Finite Group Databasebeta

← Group #376265

Character table — Group #376265

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12224444222222444444888888884444444444444444888888888888222244444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-111
χ1711-1-111-1-1-1111-1-111-1-1-11iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i1111-1-1-1-11-11-11-11-1ii−i−iii−i−i11-1-1ii−i−i11-1-1i−i1-11-1i−i
χ1811-1-111-1-1-1111-1-111-1-1-11iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i1111-1-1-1-1-11-11-11-11−i−iii−i−iii11-1-1ii−i−i11-1-1−ii-11-11−ii
χ1911-1-111-1-1-1111-1-111-1-1-11iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiii−i−i1111-1-1-1-11-1-111-1-11ii−i−i−i−iii-1-111−i−iii-1-111i−i1-1-11−ii
χ2011-1-111-1-1-1111-1-111-1-1-11iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiii−i−i1111-1-1-1-1-111-1-111-1−i−iiiii−i−i-1-111−i−iii-1-111−ii-111-1i−i
χ2111-1-111-1-1-1111-1-111-1-1-11iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-1-1-111111-11-11-11-1ii−i−iii−i−i-1-111−i−iii11-1-1−ii-11-11−ii
χ2211-1-111-1-1-1111-1-111-1-1-11iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-1-1-11111-11-11-11-11−i−iii−i−iii-1-111−i−iii11-1-1i−i1-11-1i−i
χ2311-1-111-1-1-1111-1-111-1-1-11iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1-1-111111-1-111-1-11ii−i−i−i−iii11-1-1ii−i−i-1-111−ii-111-1i−i
χ2411-1-111-1-1-1111-1-111-1-1-11iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1-1-11111-111-1-111-1−i−iiiii−i−i11-1-1ii−i−i-1-111i−i1-1-11−ii
χ2511-1-111-1-1-1111-1-111-1-1-11−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1-1-111111-1-111-1-11−i−iiiii−i−i11-1-1−i−iii-1-111i−i-111-1−ii
χ2611-1-111-1-1-1111-1-111-1-1-11−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1-1-11111-111-1-111-1ii−i−i−i−iii11-1-1−i−iii-1-111−ii1-1-11i−i
χ2711-1-111-1-1-1111-1-111-1-1-11−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-1-1-111111-11-11-11-1−i−iii−i−iii-1-111ii−i−i11-1-1i−i-11-11i−i
χ2811-1-111-1-1-1111-1-111-1-1-11−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-1-1-11111-11-11-11-11ii−i−iii−i−i-1-111ii−i−i11-1-1−ii1-11-1−ii
χ2911-1-111-1-1-1111-1-111-1-1-11−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−iii1111-1-1-1-11-1-111-1-11−i−iiiii−i−i-1-111ii−i−i-1-111−ii1-1-11i−i
χ3011-1-111-1-1-1111-1-111-1-1-11−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−iii1111-1-1-1-1-111-1-111-1ii−i−i−i−iii-1-111ii−i−i-1-111i−i-111-1−ii
χ3111-1-111-1-1-1111-1-111-1-1-11−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii1111-1-1-1-11-11-11-11-1−i−iii−i−iii11-1-1−i−iii11-1-1−ii1-11-1−ii
χ3211-1-111-1-1-1111-1-111-1-1-11−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii1111-1-1-1-1-11-11-11-11ii−i−iii−i−i11-1-1−i−iii11-1-1i−i-11-11i−i
χ332222222222-2-2-2-2-2-2-2-222222222220000000022-2-222-2-2-2-2-2-2000000000000000000000000000000002-22-200000000
χ342222222222-2-2-2-2-2-2-2-2222222222200000000-2-222-2-222-2-2-2-200000000000000000000000000000000-22-2200000000
χ352222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-20000000022-2-222-2-2222200000000000000000000000000000000-22-2200000000
χ362222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-200000000-2-222-2-2222222000000000000000000000000000000002-22-200000000
χ372222-2-2-2-2222222-2-2-2-2-2-20000000022-2-222-2-22-22-22-22-200000000000000000000000000002-22-20000000000000000
χ382222-2-2-2-2222222-2-2-2-2-2-20000000022-2-222-2-2-22-22-22-220000000000000000000000000000-22-220000000000000000
