Finite Group Databasebeta

← Group #140309

Character table — Group #140309

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order1222224444444444444444448888888888888888888888888816161616161616162488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ91111-1-1111-1-1-1-111iiii−i−i−i−i-111-1-11-1iiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i11-1-11-1i−i
χ101111-1-1111-1-1-1-111iiii−i−i−i−i-111-1-11-1iiii−i−i−i−i1111-1-1-1-1ii−i−i−i−iii-1-111-11−ii
χ111111-1-1111-1-1-1-111iiii−i−i−i−i-111-1-11-1−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i11-1-1-11−ii
χ121111-1-1111-1-1-1-111iiii−i−i−i−i-111-1-11-1−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iii-1-1111-1i−i
χ131111-1-1111-1-1-1-111−i−i−i−iiiii-111-1-11-1iiii−i−i−i−i-1-1-1-11111−i−iiiii−i−i-1-1111-1−ii
χ141111-1-1111-1-1-1-111−i−i−i−iiiii-111-1-11-1iiii−i−i−i−i-1-1-1-11111−i−iii−i−iii11-1-1-11i−i
χ151111-1-1111-1-1-1-111−i−i−i−iiiii-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−iiiii−i−i-1-111-11i−i
χ161111-1-1111-1-1-1-111−i−i−i−iiiii-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii11-1-11-1−ii
χ17222222222222222222222222-2-2-2-2-2-20000000000000000-2-2-2-2000000000000
χ18222222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-200000000000000002222000000000000
χ19222222-222-2-2-2-2-2-200000000222-2-2-222i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ20222222-222-2-2-2-2-2-200000000222-2-2-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ21222222-222-2-2-2-2-2-2000000002-2-2222-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222-222-2-2-2-2-2-2000000002-2-2222-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ23222222-2-2-2-2-222-2222-2-222-2-2-200000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ24222222-2-2-2-2-222-2222-2-222-2-2-200000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ25222222-2-2-2-2-222-22-2-222-2-222-200000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ26222222-2-2-2-2-222-22-2-222-2-222-200000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ272222-2-2222-2-2-2-2222i2i2i2i−2i−2i−2i−2i-2-2-222-220000000000000000−2i−2i2i2i000000000000
χ282222-2-2222-2-2-2-222−2i−2i−2i−2i2i2i2i2i-2-2-222-2200000000000000002i2i−2i−2i000000000000
χ292222-2-2-2222222-2-200000000-22222-2-222-2-2-2-222000000000000000000000000
χ302222-2-2-2222222-2-200000000-22222-2-2-2-22222-2-2000000000000000000000000
χ312222-2-2-2222222-2-200000000-2-2-2-2-222000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2222222-2-200000000-2-2-2-2-22200000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2-222-2-2-222i2i−2i−2i−2i−2i2i2i2000000000000000000000000002−2−22−i2i2i2−i20000
χ342222-2-2-2-2-222-2-2-222i2i−2i−2i−2i−2i2i2i200000000000000000000000000−222−2i2−i2−i2i20000
χ352222-2-2-2-2-222-2-2-22−2i−2i2i2i2i2i−2i−2i2000000000000000000000000002−2−22i2−i2−i2i20000
χ362222-2-2-2-2-222-2-2-22−2i−2i2i2i2i2i−2i−2i200000000000000000000000000−222−2−i2i2i2−i20000
χ3722-2-20002-22i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i02-22i−2i00002ζ3−2ζ32ζ−2ζ00i2−i2i2−i22−22−21+i−1−i1−i−1+i000000000000
χ3822-2-20002-22i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i02-22i−2i0000−2ζ32ζ3−2ζ2ζ00−i2i2−i2i2−22−221+i−1−i1−i−1+i000000000000
χ3922-2-20002-22i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0-22−2i2i002ζ−2ζ00002ζ3−2ζ32−2−22i2−i2−i2i2−1−i1+i−1+i1−i000000000000
χ4022-2-20002-22i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0-22−2i2i00−2ζ2ζ0000−2ζ32ζ3−222−2−i2i2i2−i2−1−i1+i−1+i1−i000000000000
χ4122-2-20002-22i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i02-22i−2i00002ζ3−2ζ32ζ−2ζ00−i2i2−i2i2−22−22−1−i1+i−1+i1−i000000000000
χ4222-2-20002-22i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i02-22i−2i0000−2ζ32ζ3−2ζ2ζ00i2−i2i2−i22−22−2−1−i1+i−1+i1−i000000000000
χ4322-2-20002-22i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0-22−2i2i002ζ−2ζ00002ζ3−2ζ3−222−2−i2i2i2−i21+i−1−i1−i−1+i000000000000
χ4422-2-20002-22i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0-22−2i2i00−2ζ2ζ0000−2ζ32ζ32−2−22i2−i2−i2i21+i−1−i1−i−1+i000000000000
χ4522-2-20002-2−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i02-2−2i2i00002ζ−2ζ2ζ3−2ζ300i2−i2i2−i2−22−221−i−1+i1+i−1−i000000000000
χ4622-2-20002-2−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i02-2−2i2i0000−2ζ2ζ−2ζ32ζ300−i2i2−i2i22−22−21−i−1+i1+i−1−i000000000000
χ4722-2-20002-2−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0-222i−2i002ζ3−2ζ300002ζ−2ζ−222−2i2−i2−i2i2−1+i1−i−1−i1+i000000000000
χ4822-2-20002-2−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0-222i−2i00−2ζ32ζ30000−2ζ2ζ2−2−22−i2i2i2−i2−1+i1−i−1−i1+i000000000000
χ4922-2-20002-2−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i02-2−2i2i00002ζ−2ζ2ζ3−2ζ300−i2i2−i2i22−22−2−1+i1−i−1−i1+i000000000000
χ5022-2-20002-2−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i02-2−2i2i0000−2ζ2ζ−2ζ32ζ300i2−i2i2−i2−22−22−1+i1−i−1−i1+i000000000000
χ5122-2-20002-2−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0-222i−2i002ζ3−2ζ300002ζ−2ζ2−2−22−i2i2i2−i21−i−1+i1+i−1−i000000000000
χ5222-2-20002-2−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0-222i−2i00−2ζ32ζ30000−2ζ2ζ−222−2i2−i2−i2i21−i−1+i1+i−1−i000000000000
χ534444444-4-444-4-44-400000000-400000000000000000000000000000000000000
χ544444-4-44-4-4-4-4444-400000000400000000000000000000000000000000000000
χ5544-4-4000-444i−4i−4i4i002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000
χ5644-4-4000-444i−4i−4i4i00−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000
χ5744-4-4000-44−4i4i4i−4i002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000
χ5844-4-4000-44−4i4i4i−4i00−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000
χ598-88-8008000000-8000000000000000000000000000000000000000000000000
χ608-88-800-80000008000000000000000000000000000000000000000000000000
χ618-8-888-800000000000000000000000000000000000000000000000000000000
χ628-8-88-8800000000000000000000000000000000000000000000000000000000

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