-11-11
χ2011-1-11-1-1111-1-1111-1-1-11-111-1-11-11-1-111-1-111-1-1−i−iii−i−iii11-11-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−ii−ii1-11-1
χ2111-1-11-1-1111-1-1111-1-1-11-111-1-11-11-1-1-1-111-1-111ii−i−iii−i−i1-11-11i−ii−i−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1−ii−ii-11-11
χ2211-1-11-1-1111-1-1111-1-1-11-111-1-11-11-1-1-1-111-1-111ii−i−iii−i−i1-11-11i−ii−i−i−iii−i−iii−i−iii−i−iii-1-111-1-111i−ii−i1-11-1
χ2311-1-11-1-1111-1-1111-1-1-11-111-1-11-11-1-1-1-111-1-111−i−iii−i−iii1-11-11−ii−iiii−i−iii−i−iii−i−iii−i−i-1-111-1-111−ii−ii1-11-1
χ2411-1-11-1-1111-1-1111-1-1-11-111-1-11-11-1-1-1-111-1-111−i−iii−i−iii1-11-11−ii−iiii−i−iii−i−i−i−iii−i−iii11-1-111-1-1i−ii−i-11-11
χ2511-1-11-1-1111-1-1-1-1-1111-1111-1-11-1-11111-1-1-1-11111-1-1-1-111-11-1-111-1-1111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−ii−i−ii−iii−i
χ2611-1-11-1-1111-1-1-1-1-1111-1111-1-11-1-11111-1-1-1-11111-1-1-1-111-11-1-111-1-1111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii−iii−ii−i−ii
χ2711-1-11-1-1111-1-1-1-1-1111-1111-1-11-1-11111-1-1-1-111-1-11111-1-1-11-1-11-111-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iiii−i−iii−i−ii
χ2811-1-11-1-1111-1-1-1-1-1111-1111-1-11-1-11111-1-1-1-111-1-11111-1-1-11-1-11-111-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i−iii−i−iii−i
χ2911-1-11-1-1111-1-1-1-1-1111-1111-1-11-1-111-1-11111-1-111-1-1-1-111-1-111-11-1-11-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i−iii−ii−i−ii
χ3011-1-11-1-1111-1-1-1-1-1111-1111-1-11-1-111-1-11111-1-111-1-1-1-111-1-111-11-1-11-1-11111-1-1−i−iiiii−i−iii−i−i−i−iiii−i−ii−iii−i
χ3111-1-11-1-1111-1-1-1-1-1111-1111-1-11-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii−iii−i−iii−i
χ3211-1-11-1-1111-1-1-1-1-1111-1111-1-11-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−ii−i−iii−i−ii
χ3322222222222222222222-2-2-2-2-2-2-2-2-20000000022222222-20000-2-2-2-200000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222000000002i2i2i2i−2i−2i−2i−2i20000−2i−2i2i2i00000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222200000000−2i−2i−2i−2i2i2i2i2i200002i2i−2i−2i00000000000000000000000000000000
χ3722222222-2-2-2-222-2-2-22-222222-2-222-22222222200000000-2-2-2-2-2000000000000000000000000000000000000
χ3822222222-2-2-2-222-2-2-22-222222-2-222-2-2-2-2-2-2-2-2-200000000-22222000000000000000000000000000000000000
χ3922222222-2-2-2-222-2-2-22-22-2-2-2-222-2-2200000000000000002000000002-22-22-22-2000000000000000000000000
χ4022222222-2-2-2-222-2-2-22-22-2-2-2-222-2-220000000000000000200000000-22-22-22-22000000000000000000000000
χ4122222222-2-2-2-2-2-2222-22-22222-2-2-2-222222-2-2-2-2000000002-2-222000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2222-22-22222-2-2-2-22-2-2-2-2222200000000222-2-2000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2222-22-2-2-2-2-22222-20000000000000000-2000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ4422222222-2-2-2-2-2-2222-22-2-2-2-2-22222-20000000000000000-200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4522-2-22-2-2222-2-2222-2-2-22-2-2-222-22-222000000002i2i−2i−2i2i2i−2i−2i-20000−2i2i−2i2i00000000000000000000000000000000
χ4622-2-22-2-2222-2-2222-2-2-22-2-2-222-22-22200000000−2i−2i2i2i−2i−2i2i2i-200002i−2i2i−2i00000000000000000000000000000000
χ4722-2-22-2-2222-2-2-2-2-2222-22-2-222-222-2-20000000022-2-2-2-22220000-222-200000000000000000000000000000000
χ4822-2-22-2-2222-2-2-2-2-2222-22-2-222-222-2-200000000-2-22222-2-2200002-2-2200000000000000000000000000000000
χ4922-2-22-2-22-2-22222-222-2-2-222-2-2-222-2222-2-222-2-200000000-2-22-22000000000000000000000000000000000000
χ5022-2-22-2-22-2-22222-222-2-2-222-2-2-222-22-2-222-2-22200000000-22-22-2000000000000000000000000000000000000
