Finite Group Databasebeta

← Group #371012

Character table — Group #371012

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12224444222222444444444444444444444444444444444444444444222244444444444444448888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ11111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ12111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111
χ1711-1-111-1-11-11-11-111-1-11111-1-1-1-11-1iiii−i−i−i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-11-11-11-1ii−i−iii−i−i11-1-111-1-1ii−i−ii−i1-1i−i1-1
χ1811-1-111-1-11-11-11-111-1-11111-1-1-1-11-1iiii−i−i−i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-1-111-1-11−i−iiiii−i−i11-1-1-1-111−i−iii−ii-11−ii-11
χ1911-1-111-1-11-11-11-111-1-11111-1-1-1-11-1iiii−i−i−i−i−i−i−i−iiiii11-1-1iiii−i−i−i−i-111-1-111-1−i−iii−i−iii-1-11111-1-1−i−iiii−i-11i−i-11
χ2011-1-111-1-11-11-11-111-1-11111-1-1-1-11-1iiii−i−i−i−i−i−i−i−iiiii11-1-1iiii−i−i−i−i-11-11-11-11ii−i−i−i−iii-1-111-1-111ii−i−i−ii1-1−ii1-1
χ2111-1-111-1-11-11-11-111-1-11111-1-1-1-11-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−i−i−iiiii-111-1-111-1ii−i−iii−i−i-1-11111-1-1ii−i−i−ii-11−ii-11
χ2211-1-111-1-11-11-11-111-1-11111-1-1-1-11-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−i−i−iiiii-11-11-11-11−i−iiiii−i−i-1-111-1-111−i−iiii−i1-1i−i1-1
χ2311-1-111-1-11-11-11-111-1-11111-1-1-1-11-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-11-11-11-1−i−iii−i−iii11-1-111-1-1−i−iii−ii1-1−ii1-1
χ2411-1-111-1-11-11-11-111-1-11111-1-1-1-11-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-1-111-1-11ii−i−i−i−iii11-1-1-1-111ii−i−ii−i-11i−i-11
χ2511-1-111-1-11-11-11-111-1-1-1-1-1-111111-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−i−i−iiiii-111-1-111-1ii−i−i−i−iii11-1-1-1-111−i−iiii−i1-1−ii-11
χ2611-1-111-1-11-11-11-111-1-1-1-1-1-111111-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−i−i−iiiii-11-11-11-11−i−iii−i−iii11-1-111-1-1ii−i−i−ii-11i−i1-1
χ2711-1-111-1-11-11-11-111-1-1-1-1-1-111111-1iiii−i−i−i−i−i−i−i−iiiii-1-111−i−i−i−iiiii1-11-11-11-1−i−iiiii−i−i-1-111-1-111ii−i−ii−i-11−ii1-1
χ2811-1-111-1-11-11-11-111-1-1-1-1-1-111111-1iiii−i−i−i−i−i−i−i−iiiii-1-111−i−i−i−iiiii1-1-111-1-11ii−i−iii−i−i-1-11111-1-1−i−iii−ii1-1i−i-11
χ2911-1-111-1-11-11-11-111-1-1-1-1-1-111111-1−i−i−i−iiiiiiiii−i−i−i−i-1-111iiii−i−i−i−i1-11-11-11-1ii−i−i−i−iii-1-111-1-111−i−iii−ii-11i−i1-1
χ3011-1-111-1-11-11-11-111-1-1-1-1-1-111111-1−i−i−i−iiiiiiiii−i−i−i−i-1-111iiii−i−i−i−i1-1-111-1-11−i−iii−i−iii-1-11111-1-1ii−i−ii−i1-1−ii-11
χ3111-1-111-1-11-11-11-111-1-1-1-1-1-111111-1−i−i−i−iiiii−i−i−i−iiiii-1-111iiii−i−i−i−i-111-1-111-1−i−iiiii−i−i11-1-1-1-111ii−i−i−ii1-1i−i-11
