Finite Group Databasebeta

← Group #140362

Character table — Group #140362

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12442224444444888888884488888888888816161616161616161616161616161616444488881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ91111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ101111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iii−i−iii
χ111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1-1-111ii−i−i−i−iii
χ121111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-11111-1-1−i−iiiii−i−i
χ131111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1-1-111−i−iiiii−i−i
χ141111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-11111-1-1ii−i−i−i−iii
χ151111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ161111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−iii−i−i
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ192222222-2-2-2-222222222222-2-2-2-2-2-20000000022-2-2-2-222000000000000000000000000
χ202222222-2-2-2-222222222222-2-2-2-2-2-200000000-2-22222-2-2000000000000000000000000
χ2122222-2-222222-2-22222-2-2-2-2-2-2-2-222000000000000000022-2-222-2-20000000000000000
χ2222222-2-222222-2-22222-2-2-2-2-2-2-2-2220000000000000000-2-222-2-2220000000000000000
χ2322222-2-222222-2-2-2-2-2-22222-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ2422222-2-222222-2-2-2-2-2-22222-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ2522222-2-2-2-2-2-22-2-22222-2-2-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ2622222-2-2-2-2-2-22-2-22222-2-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ2722222-2-2-2-2-2-22-2-2-2-2-2-2222222-2-222000000000000000022-2-2-2-2220000000000000000
χ2822222-2-2-2-2-2-22-2-2-2-2-2-2222222-2-2220000000000000000-2-22222-2-20000000000000000
χ292222-22-20000-22-222-2-222-2-2000000i2−i2i2−i2i2−i2i2−i2002-22-200i2−i2i2−i2i2−i2i2−i20000000000000000
χ302222-22-20000-22-222-2-222-2-2000000i2−i2i2−i2i2−i2i2−i200-22-2200−i2i2−i2i2−i2i2−i2i20000000000000000
χ312222-22-20000-22-222-2-222-2-2000000−i2i2−i2i2−i2i2−i2i2002-22-200−i2i2−i2i2−i2i2−i2i20000000000000000
χ322222-22-20000-22-222-2-222-2-2000000−i2i2−i2i2−i2i2−i2i200-22-2200i2−i2i2−i2i2−i2i2−i20000000000000000
χ332222-22-20000-22-2-2-222-2-2220000002−22−2−22−22002i−2i−2i2i00−i2i2−i2i2i2−i2i2−i20000000000000000
χ342222-22-20000-22-2-2-222-2-2220000002−22−2−22−2200−2i2i2i−2i00i2−i2i2−i2−i2i2−i2i20000000000000000
χ352222-22-20000-22-2-2-222-2-222000000−22−222−22−2002i−2i−2i2i00i2−i2i2−i2−i2i2−i2i20000000000000000
χ362222-22-20000-22-2-2-222-2-222000000−22−222−22−200−2i2i2i−2i00−i2i2−i2i2i2−i2i2−i20000000000000000
χ372222-2-220000-2-2222-2-2-2-222000000i2−i2−i2i2−i2i2i2−i22-200002-2i2−i2−i2i2i2−i2−i2i20000000000000000
χ382222-2-220000-2-2222-2-2-2-222000000i2−i2−i2i2−i2i2i2−i2-220000-22−i2i2i2−i2−i2i2i2−i20000000000000000
χ392222-2-220000-2-2222-2-2-2-222000000−i2i2i2−i2i2−i2−i2i22-200002-2−i2i2i2−i2−i2i2i2−i20000000000000000
χ402222-2-220000-2-2222-2-2-2-222000000−i2i2i2−i2i2−i2−i2i2-220000-22i2−i2−i2i2i2−i2−i2i20000000000000000
χ412222-2-220000-2-22-2-22222-2-20000002−2−222−2−222i−2i0000−2i2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ422222-2-220000-2-22-2-22222-2-20000002−2−222−2−22−2i2i00002i−2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ432222-2-220000-2-22-2-22222-2-2000000−222−2−222−22i−2i0000−2i2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ442222-2-220000-2-22-2-22222-2-2000000−222−2−222−2−2i2i00002i−2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ4522-2-2-22-22i2i−2i−2i2-222i−2i2i−2i2i−2i2i−2i2i−2i2-22-2000000000000000000000000002i−2i002-200000000
χ4622-2-2-22-22i2i−2i−2i2-222i−2i2i−2i2i−2i2i−2i2i−2i2-22-200000000000000000000000000−2i2i00-2200000000
χ4722-2-2-22-22i2i−2i−2i2-22−2i2i−2i2i−2i2i−2i2i2i−2i-22-22000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ4822-2-2-22-22i2i−2i−2i2-22−2i2i−2i2i−2i2i−2i2i2i−2i-22-2200000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ4922-2-2-22-2−2i−2i2i2i2-222i−2i2i−2i2i−2i2i−2i−2i2i-22-22000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ5022-2-2-22-2−2i−2i2i2i2-222i−2i2i−2i2i−2i2i−2i−2i2i-22-2200000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ5122-2-2-22-2−2i−2i2i2i2-22−2i2i−2i2i−2i2i−2i2i−2i2i2-22-2000000000000000000000000002i−2i00-2200000000
χ5222-2-2-22-2−2i−2i2i2i2-22−2i2i−2i2i−2i2i−2i2i−2i2i2-22-200000000000000000000000000−2i2i002-200000000
χ5322-2-2-2-222i2i−2i−2i22-22i−2i2i−2i−2i2i−2i2i−2i2i-222-20000000000000000000000002i−2i002-20000000000
χ5422-2-2-2-222i2i−2i−2i22-22i−2i2i−2i−2i2i−2i2i−2i2i-222-2000000000000000000000000−2i2i00-220000000000
χ5522-2-2-2-222i2i−2i−2i22-2−2i2i−2i2i2i−2i2i−2i−2i2i2-2-220000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ5622-2-2-2-222i2i−2i−2i22-2−2i2i−2i2i2i−2i2i−2i−2i2i2-2-22000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ5722-2-2-2-22−2i−2i2i2i22-22i−2i2i−2i−2i2i−2i2i2i−2i2-2-220000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ5822-2-2-2-22−2i−2i2i2i22-22i−2i2i−2i−2i2i−2i2i2i−2i2-2-22000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ5922-2-2-2-22−2i−2i2i2i22-2−2i2i−2i2i2i−2i2i−2i2i−2i-222-20000000000000000000000002i−2i00-220000000000
χ6022-2-2-2-22−2i−2i2i2i22-2−2i2i−2i2i2i−2i2i−2i2i−2i-222-2000000000000000000000000−2i2i002-20000000000
χ6144-4-44440000-4-4-44i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000
χ6244-4-44440000-4-4-4−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000
χ6344-4-44-4-40000-4444i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000
χ6444-4-44-4-40000-444−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000
χ658-88i−8i0004+4i−4−4i4−4i−4+4i000000000000000000000000000000000000000000000000000000000
χ668-88i−8i000−4−4i4+4i−4+4i4−4i000000000000000000000000000000000000000000000000000000000
χ678-8−8i8i0004−4i−4+4i4+4i−4−4i000000000000000000000000000000000000000000000000000000000
χ688-8−8i8i000−4+4i4−4i−4−4i4+4i000000000000000000000000000000000000000000000000000000000

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