Finite Group Databasebeta

← Group #196857

Character table — Group #196857

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444422224444444444444444442244444444444444888888888888888824444444
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
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
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
χ51111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1111
χ61111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-11-1-1
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111-111
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-111
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111111-1-11-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-111
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-111
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1
χ1711111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1iiii−i−i−i−i1-11-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-11-1-11-1
χ1811111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1iiii−i−i−i−i1-11-1ii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-1-11-111-11
χ1911111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1−i−i−i−iiiii1-11-1−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-1-11-111-11
χ2011111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1−i−i−i−iiiii1-11-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-11-1-11-1
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111iiii−i−i−i−i-11-11ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii1-11-11-11-1
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111iiii−i−i−i−i-11-11ii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-11-11-11-11
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111−i−i−i−iiiii-11-11−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-11-11-11-11
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111−i−i−i−iiiii-11-11−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i1-11-11-11-1
χ2511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111iiii−i−i−i−i-111-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii11-1-11-1-11
χ2611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111iiii−i−i−i−i-111-1−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-1-111-111-1
χ2711111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111−i−i−i−iiiii-111-1ii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-1-111-111-1
χ2811111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111−i−i−i−iiiii-111-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i11-1-11-1-11
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1iiii−i−i−i−i1-1-11−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-111-1-1-11
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1iiii−i−i−i−i1-1-11−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-11-1-1111-1
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1−i−i−i−iiiii1-1-11ii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-11-1-1111-1
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1−i−i−i−iiiii1-1-11ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-111-1-1-11
χ3322222222222222222222-2-2-2-2-2-2-2-22222-2-2222200000000-2-2-2-2000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-20000000022-2-2000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222200000000-2-222000000000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-22222-2-22222-2-2-2-222-2-200000000-22-22000000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-22222-2-222-2-222-2-2-2-222000000002-22-2000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222222222-2-222-2-2-2-2-2-222000000002-2-22000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222222222-2-2-2-222-2-222-2-200000000-222-2000000000000000000000000000000000000
χ41222-2-22-2-22-22-22i2i−2i−2i2i2i−2i−2i000000002-22-2002i−2i2i−2i0000000000000000000000002−22−2i2−i2i2−i22−22−2i2−i2i2−i200000000
χ42222-2-22-2-22-22-22i2i−2i−2i2i2i−2i−2i000000002-22-2002i−2i2i−2i000000000000000000000000−22−22−i2i2−i2i2−22−22−i2i2−i2i200000000
χ43222-2-22-2-22-22-22i2i−2i−2i2i2i−2i−2i00000000-22-2200−2i2i−2i2i0000000000000000000000002−22−2i2−i2i2−i2−22−22−i2i2−i2i200000000
χ44222-2-22-2-22-22-22i2i−2i−2i2i2i−2i−2i00000000-22-2200−2i2i−2i2i000000000000000000000000−22−22−i2i2−i2i22−22−2i2−i2i2−i200000000
χ45222-2-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i000000002-22-200−2i2i−2i2i0000000000000000000000002−22−2−i2i2−i2i22−22−2−i2i2−i2i200000000
χ46222-2-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i000000002-22-200−2i2i−2i2i000000000000000000000000−22−22i2−i2i2−i2−22−22i2−i2i2−i200000000