χ3211-1-111-1-11-11-11-111-1-1-1-1-1-111111-1−i−i−i−iiiii−i−i−i−iiiii-1-111iiii−i−i−i−i-11-11-11-11ii−i−iii−i−i11-1-111-1-1−i−iiii−i-11−ii1-1
χ3322222222-2-2-2-2222-22-222222222-2-20000000022-2-222-2-2-2-2-2-2000000000000000000002-22-200000000000000000000
χ3422222222-2-2-2-2222-22-222222222-2-200000000-2-222-2-222-2-2-2-200000000000000000000-22-2200000000000000000000
χ3522222222-2-2-2-2222-22-2-2-2-2-2-2-2-2-2-2-20000000022-2-222-2-2222200000000000000000000-22-2200000000000000000000
χ3622222222-2-2-2-2222-22-2-2-2-2-2-2-2-2-2-2-200000000-2-222-2-2222222000000000000000000002-22-200000000000000000000
χ372222-2-2-2-2222222-2-2-2-200000000-2-222-2-222-2-22-22-22-22-200000000000000000000000000002-22-20000000000000000
χ382222-2-2-2-2222222-2-2-2-200000000-2-222-2-222-2-2-22-22-22-220000000000000000000000000000-22-220000000000000000
χ392222-2-2-2-2222222-2-2-2-200000000-2-2-2-222-2-2222-22-22-22-20000000000000000000000000000-22-220000000000000000
χ402222-2-2-2-2222222-2-2-2-200000000-2-2-2-222-2-222-22-22-22-2200000000000000000000000000002-22-20000000000000000
χ412222-2-2-2-22-2-22-2-22-2222i2i−2i−2i2i2i−2i−2i2-200000000000000002i−2i2i−2i00000000002200-2-20000000000002i−2i2i−2i000000000000
χ422222-2-2-2-22-2-22-2-22-2222i2i−2i−2i2i2i−2i−2i2-200000000000000002i−2i2i−2i0000000000-2-20022000000000000−2i2i−2i2i000000000000
χ432222-2-2-2-22-2-22-2-22-222−2i−2i2i2i−2i−2i2i2i2-20000000000000000−2i2i−2i2i00000000002200-2-2000000000000−2i2i−2i2i000000000000
χ442222-2-2-2-22-2-22-2-22-222−2i−2i2i2i−2i−2i2i2i2-20000000000000000−2i2i−2i2i0000000000-2-200220000000000002i−2i2i−2i000000000000
χ452222-2-2-2-2-222-2-2-2222-22i2i−2i−2i2i2i−2i−2i-220000000000000000−2i2i−2i2i00000000000000002-22-20000000000002i−2i2i−2i00000000
χ462222-2-2-2-2-222-2-2-2222-22i2i−2i−2i2i2i−2i−2i-220000000000000000−2i2i−2i2i0000000000000000-22-22000000000000−2i2i−2i2i00000000
χ472222-2-2-2-2-222-2-2-2222-2−2i−2i2i2i−2i−2i2i2i-2200000000000000002i−2i2i−2i00000000000000002-22-2000000000000−2i2i−2i2i00000000
χ482222-2-2-2-2-222-2-2-2222-2−2i−2i2i2i−2i−2i2i2i-2200000000000000002i−2i2i−2i0000000000000000-22-220000000000002i−2i2i−2i00000000
χ492222-2-2-2-2-2-2-2-222-22-220000000022000000002-2-222-2-22000022-2-222-2-22200-2-2000000000000000000000000000000
χ502222-2-2-2-2-2-2-2-222-22-220000000022000000002-2-222-2-220000-2-222-2-222-2-20022000000000000000000000000000000
χ512222-2-2-2-2-2-2-2-222-22-22000000002200000000-222-2-222-2000022-2-222-2-2-2-20022000000000000000000000000000000
χ522222-2-2-2-2-2-2-2-222-22-22000000002200000000-222-2-222-20000-2-222-2-2222200-2-2000000000000000000000000000000
χ5322-2-222-2-2-22-222-22-2-222222-2-2-2-2-22000000002i2i−2i−2i−2i−2i2i2i-2-222000000000000000000002i−2i−2i2i00000000000000000000
