Finite Group Databasebeta

← Group #124669

Character table — Group #124669

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order1222444422444444444422448888448888888888888888888888444488881616161616161616
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
χ511111111111111111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ1011111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ1111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ1211111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ1311111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222222222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ1922222222222-2-2-2-22-2-2-2-222222222-2-222-2-2-2-200000000000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000
χ212222-2-2-2-222-20000-2000022-2-22i2i−2i−2i002i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ222222-2-2-2-222-20000-2000022-2-22i2i−2i−2i002i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ232222-2-2-2-222-20000-2000022-2-2−2i−2i2i2i00−2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ242222-2-2-2-222-20000-2000022-2-2−2i−2i2i2i00−2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ252222-2-2-2-222-20000-20000-2-2222i2i−2i−2i00−2i2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ262222-2-2-2-222-20000-20000-2-2222i2i−2i−2i00−2i2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ272222-2-2-2-222-20000-20000-2-222−2i−2i2i2i002i−2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ282222-2-2-2-222-20000-20000-2-222−2i−2i2i2i002i−2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ292222-2-2-2-2-2-222i2i−2i−2i22i2i−2i−2i00002i−2i2i−2i00002-2000000000000000000002-2002i−2i00000000
χ302222-2-2-2-2-2-222i2i−2i−2i22i2i−2i−2i00002i−2i2i−2i00002-200000000000000000000-2200−2i2i00000000
χ312222-2-2-2-2-2-222i2i−2i−2i22i2i−2i−2i0000−2i2i−2i2i0000-220000000000000000002-2002i−2i0000000000
χ322222-2-2-2-2-2-222i2i−2i−2i22i2i−2i−2i0000−2i2i−2i2i0000-22000000000000000000-2200−2i2i0000000000
χ332222-2-2-2-2-2-22−2i−2i2i2i2−2i−2i2i2i00002i−2i2i−2i0000-220000000000000000002-200−2i2i0000000000
χ342222-2-2-2-2-2-22−2i−2i2i2i2−2i−2i2i2i00002i−2i2i−2i0000-22000000000000000000-22002i−2i0000000000
χ352222-2-2-2-2-2-22−2i−2i2i2i2−2i−2i2i2i0000−2i2i−2i2i00002-2000000000000000000002-200−2i2i00000000
χ362222-2-2-2-2-2-22−2i−2i2i2i2−2i−2i2i2i0000−2i2i−2i2i00002-200000000000000000000-22002i−2i00000000
χ3722-2-222-2-2-2222222-2-2-2-2-22-22-200002-20000000000000000000000000000002−22−22−22−2
χ3822-2-222-2-2-2222222-2-2-2-2-22-22-200002-2000000000000000000000000000000−22−22−22−22
χ3922-2-222-2-2-2222222-2-2-2-2-2-22-220000-220000000000000000000000000000002−22−2−22−22
χ4022-2-222-2-2-2222222-2-2-2-2-2-22-220000-22000000000000000000000000000000−22−222−22−2
χ4122-2-222-2-2-222-2-2-2-2-222222-22-20000-22000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ4222-2-222-2-2-222-2-2-2-2-222222-22-20000-22000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ4322-2-222-2-2-222-2-2-2-2-22222-22-2200002-2000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ4422-2-222-2-2-222-2-2-2-2-22222-22-2200002-2000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ4544444444-4-4-40000-4000000004-4-440000000000000000000000000000000000000000
χ4644444444-4-4-40000-400000000-444-40000000000000000000000000000000000000000
χ4744-4-444-4-44-4-4000040000000000000000004-400000000000000000000000000000000
χ4844-4-444-4-44-4-400004000000000000000000-4400000000000000000000000000000000
χ4944-4-4-4-4444-444i4i−4i−4i-4−4i−4i4i4i000000000000000000000000000000000000000000000000
χ5044-4-4-4-4444-44−4i−4i4i4i-44i4i−4i−4i000000000000000000000000000000000000000000000000
χ5144-4-4-4-444-44-40000400004-4-4400000000000000000000000000000000000000000000
χ5244-4-4-4-444-44-4000040000-444-400000000000000000000000000000000000000000000
χ534-44-44i−4i4i−4i0002+2i−2−2i2−2i−2+2i02+2i−2−2i2−2i−2+2i00000000000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ000000000000000000000000
χ544-44-44i−4i4i−4i0002+2i−2−2i2−2i−2+2i02+2i−2−2i2−2i−2+2i0000000000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ554-44-44i−4i4i−4i000−2−2i2+2i−2+2i2−2i0−2−2i2+2i−2+2i2−2i00000000000000002ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ3000000000000000000000000
χ564-44-44i−4i4i−4i000−2−2i2+2i−2+2i2−2i0−2−2i2+2i−2+2i2−2i0000000000000000−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ3000000000000000000000000
χ574-44-4−4i4i−4i4i0002−2i−2+2i2+2i−2−2i02−2i−2+2i2+2i−2−2i00000000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ584-44-4−4i4i−4i4i0002−2i−2+2i2+2i−2−2i02−2i−2+2i2+2i−2−2i0000000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ594-44-4−4i4i−4i4i000−2+2i2−2i−2−2i2+2i0−2+2i2−2i−2−2i2+2i00000000000000002ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ000000000000000000000000
χ604-44-4−4i4i−4i4i000−2+2i2−2i−2−2i2+2i0−2+2i2−2i−2−2i2+2i0000000000000000−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ000000000000000000000000
χ614-4-444i−4i−4i4i0002+2i−2−2i2−2i−2+2i0−2−2i2+2i−2+2i2−2i0000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ30000000000000000
χ624-4-444i−4i−4i4i0002+2i−2−2i2−2i−2+2i0−2−2i2+2i−2+2i2−2i000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ30000000000000000
χ634-4-444i−4i−4i4i000−2−2i2+2i−2+2i2−2i02+2i−2−2i2−2i−2+2i0000000000000000000000002ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ0000000000000000
χ644-4-444i−4i−4i4i000−2−2i2+2i−2+2i2−2i02+2i−2−2i2−2i−2+2i000000000000000000000000−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ0000000000000000
χ654-4-44−4i4i4i−4i0002−2i−2+2i2+2i−2−2i0−2+2i2−2i−2−2i2+2i0000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ0000000000000000
χ664-4-44−4i4i4i−4i0002−2i−2+2i2+2i−2−2i0−2+2i2−2i−2−2i2+2i000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ0000000000000000
χ674-4-44−4i4i4i−4i000−2+2i2−2i−2−2i2+2i02−2i−2+2i2+2i−2−2i0000000000000000000000002ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ30000000000000000
χ684-4-44−4i4i4i−4i000−2+2i2−2i−2−2i2+2i02−2i−2+2i2+2i−2−2i000000000000000000000000−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ30000000000000000

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