Finite Group Databasebeta

← Group #450136

Character table — Group #450136

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444222222444444444488882222444444444488888888884444444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111-1-1111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1
χ911111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ1011111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1
χ1111111111111111111111-1-1-1-11111-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ1311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-11111-1-1
χ17222222222-2-22-2-22-2-2-22-20000222200000000002i2i−2i−2i-2-200000000000000002i−2i000000
χ18222222222-2-22-2-22-2-2-22-2000022220000000000−2i−2i2i2i-2-20000000000000000−2i2i000000
χ19222222222-2-22-2-22-2-2-22-20000-2-2-2-200000000002i2i−2i−2i220000000000000000−2i2i000000
χ20222222222-2-22-2-22-2-2-22-20000-2-2-2-20000000000−2i−2i2i2i2200000000000000002i−2i000000
χ2122222222-22-2-2-22-222-2-2-22222000000000000-2-200000000002i2i−2i−2i002i−2i000000000000
χ2222222222-22-2-2-22-222-2-2-22222000000000000-2-20000000000−2i−2i2i2i00−2i2i000000000000
χ2322222222-22-2-2-22-222-2-2-2-2-2-2-20000000000002200000000002i2i−2i−2i00−2i2i000000000000
χ2422222222-22-2-2-22-222-2-2-2-2-2-2-2000000000000220000000000−2i−2i2i2i002i−2i000000000000
χ252222-2-2-2-22-2-22-2-2-2222-222i2i−2i−2i0000002200-2-22i−2i0000000000000000000000002i−2i0000
χ262222-2-2-2-22-2-22-2-2-2222-222i2i−2i−2i000000-2-200222i−2i000000000000000000000000−2i2i0000
χ272222-2-2-2-22-2-22-2-2-2222-22−2i−2i2i2i0000002200-2-2−2i2i000000000000000000000000−2i2i0000
χ282222-2-2-2-22-2-22-2-2-2222-22−2i−2i2i2i000000-2-20022−2i2i0000000000000000000000002i−2i0000
χ292222-2-2-2-2-22-2-2-222-2-2222000022-2-22200-2-2000000002-2000000002-200000000000000
χ302222-2-2-2-2-22-2-2-222-2-2222000022-2-2-2-20022000000002-200000000-2200000000000000
χ312222-2-2-2-2-22-2-2-222-2-22220000-2-2222200-2-200000000-2200000000-2200000000000000
χ322222-2-2-2-2-22-2-2-222-2-22220000-2-222-2-2002200000000-22000000002-200000000000000
χ332222-2-2-2-2-2-22-22-2222-22-22i2i−2i−2i22-2-200000000−2i2i0000-222i2i−2i−2i00000000000000000000
χ342222-2-2-2-2-2-22-22-2222-22-22i2i−2i−2i-2-22200000000−2i2i00002-2−2i−2i2i2i00000000000000000000
χ352222-2-2-2-2-2-22-22-2222-22-2−2i−2i2i2i22-2-2000000002i−2i0000-22−2i−2i2i2i00000000000000000000
χ362222-2-2-2-2-2-22-22-2222-22-2−2i−2i2i2i-2-222000000002i−2i00002-22i2i−2i−2i00000000000000000000
χ372-2-2222-2-2222-2-2-222-22-2-2000000002-22-22-22-200000000000000000000000000002-200
χ382-2-2222-2-2222-2-2-222-22-2-2000000002-2-222-2-220000000000000000000000000000-2200
χ392-2-2222-2-2222-2-2-222-22-2-200000000-222-2-222-20000000000000000000000000000-2200
χ402-2-2222-2-2222-2-2-222-22-2-200000000-22-22-22-2200000000000000000000000000002-200
χ412-2-22-2-222222-2-2-2-2-22-2220000000000000000002i−2i2i−2i0000002-22-20000002i−2i00000000
χ422-2-22-2-222222-2-2-2-2-22-2220000000000000000002i−2i2i−2i000000-22-22000000−2i2i00000000
χ432-2-22-2-222222-2-2-2-2-22-222000000000000000000−2i2i−2i2i0000002-22-2000000−2i2i00000000
χ442-2-22-2-222222-2-2-2-2-22-222000000000000000000−2i2i−2i2i000000-22-220000002i−2i00000000
χ452-2-22-2-2222-2-2-222-22-222-200000000002-200-22002-2-22000000000000002-20000000000
χ462-2-22-2-2222-2-2-222-22-222-200000000002-200-2200-222-200000000000000-220000000000
χ472-2-22-2-2222-2-2-222-22-222-20000000000-22002-2002-2-2200000000000000-220000000000
χ482-2-22-2-2222-2-2-222-22-222-20000000000-22002-200-222-2000000000000002-20000000000
χ492-2-22-2-222-22-222-22-222-2-2000000002-200-22000000000000002i−2i−2i2i000000000000002i−2i
χ502-2-22-2-222-22-222-22-222-2-2000000002-200-2200000000000000−2i2i2i−2i00000000000000−2i2i
χ512-2-22-2-222-22-222-22-222-2-200000000-22002-2000000000000002i−2i−2i2i00000000000000−2i2i
χ522-2-22-2-222-22-222-22-222-2-200000000-22002-200000000000000−2i2i2i−2i000000000000002i−2i
χ5344444444-4-44-44-4-4-4-44-44000000000000000000000000000000000000000000000000
χ544444-4-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ5544-4-44i−4i4i−4i0000000000002+2i−2−2i2−2i−2+2i2i2−2i222−2200000000000000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ5644-4-44i−4i4i−4i0000000000002+2i−2−2i2−2i−2+2i−2i22i2−22220000000000000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5744-4-44i−4i4i−4i000000000000−2−2i2+2i−2+2i2−2i2i2−2i222−220000000000000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5844-4-44i−4i4i−4i000000000000−2−2i2+2i−2+2i2−2i−2i22i2−222200000000000000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ5944-4-4−4i4i−4i4i0000000000002−2i−2+2i2+2i−2−2i2i2−2i2−222200000000000000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ6044-4-4−4i4i−4i4i0000000000002−2i−2+2i2+2i−2−2i−2i22i222−220000000000000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ6144-4-4−4i4i−4i4i000000000000−2+2i2−2i−2−2i2+2i2i2−2i2−22220000000000000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ6244-4-4−4i4i−4i4i000000000000−2+2i2−2i−2−2i2+2i−2i22i222−2200000000000000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ634-4-4444-4-44-4-4-4444-44-4-44000000000000000000000000000000000000000000000000
χ644-4-4444-4-4-44-444-4-44-4-444000000000000000000000000000000000000000000000000
χ654-4-4444-4-4-4-444-44-4-4444-4000000000000000000000000000000000000000000000000
χ664-4-44-4-444-4-444-4444-4-4-44000000000000000000000000000000000000000000000000
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.