χ5422-2-222-2-2-22-222-22-2-222222-2-2-2-2-2200000000−2i−2i2i2i2i2i−2i−2i-2-22200000000000000000000−2i2i2i−2i00000000000000000000
χ5522-2-222-2-2-22-222-22-2-22-2-2-2-22222-22000000002i2i−2i−2i−2i−2i2i2i22-2-200000000000000000000−2i2i2i−2i00000000000000000000
χ5622-2-222-2-2-22-222-22-2-22-2-2-2-22222-2200000000−2i−2i2i2i2i2i−2i−2i22-2-2000000000000000000002i−2i−2i2i00000000000000000000
χ5722-2-2-2-22222-2-2-222-2-2-22i2i−2i−2i−2i−2i2i2i2200000000000000002i−2i−2i2i00000000002-200-220000000000002i−2i−2i2i000000000000
χ5822-2-2-2-22222-2-2-222-2-2-22i2i−2i−2i−2i−2i2i2i2200000000000000002i−2i−2i2i0000000000-22002-2000000000000−2i2i2i−2i000000000000
χ5922-2-2-2-22222-2-2-222-2-2-2−2i−2i2i2i2i2i−2i−2i220000000000000000−2i2i2i−2i00000000002-200-22000000000000−2i2i2i−2i000000000000
χ6022-2-2-2-22222-2-2-222-2-2-2−2i−2i2i2i2i2i−2i−2i220000000000000000−2i2i2i−2i0000000000-22002-20000000000002i−2i−2i2i000000000000
χ6122-2-2-2-2222-22-22-2-2-22200000000-222i2i−2i−2i−2i−2i2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000002-2-220000000000000000
χ6222-2-2-2-2222-22-22-2-2-22200000000-222i2i−2i−2i−2i−2i2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000-222-20000000000000000
χ6322-2-2-2-2222-22-22-2-2-22200000000-22−2i−2i2i2i2i2i−2i−2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000-222-20000000000000000
χ6422-2-2-2-2222-22-22-2-2-22200000000-22−2i−2i2i2i2i2i−2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000002-2-220000000000000000
χ6522-2-2-2-222-22-222-2-222-2000000002-2000000002i−2i−2i2i−2i2i2i−2i00002i2i−2i−2i−2i−2i2i2i2-200-22000000000000000000000000000000
χ6622-2-2-2-222-22-222-2-222-2000000002-2000000002i−2i−2i2i−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i-22002-2000000000000000000000000000000
χ6722-2-2-2-222-22-222-2-222-2000000002-200000000−2i2i2i−2i2i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i-22002-2000000000000000000000000000000
χ6822-2-2-2-222-22-222-2-222-2000000002-200000000−2i2i2i−2i2i−2i−2i2i0000−2i−2i2i2i2i2i−2i−2i2-200-22000000000000000000000000000000
χ6922-2-2-2-222-2-222-2222-222i2i−2i−2i−2i−2i2i2i-2-20000000000000000−2i2i2i−2i00000000000000002i−2i−2i2i000000000000-222-200000000
χ7022-2-2-2-222-2-222-2222-222i2i−2i−2i−2i−2i2i2i-2-20000000000000000−2i2i2i−2i0000000000000000−2i2i2i−2i0000000000002-2-2200000000
χ7122-2-2-2-222-2-222-2222-22−2i−2i2i2i2i2i−2i−2i-2-200000000000000002i−2i−2i2i00000000000000002i−2i−2i2i0000000000002-2-2200000000
χ7222-2-2-2-222-2-222-2222-22−2i−2i2i2i2i2i−2i−2i-2-200000000000000002i−2i−2i2i0000000000000000−2i2i2i−2i000000000000-222-200000000
χ73444444444-4-44-4-4-44-4-400000000-440000000000000000000000000000000000000000000000000000000000000000
