Finite Group Databasebeta

← Group #426702

Character table — Group #426702

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244448888888888888888888888888888881616161616161616161616161616
order12224444222222444444888822444444444488888888888888888844444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111
χ5111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1
χ911111111111111111111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ1111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-11111-1-111-1-111-1-1-1-1-1-1
χ1211111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-111
χ17222222222-22-2-2-2-2-2-2-22222222-200002-20000000000000000-2-200000000000000002-2
χ18222222222-22-2-2-2-2-2-2-2222222-220000-220000000000000000-2-20000000000000000-22
χ19222222222-22-2-2-2-2-2-2-222-2-2-2-22-200002-20000000000000000220000000000000000-22
χ20222222222-22-2-2-2-2-2-2-222-2-2-2-2-220000-2200000000000000002200000000000000002-2
χ212222-2-2-2-2222222-2-2-2-2-2-200002-20000-2200002i2i−2i−2i00000000002i2i−2i−2i00000000000000
χ222222-2-2-2-2222222-2-2-2-2-2-200002-20000-220000−2i−2i2i2i0000000000−2i−2i2i2i00000000000000
χ232222-2-2-2-2222222-2-2-2-2-2-20000-2200002-200002i2i−2i−2i0000000000−2i−2i2i2i00000000000000
χ242222-2-2-2-2222222-2-2-2-2-2-20000-2200002-20000−2i−2i2i2i00000000002i2i−2i−2i00000000000000
χ252222-2-2-2-22-22-2-2-22222-2-200002222-2-2-2-222-2-200000000000000000000000000000000
χ262222-2-2-2-22-22-2-2-22222-2-2000022-2-222-2-2-2-22200000000000000000000000000000000
χ272222-2-2-2-22-22-2-2-22222-2-20000-2-222-2-222-2-22200000000000000000000000000000000
χ282222-2-2-2-22-22-2-2-22222-2-20000-2-2-2-2222222-2-200000000000000000000000000000000
χ292222-2-2-2-2-22-2-2-2222-2-22222-2-200000000000000002i2i−2i−2i00002-20000000000002i−2i0000
χ302222-2-2-2-2-22-2-2-2222-2-22222-2-20000000000000000−2i−2i2i2i00002-2000000000000−2i2i0000
χ312222-2-2-2-2-22-2-2-2222-2-222-2-22200000000000000002i2i−2i−2i0000-22000000000000−2i2i0000
χ322222-2-2-2-2-22-2-2-2222-2-222-2-2220000000000000000−2i−2i2i2i0000-220000000000002i−2i0000
χ332222-2-2-2-2-2-2-222-2-2-2222222-2-2000000000000000000002i2i−2i−2i-22000000000000002i−2i00
χ342222-2-2-2-2-2-2-222-2-2-2222222-2-200000000000000000000−2i−2i2i2i-2200000000000000−2i2i00
χ352222-2-2-2-2-2-2-222-2-2-22222-2-222000000000000000000002i2i−2i−2i2-200000000000000−2i2i00
χ362222-2-2-2-2-2-2-222-2-2-22222-2-22200000000000000000000−2i−2i2i2i2-2000000000000002i−2i00
χ372-2-2222-2-22-2-22-222-22-2-220000002i−2i2i−2i00000000002i−2i2i−2i00000000002-2000000000000
χ382-2-2222-2-22-2-22-222-22-2-220000002i−2i2i−2i0000000000−2i2i−2i2i0000000000-22000000000000
χ392-2-2222-2-22-2-22-222-22-2-22000000−2i2i−2i2i00000000002i−2i2i−2i0000000000-22000000000000
χ402-2-2222-2-22-2-22-222-22-2-22000000−2i2i−2i2i0000000000−2i2i−2i2i00000000002-2000000000000
χ412-2-2222-2-2-2-22-222-222-22-20000000000000000000000002i−2i2i−2i002i−2i2i−2i0000002-2000000
χ422-2-2222-2-2-2-22-222-222-22-20000000000000000000000002i−2i2i−2i00−2i2i−2i2i000000-22000000
χ432-2-2222-2-2-2-22-222-222-22-2000000000000000000000000−2i2i−2i2i002i−2i2i−2i000000-22000000
χ442-2-2222-2-2-2-22-222-222-22-2000000000000000000000000−2i2i−2i2i00−2i2i−2i2i0000002-2000000
χ452-2-22-2-22222-2-22-22-22-22-20000002i−2i−2i2i000000000000002-2-2200000000002i−2i00000000
χ462-2-22-2-22222-2-22-22-22-22-20000002i−2i−2i2i00000000000000-222-20000000000−2i2i00000000
χ472-2-22-2-22222-2-22-22-22-22-2000000−2i2i2i−2i000000000000002-2-220000000000−2i2i00000000
χ482-2-22-2-22222-2-22-22-22-22-2000000−2i2i2i−2i00000000000000-222-200000000002i−2i00000000
χ492-2-22-2-222-2-22-2222-2-22-22000000000000000000002-2-220000002-2-22002-20000000000
χ502-2-22-2-222-2-22-2222-2-22-22000000000000000000002-2-22000000-222-200-220000000000
χ512-2-22-2-222-2-22-2222-2-22-2200000000000000000000-222-20000002-2-2200-220000000000
χ522-2-22-2-222-2-22-2222-2-22-2200000000000000000000-222-2000000-222-2002-20000000000
χ5344444444-44-4-4-44-4-444-4-4000000000000000000000000000000000000000000000000
χ5444444444-4-4-444-444-4-4-4-4000000000000000000000000000000000000000000000000
χ5544-4-44i−4i4i−4i0000000000002i2−2i222−22000000002-22i−2i2ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ5644-4-44i−4i4i−4i0000000000002i2−2i222−2200000000-22−2i2i−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ5744-4-44i−4i4i−4i000000000000−2i22i2−2222000000002-22i−2i−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ5844-4-44i−4i4i−4i000000000000−2i22i2−222200000000-22−2i2i2ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ5944-4-4−4i4i−4i4i0000000000002i2−2i2−2222000000002-2−2i2i2ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ6044-4-4−4i4i−4i4i0000000000002i2−2i2−222200000000-222i−2i−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ6144-4-4−4i4i−4i4i000000000000−2i22i222−22000000002-2−2i2i−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ6244-4-4−4i4i−4i4i000000000000−2i22i222−2200000000-222i−2i2ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ634-4-4444-4-444-4-44-4-44-44-44000000000000000000000000000000000000000000000000
χ644-4-4444-4-4-4444-4-44-4-444-4000000000000000000000000000000000000000000000000
χ654-4-44-4-4444-4-44-44-44-444-4000000000000000000000000000000000000000000000000
χ664-4-44-4-444-4444-4-4-444-4-44000000000000000000000000000000000000000000000000
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.