Finite Group Databasebeta

← Group #136646

Character table — Group #136646

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order122244442244444444448888888824448888161616161616161616161616161616162244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ131111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ141111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ151111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-2000000002-2-220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ202222222222-2-2-2-222-2-2-2-2000000002-2-220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ212222222222-2-2-2-222-2-2-2-200000000-222-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ222222222222-2-2-2-222-2-2-2-200000000-222-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ2322222222-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000002i−2i2i−2i
χ2422222222-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000−2i2i−2i2i
χ2522222222-2-2-2-222-2-222-2-2-2-222-2-222000000000000000000000000000000002i−2i2i−2i0000
χ2622222222-2-2-2-222-2-222-2-2-2-222-2-22200000000000000000000000000000000−2i2i−2i2i0000
χ272222-2-2-2-22222-2-2-2-222-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000
χ282222-2-2-2-22222-2-2-2-222-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000000000
χ292222-2-2-2-222-2-222-2-2-2-222000000002-22-2000022−2−2−2−22222−2−2−2−2220000000000000000
χ302222-2-2-2-222-2-222-2-2-2-222000000002-22-20000−2−22222−2−2−2−22222−2−20000000000000000
χ312222-2-2-2-222-2-222-2-2-2-22200000000-22-22000022−2−2−2−222−2−22222−2−20000000000000000
χ322222-2-2-2-222-2-222-2-2-2-22200000000-22-220000−2−22222−2−222−2−2−2−2220000000000000000
χ332222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2220000000000000000000000000000000000002-2-22
χ342222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222000000000000000000000000000000000000-222-2
χ352222-2-2-2-2-2-2-2-2-2-2222222-2-22222-2-2000000000000000000000000000000002-2-220000
χ362222-2-2-2-2-2-2-2-2-2-2222222-2-22222-2-200000000000000000000000000000000-222-20000
χ3722-2-22i2i−2i−2i2-22-22i−2i2i−2i2-22i−2i0000000000002i−2i2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ3822-2-22i2i−2i−2i2-22-22i−2i2i−2i2-22i−2i0000000000002i−2i2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ3922-2-22i2i−2i−2i2-22-22i−2i2i−2i2-22i−2i000000000000−2i2i-221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4022-2-22i2i−2i−2i2-22-22i−2i2i−2i2-22i−2i000000000000−2i2i-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4122-2-22i2i−2i−2i2-2-22−2i2i2i−2i-22−2i2i2-22-22i−2i2i−2i00000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ4222-2-22i2i−2i−2i2-2-22−2i2i2i−2i-22−2i2i2-22-22i−2i2i−2i0000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ4322-2-22i2i−2i−2i2-2-22−2i2i2i−2i-22−2i2i-22-22−2i2i−2i2i000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ4422-2-22i2i−2i−2i2-2-22−2i2i2i−2i-22−2i2i-22-22−2i2i−2i2i00000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ4522-2-22i2i−2i−2i-222-2−2i2i−2i2i-222i−2i2-2-222i−2i−2i2i0000000000000000000000002-22i−2i000000000000
χ4622-2-22i2i−2i−2i-222-2−2i2i−2i2i-222i−2i2-2-222i−2i−2i2i000000000000000000000000-22−2i2i000000000000
χ4722-2-22i2i−2i−2i-222-2−2i2i−2i2i-222i−2i-222-2−2i2i2i−2i00000000000000000000000000002-22i−2i00000000
χ4822-2-22i2i−2i−2i-222-2−2i2i−2i2i-222i−2i-222-2−2i2i2i−2i0000000000000000000000000000-22−2i2i00000000
χ4922-2-2−2i−2i2i2i2-22-2−2i2i−2i2i2-2−2i2i0000000000002i−2i-221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5022-2-2−2i−2i2i2i2-22-2−2i2i−2i2i2-2−2i2i0000000000002i−2i-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5122-2-2−2i−2i2i2i2-22-2−2i2i−2i2i2-2−2i2i000000000000−2i2i2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5222-2-2−2i−2i2i2i2-22-2−2i2i−2i2i2-2−2i2i000000000000−2i2i2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5322-2-2−2i−2i2i2i2-2-222i−2i−2i2i-222i−2i2-22-2−2i2i−2i2i00000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ5422-2-2−2i−2i2i2i2-2-222i−2i−2i2i-222i−2i2-22-2−2i2i−2i2i0000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ5522-2-2−2i−2i2i2i2-2-222i−2i−2i2i-222i−2i-22-222i−2i2i−2i000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ5622-2-2−2i−2i2i2i2-2-222i−2i−2i2i-222i−2i-22-222i−2i2i−2i00000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ5722-2-2−2i−2i2i2i-222-22i−2i2i−2i-22−2i2i2-2-22−2i2i2i−2i0000000000000000000000002-2−2i2i000000000000
χ5822-2-2−2i−2i2i2i-222-22i−2i2i−2i-22−2i2i2-2-22−2i2i2i−2i000000000000000000000000-222i−2i000000000000
χ5922-2-2−2i−2i2i2i-222-22i−2i2i−2i-22−2i2i-222-22i−2i−2i2i00000000000000000000000000002-2−2i2i00000000
χ6022-2-2−2i−2i2i2i-222-22i−2i2i−2i-22−2i2i-222-22i−2i−2i2i0000000000000000000000000000-222i−2i00000000
χ6144444444-4-444-4-4-4-4-4-444000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-4444444-4-4-4-4000000000000000000000000000000000000000000000000
χ6344-4-44i4i−4i−4i-44-444i−4i−4i4i4-4−4i4i000000000000000000000000000000000000000000000000
χ6444-4-4−4i−4i4i4i-44-44−4i4i4i−4i4-44i−4i000000000000000000000000000000000000000000000000
χ658-88-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000
χ668-88-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ678-8-888-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

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