Finite Group Databasebeta

← Group #138513

Character table — Group #138513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222224444442224448888888824888816161616161616161616161616161616888888882444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-11-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111-1-11-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-111-1-111-1-1-1111-1-11111-1-1-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-111-1-111-1-1-1111-1-11111-1-1-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-111-1-111-1-1-1111-1-11111-1-1-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-111-1-111-1-1-1111-1-11111-1-1-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-111-1-111-1-1-1-1-11111111-1-1-1-11-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-111-1-111-1-1-1-1-11111111-1-1-1-11-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-111-1-111-1-1-1-1-11111111-1-1-1-11-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-111-1-111-1-1-1-1-11111111-1-1-1-11-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ18222222222222222-2-22-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ1922222222-2-2-2-2-2-2222-2-2-2000000002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2022222222-2-2-2-2-2-2222-2-2-2000000002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2122222222-2-2-2-2-2-22-2-2-22200000000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2222222222-2-2-2-2-2-22-2-2-22200000000-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ23222222-2-22222-2-2-200-20022-2-222-2-2000000000000000000000000002i−2i2i−2i0000
χ24222222-2-22222-2-2-200-20022-2-222-2-200000000000000000000000000−2i2i−2i2i0000
χ25222222-2-22222-2-2-200-200-2-222-2-22200000000000000000000002i−2i2i−2i00000000
χ26222222-2-22222-2-2-200-200-2-222-2-2220000000000000000000000−2i2i−2i2i00000000
χ272222-2-22222-2-222-222-22200000000-2-2000022−2−2−2−22222−2−2−2−222000000000000
χ282222-2-22222-2-222-222-22200000000-2-20000−2−22222−2−2−2−22222−2−2000000000000
χ292222-2-22222-2-222-2-2-2-2-2-20000000022000022−2−2−2−222−2−22222−2−2000000000000
χ302222-2-22222-2-222-2-2-2-2-2-200000000220000−2−22222−2−222−2−2−2−222000000000000
χ312222-2-222-2-222-2-2-2222-2-2-2-2-2-22222-22-2-2220000000000000000000000000000
χ322222-2-222-2-222-2-2-2-2-2222-2-2-2-222222-222-2-20000000000000000000000000000
χ332222-2-2-2-2-2-22222200-20022-2-2-2-222000000000000000000000000002-2-220000
χ342222-2-2-2-2-2-22222200-20022-2-2-2-22200000000000000000000000000-222-20000
χ352222-2-2-2-2-2-22222200-200-2-22222-2-200000000000000000000002-2-2200000000
χ362222-2-2-2-2-2-22222200-200-2-22222-2-20000000000000000000000-222-200000000
χ3722-2-2002-22i−2i002i−2i02-202i−2i2−22−2i2−i2i2−i2002−2i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ3822-2-2002-22i−2i002i−2i02-202i−2i2−22−2i2−i2i2−i2002−2i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ3922-2-2002-22i−2i002i−2i02-202i−2i−22−22−i2i2−i2i200−22−i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3000000000000
χ4022-2-2002-22i−2i002i−2i02-202i−2i−22−22−i2i2−i2i200−22−i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3000000000000
χ4122-2-2002-22i−2i002i−2i0-220−2i2i2−22−2i2−i2i2−i200−22−i2i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ4222-2-2002-22i−2i002i−2i0-220−2i2i2−22−2i2−i2i2−i200−22−i2i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ4322-2-2002-22i−2i002i−2i0-220−2i2i−22−22−i2i2−i2i2002−2i2−i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3000000000000
χ4422-2-2002-22i−2i002i−2i0-220−2i2i−22−22−i2i2−i2i2002−2i2−i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3000000000000
χ4522-2-2002-2−2i2i00−2i2i02-20−2i2i2−22−2−i2i2−i2i2002−2−i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3000000000000
χ4622-2-2002-2−2i2i00−2i2i02-20−2i2i2−22−2−i2i2−i2i2002−2−i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3000000000000
χ4722-2-2002-2−2i2i00−2i2i02-20−2i2i−22−22i2−i2i2−i200−22i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ4822-2-2002-2−2i2i00−2i2i02-20−2i2i−22−22i2−i2i2−i200−22i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ4922-2-2002-2−2i2i00−2i2i0-2202i−2i2−22−2−i2i2−i2i200−22i2−i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3000000000000
χ5022-2-2002-2−2i2i00−2i2i0-2202i−2i2−22−2−i2i2−i2i200−22i2−i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3000000000000
χ5122-2-2002-2−2i2i00−2i2i0-2202i−2i−22−22i2−i2i2−i2002−2−i2i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ5222-2-2002-2−2i2i00−2i2i0-2202i−2i−22−22i2−i2i2−i2002−2−i2i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ53444444-4-4-4-4-4-444-400400000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-4-4-4400400000000000000000000000000000000000000000000
χ5544-4-400-444i−4i00−4i4i00000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000
χ5644-4-400-444i−4i00−4i4i000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000
χ5744-4-400-44−4i4i004i−4i00000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000
χ5844-4-400-44−4i4i004i−4i000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000
χ598-88-80000008-800000000000000000000000000000000000000000000000000
χ608-88-8000000-8800000000000000000000000000000000000000000000000000
χ618-8-888-800000000000000000000000000000000000000000000000000000000
χ628-8-88-8800000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.