Finite Group Databasebeta

← Group #125261

Character table — Group #125261

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444422444488888888888888884444444488888888
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
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-22222-2-222-2-200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ212222-2-2-2-2-2-2220000002i2i−2i−2i00002i2i−2i−2i2-200001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000000000000000
χ222222-2-2-2-2-2-2220000002i2i−2i−2i00002i2i−2i−2i2-20000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000000000000000
χ232222-2-2-2-2-2-2220000002i2i−2i−2i0000−2i−2i2i2i-2200001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000000000000000
χ242222-2-2-2-2-2-2220000002i2i−2i−2i0000−2i−2i2i2i-220000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000000000000000
χ252222-2-2-2-2-2-222000000−2i−2i2i2i00002i2i−2i−2i-2200001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000000000000000
χ262222-2-2-2-2-2-222000000−2i−2i2i2i00002i2i−2i−2i-220000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000000000000000
χ272222-2-2-2-2-2-222000000−2i−2i2i2i0000−2i−2i2i2i2-200001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000000000000000
χ282222-2-2-2-2-2-222000000−2i−2i2i2i0000−2i−2i2i2i2-20000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000000000000000
χ2922-2-22-2-222-22-22i2i−2i−2i2i−2i000000002-22-2002i−2i00i2−i2i2−i22−22−22−22−2i2−i2i2−i20000000000000000
χ3022-2-22-2-222-22-22i2i−2i−2i2i−2i000000002-22-2002i−2i00−i2i2−i2i2−22−22−22−22−i2i2−i2i20000000000000000
χ3122-2-22-2-222-22-22i2i−2i−2i2i−2i00000000-22-2200−2i2i002−22−2−i2i2−i2i2i2−i2i2−i2−22−220000000000000000
χ3222-2-22-2-222-22-22i2i−2i−2i2i−2i00000000-22-2200−2i2i00−22−22i2−i2i2−i2−i2i2−i2i22−22−20000000000000000
χ3322-2-22-2-222-22-2−2i−2i2i2i−2i2i000000002-22-200−2i2i00i2−i2i2−i2−22−22−22−22i2−i2i2−i20000000000000000
χ3422-2-22-2-222-22-2−2i−2i2i2i−2i2i000000002-22-200−2i2i00−i2i2−i2i22−22−22−22−2−i2i2−i2i20000000000000000
χ3522-2-22-2-222-22-2−2i−2i2i2i−2i2i00000000-22-22002i−2i002−22−2i2−i2i2−i2−i2i2−i2i2−22−220000000000000000
χ3622-2-22-2-222-22-2−2i−2i2i2i−2i2i00000000-22-22002i−2i00−22−22−i2i2−i2i2i2−i2i2−i22−22−20000000000000000
χ3722-2-22-2-22-22-222i2i−2i−2i−2i2i2-22-22i2i−2i−2i00000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ3822-2-22-2-22-22-222i2i−2i−2i−2i2i2-22-22i2i−2i−2i0000000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ3922-2-22-2-22-22-222i2i−2i−2i−2i2i-22-22−2i−2i2i2i00000000000000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i
χ4022-2-22-2-22-22-222i2i−2i−2i−2i2i-22-22−2i−2i2i2i0000000000000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i
χ4122-2-22-2-22-22-22−2i−2i2i2i2i−2i2-22-2−2i−2i2i2i00000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ4222-2-22-2-22-22-22−2i−2i2i2i2i−2i2-22-2−2i−2i2i2i0000000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ4322-2-22-2-22-22-22−2i−2i2i2i2i−2i-22-222i2i−2i−2i00000000000000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i
χ4422-2-22-2-22-22-22−2i−2i2i2i2i−2i-22-222i2i−2i−2i0000000000000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i
χ4522-2-2-222-2-222-200000000002i−2i2i−2i2i−2i−2i2i00002-200002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
χ4622-2-2-222-2-222-200000000002i−2i2i−2i2i−2i−2i2i00002-20000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ4722-2-2-222-2-222-200000000002i−2i2i−2i−2i2i2i−2i0000-222ζ−2ζ−2ζ2ζ000000002ζ3−2ζ3−2ζ32ζ30000000000000000
χ4822-2-2-222-2-222-200000000002i−2i2i−2i−2i2i2i−2i0000-22−2ζ2ζ2ζ−2ζ00000000−2ζ32ζ32ζ3−2ζ30000000000000000
χ4922-2-2-222-2-222-20000000000−2i2i−2i2i2i−2i−2i2i0000-222ζ3−2ζ3−2ζ32ζ3000000002ζ−2ζ−2ζ2ζ0000000000000000
χ5022-2-2-222-2-222-20000000000−2i2i−2i2i2i−2i−2i2i0000-22−2ζ32ζ32ζ3−2ζ300000000−2ζ2ζ2ζ−2ζ0000000000000000
χ5122-2-2-222-2-222-20000000000−2i2i−2i2i−2i2i2i−2i00002-200002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ5222-2-2-222-2-222-20000000000−2i2i−2i2i−2i2i2i−2i00002-20000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ5344444444-4-4-4-44444-4-400000000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ554444-4-4-4-444-4-400000000004-4-44000000000000000000000000000000000000000000
χ564444-4-4-4-444-4-40000000000-444-4000000000000000000000000000000000000000000
χ5744-4-4-444-44-4-440000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ5844-4-4-444-44-4-44000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ594-44-444-4-400004-44-40000000000000000000000000000000000002i−2i2i−2i000000000000
χ604-44-444-4-400004-44-4000000000000000000000000000000000000−2i2i−2i2i000000000000
χ614-44-444-4-40000-44-440000000000000000000000000000000000002i−2i−2i2i000000000000
χ624-44-444-4-40000-44-44000000000000000000000000000000000000−2i2i2i−2i000000000000
χ634-4-444-44-400004i−4i−4i4i00000000000000000000000000000000000000002i−2i2-200000000
χ644-4-444-44-400004i−4i−4i4i0000000000000000000000000000000000000000−2i2i-2200000000
χ654-4-444-44-40000−4i4i4i−4i00000000000000000000000000000000000000002i−2i-2200000000
χ664-4-444-44-40000−4i4i4i−4i0000000000000000000000000000000000000000−2i2i2-200000000
χ678-88-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-88-88-88000000000000000000000000000000000000000000000000000000000000

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