Finite Group Databasebeta

← Group #419784

Character table — Group #419784

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244448888888888888888888888888888881616161616161616161616161616
order12224444222222444444888822222244444488888888888888888824444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ7111111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111
χ911111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1011111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ1111111111111111111111-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111
χ1211111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-11111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111111111-1-1-1-111-1-1
χ17222222222-2-22-2-2-2-2-222-2222200000000000022-2-200000000-2-20000002-20000000000
χ18222222222-2-22-2-2-2-2-222-22222000000000000-2-22200000000-2-2000000-220000000000
χ19222222222-2-22-2-2-2-2-222-2-2-2-2-200000000000022-2-20000000022000000-220000000000
χ20222222222-2-22-2-2-2-2-222-2-2-2-2-2000000000000-2-22200000000220000002-20000000000
χ212222-2-2-2-2222222-2-2-2-2-2-20000220000-2-200002i−2i2i−2i00000000002i2i−2i−2i00000000000000
χ222222-2-2-2-2222222-2-2-2-2-2-20000220000-2-20000−2i2i−2i2i0000000000−2i−2i2i2i00000000000000
χ232222-2-2-2-2222222-2-2-2-2-2-20000-2-200002200002i−2i2i−2i0000000000−2i−2i2i2i00000000000000
χ242222-2-2-2-2222222-2-2-2-2-2-20000-2-20000220000−2i2i−2i2i00000000002i2i−2i−2i00000000000000
χ252222-2-2-2-22-2-22-2-2222-2-22000000220000-2-2002i−2i−2i2i00002i2i−2i−2i00000000000000000000
χ262222-2-2-2-22-2-22-2-2222-2-22000000220000-2-200−2i2i2i−2i0000−2i−2i2i2i00000000000000000000
χ272222-2-2-2-22-2-22-2-2222-2-22000000-2-2000022002i−2i−2i2i0000−2i−2i2i2i00000000000000000000
χ282222-2-2-2-22-2-22-2-2222-2-22000000-2-200002200−2i2i2i−2i00002i2i−2i−2i00000000000000000000
χ292222-2-2-2-2-222-2-2-222-222-222-2-200000000000000002i2i−2i−2i00002-20000000000002i−2i0000
χ302222-2-2-2-2-222-2-2-222-222-222-2-20000000000000000−2i−2i2i2i00002-2000000000000−2i2i0000
χ312222-2-2-2-2-222-2-2-222-222-2-2-22200000000000000002i2i−2i−2i0000-22000000000000−2i2i0000
χ322222-2-2-2-2-222-2-2-222-222-2-2-2220000000000000000−2i−2i2i2i0000-220000000000002i−2i0000
χ332222-2-2-2-2-2-2-2-222-2-2222222-2-20000220000-2-2000000000000-2200002-2000000000000
χ342222-2-2-2-2-2-2-2-222-2-2222222-2-20000-2-2000022000000000000-220000-22000000000000
χ352222-2-2-2-2-2-2-2-222-2-22222-2-2220000220000-2-20000000000002-20000-22000000000000
χ362222-2-2-2-2-2-2-2-222-2-22222-2-2220000-2-20000220000000000002-200002-2000000000000
χ372-2-2222-2-222-2-22-22-222-2-2000000000000000000002i−2i2i−2i0000002i−2i2i−2i00002-200000000
χ382-2-2222-2-222-2-22-22-222-2-2000000000000000000002i−2i2i−2i000000−2i2i−2i2i0000-2200000000
χ392-2-2222-2-222-2-22-22-222-2-200000000000000000000−2i2i−2i2i0000002i−2i2i−2i0000-2200000000
χ402-2-2222-2-222-2-22-22-222-2-200000000000000000000−2i2i−2i2i000000−2i2i−2i2i00002-200000000
χ412-2-2222-2-2-2-2222-22-2-2-2220000002-22-2002-22-200000000000000000000000000002-200
χ422-2-2222-2-2-2-2222-22-2-2-2220000002-2-22002-2-220000000000000000000000000000-2200
χ432-2-2222-2-2-2-2222-22-2-2-222000000-222-200-222-20000000000000000000000000000-2200
χ442-2-2222-2-2-2-2222-22-2-2-222000000-22-2200-22-2200000000000000000000000000002-200
χ452-2-22-2-22222-2-22-2-22-2-222000000002-20000-22000000000000002-2-220000000000002-2
χ462-2-22-2-22222-2-22-2-22-2-222000000002-20000-2200000000000000-222-2000000000000-22
χ472-2-22-2-22222-2-22-2-22-2-22200000000-2200002-2000000000000002-2-22000000000000-22
χ482-2-22-2-22222-2-22-2-22-2-22200000000-2200002-200000000000000-222-20000000000002-2
χ492-2-22-2-222-22-22-222-2-22-220000002-20000-220000002-2-2200000000000000002-2000000
χ502-2-22-2-222-22-22-222-2-22-220000002-20000-22000000-222-20000000000000000-22000000
χ512-2-22-2-222-22-22-222-2-22-22000000-2200002-20000002-2-220000000000000000-22000000
χ522-2-22-2-222-22-22-222-2-22-22000000-2200002-2000000-222-200000000000000002-2000000
χ5344444444-444-4-4-4-4-44-4-44000000000000000000000000000000000000000000000000
χ5444444444-4-4-4-44444-4-4-4-4000000000000000000000000000000000000000000000000
χ5544-4-44i−4i4i−4i00000000000022−222i2−2i22-200002i−2i0000000000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ5644-4-44i−4i4i−4i00000000000022−222i2−2i2-220000−2i2i000000000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ5744-4-44i−4i4i−4i000000000000−2222−2i22i22-200002i−2i000000000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ5844-4-44i−4i4i−4i000000000000−2222−2i22i2-220000−2i2i0000000000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ5944-4-4−4i4i−4i4i00000000000022−22−2i22i22-20000−2i2i000000000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ6044-4-4−4i4i−4i4i00000000000022−22−2i22i2-2200002i−2i0000000000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ6144-4-4−4i4i−4i4i000000000000−22222i2−2i22-20000−2i2i0000000000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ6244-4-4−4i4i−4i4i000000000000−22222i2−2i2-2200002i−2i000000000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ634-4-4444-4-44-44-4-44-44-44-44000000000000000000000000000000000000000000000000
χ644-4-4444-4-4-44-44-44-444-44-4000000000000000000000000000000000000000000000000
χ654-4-44-4-4444-44-4-444-44-44-4000000000000000000000000000000000000000000000000
χ664-4-44-4-444-4-4444-4-4444-4-4000000000000000000000000000000000000000000000000
χ678-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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