χ47222-2-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i00000000-22-22002i−2i2i−2i0000000000000000000000002−22−2−i2i2−i2i2−22−22i2−i2i2−i200000000
χ48222-2-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i00000000-22-22002i−2i2i−2i000000000000000000000000−22−22i2−i2i2−i22−22−2−i2i2−i2i200000000
χ49222-2-22-2-2-22-222i2i−2i−2i−2i−2i2i2i000000002-2-22002i−2i−2i2i000000000000000000000000i2−i2−i2i2−222−2i2−i2−i2i2−222−200000000
χ50222-2-22-2-2-22-222i2i−2i−2i−2i−2i2i2i000000002-2-22002i−2i−2i2i000000000000000000000000−i2i2i2−i22−2−22−i2i2i2−i22−2−2200000000
χ51222-2-22-2-2-22-222i2i−2i−2i−2i−2i2i2i00000000-222-200−2i2i2i−2i000000000000000000000000i2−i2−i2i2−222−2−i2i2i2−i22−2−2200000000
χ52222-2-22-2-2-22-222i2i−2i−2i−2i−2i2i2i00000000-222-200−2i2i2i−2i000000000000000000000000−i2i2i2−i22−2−22i2−i2−i2i2−222−200000000
χ53222-2-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i000000002-2-2200−2i2i2i−2i000000000000000000000000i2−i2−i2i22−2−22i2−i2−i2i22−2−2200000000
χ54222-2-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i000000002-2-2200−2i2i2i−2i000000000000000000000000−i2i2i2−i2−222−2−i2i2i2−i2−222−200000000
χ55222-2-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i00000000-222-2002i−2i−2i2i000000000000000000000000i2−i2−i2i22−2−22−i2i2i2−i2−222−200000000
χ56222-2-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i00000000-222-2002i−2i−2i2i000000000000000000000000−i2i2i2−i2−222−2i2−i2−i2i22−2−2200000000
χ572-2-2-2-222222-2-22-22-22-22-222-2-22-22-200002-2000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ582-2-2-2-222222-2-22-22-22-22-222-2-22-22-200002-200000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ592-2-2-2-222222-2-22-22-22-22-2-2-222-22-220000-2200002i2i−2i−2i2i2i−2i−2i00002i−2i2i−2i00000000000000000000000000000000
χ602-2-2-2-222222-2-22-22-22-22-2-2-222-22-220000-220000−2i−2i2i2i−2i−2i2i2i0000−2i2i−2i2i00000000000000000000000000000000
χ612-2-2-2-222222-2-2-22-22-22-2222-2-2-22-2200002-2000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ622-2-2-2-222222-2-2-22-22-22-2222-2-2-22-2200002-200000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ632-2-2-2-222222-2-2-22-22-22-22-2-2222-22-20000-2200002i2i−2i−2i2i2i−2i−2i0000−2i2i−2i2i00000000000000000000000000000000
χ642-2-2-2-222222-2-2-22-22-22-22-2-2222-22-20000-220000−2i−2i2i2i−2i−2i2i2i00002i−2i2i−2i00000000000000000000000000000000
χ652-2-2-2-2222-2-2222-22-2-22-2222-2-2-222-20000-22000022-2-2-2-22200002-2-2200000000000000000000000000000000
χ662-2-2-2-2222-2-2222-22-2-22-2222-2-2-222-20000-220000-2-22222-2-20000-222-200000000000000000000000000000000
χ672-2-2-2-2222-2-2222-22-2-22-22-2-2222-2-2200002-2000000000000000000002-2-222-2-22000000000000000000000000
χ682-2-2-2-2222-2-2222-22-2-22-22-2-2222-2-2200002-200000000000000000000-222-2-222-2000000000000000000000000
χ692-2-2-2-2222-2-222-22-222-22-222-2-22-2-220000-22000022-2-2-2-2220000-222-200000000000000000000000000000000
χ702-2-2-2-2222-2-222-22-222-22-222-2-22-2-220000-220000-2-22222-2-200002-2-2200000000000000000000000000000000
χ712-2-2-2-2222-2-222-22-222-22-2-2-222-222-200002-2000000000000000000002-2-22-222-2000000000000000000000000
χ722-2-2-2-2222-2-222-22-222-22-2-2-222-222-200002-200000000000000000000-222-22-2-22000000000000000000000000
χ7344-44-4-44-40000000000004i−4i4i−4i000000000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i0000000000000000000000000000000000000000
χ7444-44-4-44-40000000000004i−4i4i−4i00000000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i0000000000000000000000000000000000000000
χ7544-44-4-44-4000000000000−4i4i−4i4i000000000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i0000000000000000000000000000000000000000
χ7644-44-4-44-4000000000000−4i4i−4i4i00000000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i0000000000000000000000000000000000000000
χ774-44-44-44-40000000000004i−4i−4i4i000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000
χ784-44-44-44-40000000000004i−4i−4i4i00000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000000
χ794-44-44-44-4000000000000−4i4i4i−4i000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000000
χ804-44-44-44-4000000000000−4i4i4i−4i00000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000
χ814-4-4444-4-44-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ824-4-4444-4-44-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-4-4-444-44i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ844-4-4444-4-4-444-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ8588-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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