χ5122-2-22-2-22-2-22222-222-2-2-2-2-2222-2-22-200000000000000002000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ5222-2-22-2-22-2-22222-222-2-2-2-2-2222-2-22-20000000000000000200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ5322-2-22-2-22-2-222-2-22-2-222222-2-2-22-22-222-2-2-2-222000000002-222-2000000000000000000000000000000000000
χ5422-2-22-2-22-2-222-2-22-2-222222-2-2-22-22-2-2-22222-2-20000000022-2-22000000000000000000000000000000000000
χ5522-2-22-2-22-2-222-2-22-2-2222-2-2222-22-220000000000000000-2000000002-2-22-222-2000000000000000000000000
χ5622-2-22-2-22-2-222-2-22-2-2222-2-2222-22-220000000000000000-200000000-222-22-2-22000000000000000000000000
χ572-222-2-2-222-22-22-222-2-2-22000000000000000002-22-22-22-200000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ582-222-2-2-222-22-22-222-2-2-22000000000000000002-22-22-22-200000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ592-222-2-2-222-22-22-222-2-2-2200000000000000000-22-22-22-2200000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ602-222-2-2-222-22-22-222-2-2-2200000000000000000-22-22-22-2200000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ612-222-2-2-222-22-2-22-2-2222-2000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−200000000
χ622-222-2-2-222-22-2-22-2-2222-2000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000
χ632-222-2-2-222-22-2-22-2-2222-200000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000
χ642-222-2-2-222-22-2-22-2-2222-200000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000
χ652-2-2-2-22222-2-222-22-222-2-2000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i200000000
χ662-2-2-2-22222-2-222-22-222-2-2000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000−222−2−222−2i2−i2−i2i2i2−i2−i2i200000000
χ672-2-2-2-22222-2-222-22-222-2-200000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i200000000
χ682-2-2-2-22222-2-222-22-222-2-200000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000−222−2−222−2−i2i2i2−i2−i2i2i2−i200000000
χ692-2-2-2-22222-2-22-22-22-2-222000000000000000002-2-22-222-2000000000000000002−2−22−222−2−222−22−2−2200000000
χ702-2-2-2-22222-2-22-22-22-2-222000000000000000002-2-22-222-200000000000000000−222−22−2−222−2−22−222−200000000
χ712-2-2-2-22222-2-22-22-22-2-22200000000000000000-222-22-2-22000000000000000002−2−22−222−22−2−22−222−200000000
χ722-2-2-2-22222-2-22-22-22-2-22200000000000000000-222-22-2-2200000000000000000−222−22−2−22−222−22−2−2200000000
χ734-444-4-4-44-44-444-4-4-44-444000000000000000000000000000000000000000000000000000000000000000000
χ744-444-4-4-44-44-44-4444-44-4-4000000000000000000000000000000000000000000000000000000000000000000
χ754-44-444-4-40000000000004-44-40000000004i−4i4i−4i0000000000000000000000000000000000000000000000000
χ764-44-444-4-40000000000004-44-4000000000−4i4i−4i4i0000000000000000000000000000000000000000000000000
χ774-44-444-4-4000000000000-44-44000004i−4i4i−4i00000000000000000000000000000000000000000000000000000
χ784-44-444-4-4000000000000-44-4400000−4i4i−4i4i00000000000000000000000000000000000000000000000000000
χ794-4-444-44-40000000000004-4-440000000004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ804-4-444-44-40000000000004-4-44000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ814-4-444-44-4000000000000-444-4000004i−4i−4i4i00000000000000000000000000000000000000000000000000000
χ824-4-444-44-4000000000000-444-400000−4i4i4i−4i00000000000000000000000000000000000000000000000000000
χ834-4-4-4-4444-444-44-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000
χ844-4-4-4-4444-444-4-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000
χ85888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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