χ392222-2-2-2-2222222-2-2-2-2-2-200000000-2-222-2-2222-22-22-22-20000000000000000000000000000-22-220000000000000000
χ402222-2-2-2-2222222-2-2-2-2-2-200000000-2-222-2-222-22-22-22-2200000000000000000000000000002-22-20000000000000000
χ412222-2-2-2-222-2-2-2-22222-2-200000000000000002-2-222-2-2200002i2i−2i−2i2i2i−2i−2i000000000000000000002i−2i2i−2i000000000000
χ422222-2-2-2-222-2-2-2-22222-2-200000000000000002-2-222-2-220000−2i−2i2i2i−2i−2i2i2i00000000000000000000−2i2i−2i2i000000000000
χ432222-2-2-2-222-2-2-2-22222-2-20000000000000000-222-2-222-200002i2i−2i−2i2i2i−2i−2i00000000000000000000−2i2i−2i2i000000000000
χ442222-2-2-2-222-2-2-2-22222-2-20000000000000000-222-2-222-20000−2i−2i2i2i−2i−2i2i2i000000000000000000002i−2i2i−2i000000000000
χ452222-2-2-2-2-2-22-22-22-22-22222-2-222-2-200000000000000002-22-200000000002200-2-200002-22-200000000000000000000
χ462222-2-2-2-2-2-22-22-22-22-22222-2-222-2-200000000000000002-22-20000000000-2-200220000-22-2200000000000000000000
χ472222-2-2-2-2-2-22-22-22-22-222-2-222-2-2220000000000000000-22-2200000000002200-2-20000-22-2200000000000000000000
χ482222-2-2-2-2-2-22-22-22-22-222-2-222-2-2220000000000000000-22-220000000000-2-2002200002-22-200000000000000000000
χ492222-2-2-2-2-2-2-22-22-22-222222-2-222-2-20000000000000000-22-22000000002200-2-2002-22-2000000000000000000000000
χ502222-2-2-2-2-2-2-22-22-22-222222-2-222-2-20000000000000000-22-2200000000-2-2002200-22-22000000000000000000000000
χ512222-2-2-2-2-2-2-22-22-22-2222-2-222-2-22200000000000000002-22-2000000002200-2-200-22-22000000000000000000000000
χ522222-2-2-2-2-2-2-22-22-22-2222-2-222-2-22200000000000000002-22-200000000-2-20022002-22-2000000000000000000000000
χ5322-2-222-2-2-22-2-222-2-222-222i2i2i2i−2i−2i−2i−2i000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000002-2-2200000000
χ5422-2-222-2-2-22-2-222-2-222-222i2i2i2i−2i−2i−2i−2i00000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000-222-200000000
χ5522-2-222-2-2-22-2-222-2-222-22−2i−2i−2i−2i2i2i2i2i000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000-222-200000000
χ5622-2-222-2-2-22-2-222-2-222-22−2i−2i−2i−2i2i2i2i2i00000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000002-2-2200000000
χ5722-2-2-2-2222-22-2-222-2-22-222i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i00000000002-200-2200002i−2i−2i2i00000000000000000000
χ5822-2-2-2-2222-22-2-222-2-22-222i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i0000000000-22002-20000−2i2i2i−2i00000000000000000000
χ5922-2-2-2-2222-22-2-222-2-22-22−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i00000000002-200-220000−2i2i2i−2i00000000000000000000
χ6022-2-2-2-2222-22-2-222-2-22-22−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i0000000000-22002-200002i−2i−2i2i00000000000000000000
χ6122-2-2-2-2222-2-222-2-222-2-222i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i000000002-200-22002i−2i−2i2i000000000000000000000000
χ6222-2-2-2-2222-2-222-2-222-2-222i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i00000000-22002-200−2i2i2i−2i000000000000000000000000
χ6322-2-2-2-2222-2-222-2-222-2-22−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i000000002-200-2200−2i2i2i−2i000000000000000000000000
χ6422-2-2-2-2222-2-222-2-222-2-22−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i00000000-22002-2002i−2i−2i2i000000000000000000000000
χ6522-2-2-2-222-2222-2-2-2-2222-2000000002i2i−2i−2i−2i−2i2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000002-2-220000000000000000