χ7444444444-444-4-4-4-4-4-44000000004-40000000000000000000000000000000000000000000000000000000000000000
χ7544-4-444-4-444-4-4-44-444400000000-4-40000000000000000000000000000000000000000000000000000000000000000
χ7644-4-444-4-4-4-444-44-4-44-400000000440000000000000000000000000000000000000000000000000000000000000000
χ774-44-44i−4i4i−4i00000000002+2i−2−2i2−2i−2+2i2+2i−2−2i2−2i−2+2i002-22i−2i2-22i−2i0000000000002-22i−2i2-22i−2i000000000000000000000000000000000000
χ784-44-44i−4i4i−4i00000000002+2i−2−2i2−2i−2+2i2+2i−2−2i2−2i−2+2i00-22−2i2i-22−2i2i000000000000-22−2i2i-22−2i2i000000000000000000000000000000000000
χ794-44-44i−4i4i−4i0000000000−2−2i2+2i−2+2i2−2i−2−2i2+2i−2+2i2−2i002-22i−2i2-22i−2i000000000000-22−2i2i-22−2i2i000000000000000000000000000000000000
χ804-44-44i−4i4i−4i0000000000−2−2i2+2i−2+2i2−2i−2−2i2+2i−2+2i2−2i00-22−2i2i-22−2i2i0000000000002-22i−2i2-22i−2i000000000000000000000000000000000000
χ814-44-4−4i4i−4i4i00000000002−2i−2+2i2+2i−2−2i2−2i−2+2i2+2i−2−2i002-2−2i2i2-2−2i2i0000000000002-2−2i2i2-2−2i2i000000000000000000000000000000000000
χ824-44-4−4i4i−4i4i00000000002−2i−2+2i2+2i−2−2i2−2i−2+2i2+2i−2−2i00-222i−2i-222i−2i000000000000-222i−2i-222i−2i000000000000000000000000000000000000
χ834-44-4−4i4i−4i4i0000000000−2+2i2−2i−2−2i2+2i−2+2i2−2i−2−2i2+2i002-2−2i2i2-2−2i2i000000000000-222i−2i-222i−2i000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i0000000000−2+2i2−2i−2−2i2+2i−2+2i2−2i−2−2i2+2i00-222i−2i-222i−2i0000000000002-2−2i2i2-2−2i2i000000000000000000000000000000000000
χ854-4-444i−4i−4i4i00000000002+2i−2−2i2−2i−2+2i−2−2i2+2i−2+2i2−2i002i−2i-22−2i2i2-20000000000002i−2i-22−2i2i2-2000000000000000000000000000000000000
χ864-4-444i−4i−4i4i00000000002+2i−2−2i2−2i−2+2i−2−2i2+2i−2+2i2−2i00−2i2i2-22i−2i-22000000000000−2i2i2-22i−2i-22000000000000000000000000000000000000
χ874-4-444i−4i−4i4i0000000000−2−2i2+2i−2+2i2−2i2+2i−2−2i2−2i−2+2i002i−2i-22−2i2i2-2000000000000−2i2i2-22i−2i-22000000000000000000000000000000000000
χ884-4-444i−4i−4i4i0000000000−2−2i2+2i−2+2i2−2i2+2i−2−2i2−2i−2+2i00−2i2i2-22i−2i-220000000000002i−2i-22−2i2i2-2000000000000000000000000000000000000
χ894-4-44−4i4i4i−4i00000000002−2i−2+2i2+2i−2−2i−2+2i2−2i−2−2i2+2i002i−2i2-2−2i2i-220000000000002i−2i2-2−2i2i-22000000000000000000000000000000000000
χ904-4-44−4i4i4i−4i00000000002−2i−2+2i2+2i−2−2i−2+2i2−2i−2−2i2+2i00−2i2i-222i−2i2-2000000000000−2i2i-222i−2i2-2000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i0000000000−2+2i2−2i−2−2i2+2i2−2i−2+2i2+2i−2−2i002i−2i2-2−2i2i-22000000000000−2i2i-222i−2i2-2000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i0000000000−2+2i2−2i−2−2i2+2i2−2i−2+2i2+2i−2−2i00−2i2i-222i−2i2-20000000000002i−2i2-2−2i2i-22000000000000000000000000000000000000

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