χ6622-2-2-2-222-2222-2-2-2-2222-2000000002i2i−2i−2i−2i−2i2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000-222-20000000000000000
χ6722-2-2-2-222-2222-2-2-2-2222-200000000−2i−2i2i2i2i2i−2i−2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000-222-20000000000000000
χ6822-2-2-2-222-2222-2-2-2-2222-200000000−2i−2i2i2i2i2i−2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000002-2-220000000000000000
χ6922-2-2-2-222-22-2-22222-2-22-200000000000000002i−2i−2i2i−2i2i2i−2i00002i2i−2i−2i−2i−2i2i2i00000000000000000000-222-2000000000000
χ7022-2-2-2-222-22-2-22222-2-22-200000000000000002i−2i−2i2i−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000002-2-22000000000000
χ7122-2-2-2-222-22-2-22222-2-22-20000000000000000−2i2i2i−2i2i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i000000000000000000002-2-22000000000000
χ7222-2-2-2-222-22-2-22222-2-22-20000000000000000−2i2i2i−2i2i−2i−2i2i0000−2i−2i2i2i2i2i−2i−2i00000000000000000000-222-2000000000000
χ7344444444-4-44-44-4-44-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ7444444444-4-4-44-444-44-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-444-4-44-44-4-44-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ7644-4-444-4-44-4-444-44-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ774-44-44i−4i4i−4i0000000000002i2−2i222−222i2−2i222−222-22i−2i2-22i−2i0000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000000000000000
χ784-44-44i−4i4i−4i0000000000002i2−2i222−222i2−2i222−22-22−2i2i-22−2i2i000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000000000000000
χ794-44-44i−4i4i−4i000000000000−2i22i2−2222−2i22i2−22222-22i−2i2-22i−2i000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000000000000000
χ804-44-44i−4i4i−4i000000000000−2i22i2−2222−2i22i2−2222-22−2i2i-22−2i2i0000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000000000000000
χ814-44-4−4i4i−4i4i0000000000002i2−2i2−22222i2−2i2−22222-2−2i2i2-2−2i2i0000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000000000000000
χ824-44-4−4i4i−4i4i0000000000002i2−2i2−22222i2−2i2−2222-222i−2i-222i−2i000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000000000000000
χ834-44-4−4i4i−4i4i000000000000−2i22i222−22−2i22i222−222-2−2i2i2-2−2i2i000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i000000000000−2i22i222−22−2i22i222−22-222i−2i-222i−2i0000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000000000000000
χ854-4-444i−4i−4i4i00000000000022−22−2i22i2−22222i2−2i22i−2i-22−2i2i2-2000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000000000000000
χ864-4-444i−4i−4i4i00000000000022−22−2i22i2−22222i2−2i2−2i2i2-22i−2i-220000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000000000000000
χ874-4-444i−4i−4i4i000000000000−22222i2−2i222−22−2i22i22i−2i-22−2i2i2-20000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000000000000000
χ884-4-444i−4i−4i4i000000000000−22222i2−2i222−22−2i22i2−2i2i2-22i−2i-22000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000000000000000
χ894-4-44−4i4i4i−4i00000000000022−222i2−2i2−2222−2i22i22i−2i2-2−2i2i-22000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000000000000000
χ904-4-44−4i4i4i−4i00000000000022−222i2−2i2−2222−2i22i2−2i2i-222i−2i2-20000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i000000000000−2222−2i22i222−222i2−2i22i−2i2-2−2i2i-220000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i000000000000−2222−2i22i222−222i2−2i2−2i2i-222i−2i2-2000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.