Finite Group Databasebeta

← Group #430508

Character table — Group #430508

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12224444222222444444444444448888888888888888224488888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11-11-1-1-111-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-11-11-1-1-1-111-1-1-1-1-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1111111-1-111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-111111-1-111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-11-1111-1-1-1-1-1-1-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-1111111-1-1-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1
χ1722222222-2-222-2-2-2-222-2-22222-2-2-2-200000000000000000000000022-2-200000000000000002-2
χ1822222222-2-222-2-2-2-222-2-22222-2-2-2-2000000000000000000000000-2-2220000000000000000-22
χ1922222222-2-222-2-2-2-222-2-2-2-2-2-2222200000000000000000000000022-2-20000000000000000-22
χ2022222222-2-222-2-2-2-222-2-2-2-2-2-22222000000000000000000000000-2-22200000000000000002-2
χ212222-2-2-2-2222222-2-2-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i00000000000000002i−2i2i−2i000000002-200000000
χ222222-2-2-2-2222222-2-2-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i0000000000000000−2i2i−2i2i00000000-2200000000
χ232222-2-2-2-2222222-2-2-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i00000000000000002i−2i2i−2i00000000-2200000000
χ242222-2-2-2-2222222-2-2-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i0000000000000000−2i2i−2i2i000000002-200000000
χ252222-2-2-2-22-2-2-22-22-2222-22i2i−2i−2i2i2i−2i−2i000000000000000000002i2i−2i−2i000020-2000000000000000
χ262222-2-2-2-22-2-2-22-22-2222-22i2i−2i−2i2i2i−2i−2i00000000000000000000−2i−2i2i2i0000-202000000000000000
χ272222-2-2-2-22-2-2-22-22-2222-2−2i−2i2i2i−2i−2i2i2i000000000000000000002i2i−2i−2i0000-202000000000000000
χ282222-2-2-2-22-2-2-22-22-2222-2−2i−2i2i2i−2i−2i2i2i00000000000000000000−2i−2i2i2i000020-2000000000000000
χ292222-2-2-2-2-22-2-2-22-2222-222i2i−2i−2i−2i−2i2i2i000000000000000022-2-20000000000000000002i−2i000000
χ302222-2-2-2-2-22-2-2-22-2222-222i2i−2i−2i−2i−2i2i2i0000000000000000-2-222000000000000000000−2i2i000000
χ312222-2-2-2-2-22-2-2-22-2222-22−2i−2i2i2i2i2i−2i−2i000000000000000022-2-2000000000000000000−2i2i000000
χ322222-2-2-2-2-22-2-2-22-2222-22−2i−2i2i2i2i2i−2i−2i0000000000000000-2-2220000000000000000002i−2i000000
χ332222-2-2-2-2-2-222-2-222-2-22200000000000000002i2i2i2i−2i−2i−2i−2i000000002i−2i−2i2i020-200000000000000
χ342222-2-2-2-2-2-222-2-222-2-22200000000000000002i2i2i2i−2i−2i−2i−2i00000000−2i2i2i−2i0-20200000000000000
χ352222-2-2-2-2-2-222-2-222-2-2220000000000000000−2i−2i−2i−2i2i2i2i2i000000002i−2i−2i2i0-20200000000000000
χ362222-2-2-2-2-2-222-2-222-2-2220000000000000000−2i−2i−2i−2i2i2i2i2i00000000−2i2i2i−2i020-200000000000000
χ372-2-2222-2-2222-2-2-22-22-2-2200000000000000002i2i−2i−2i2i2i−2i−2i2-22-20000000000002i−2i000000000000
χ382-2-2222-2-2222-2-2-22-22-2-2200000000000000002i2i−2i−2i2i2i−2i−2i-22-22000000000000−2i2i000000000000
χ392-2-2222-2-2222-2-2-22-22-2-220000000000000000−2i−2i2i2i−2i−2i2i2i2-22-2000000000000−2i2i000000000000
χ402-2-2222-2-2222-2-2-22-22-2-220000000000000000−2i−2i2i2i−2i−2i2i2i-22-220000000000002i−2i000000000000
χ412-2-2222-2-2-22-222-222-22-2-2000000002i2i−2i−2i2i2i−2i−2i0000000000002i−2i2i−2i00000000002-20000000000
χ422-2-2222-2-2-22-222-222-22-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000−2i2i−2i2i0000000000-220000000000
χ432-2-2222-2-2-22-222-222-22-2-200000000−2i−2i2i2i−2i−2i2i2i0000000000002i−2i2i−2i0000000000-220000000000
χ442-2-2222-2-2-22-222-222-22-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000−2i2i−2i2i00000000002-20000000000
χ452-2-22-2-222-22-222-2-2-22-2220000000022-2-2-2-222000000002-2-22000000000000000000002-20000
χ462-2-22-2-222-22-222-2-2-22-2220000000022-2-2-2-22200000000-222-200000000000000000000-220000
χ472-2-22-2-222-22-222-2-2-22-22200000000-2-22222-2-2000000002-2-2200000000000000000000-220000
χ482-2-22-2-222-22-222-2-2-22-22200000000-2-22222-2-200000000-222-2000000000000000000002-20000
χ492-2-22-2-222-2-22-2222-2-22-22000000000000000022-2-2-2-22200002-2-220000000000000000002-200
χ502-2-22-2-222-2-22-2222-2-22-22000000000000000022-2-2-2-2220000-222-2000000000000000000-2200
χ512-2-22-2-222-2-22-2222-2-22-220000000000000000-2-22222-2-200002-2-22000000000000000000-2200
χ522-2-22-2-222-2-22-2222-2-22-220000000000000000-2-22222-2-20000-222-20000000000000000002-200
χ53444444444-4-4-44-4-44-4-4-44000000000000000000000000000000000000000000000000000000
χ5444444444-44-4-4-444-4-4-44-4000000000000000000000000000000000000000000000000000000
χ5544-4-44i−4i4i−4i00000000000000002+2i−2−2i2−2i−2+2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000
χ5644-4-44i−4i4i−4i00000000000000002+2i−2−2i2−2i−2+2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000
χ5744-4-44i−4i4i−4i0000000000000000−2−2i2+2i−2+2i2−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000
χ5844-4-44i−4i4i−4i0000000000000000−2−2i2+2i−2+2i2−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000
χ5944-4-4−4i4i−4i4i00000000000000002−2i−2+2i2+2i−2−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000000000
χ6044-4-4−4i4i−4i4i00000000000000002−2i−2+2i2+2i−2−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000000000
χ6144-4-4−4i4i−4i4i0000000000000000−2+2i2−2i−2−2i2+2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000000000
χ6244-4-4−4i4i−4i4i0000000000000000−2+2i2−2i−2−2i2+2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000000000
χ634-44-44i−4i−4i4i0000000000002−2i−2+2i2+2i−2−2i00002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ644-44-44i−4i−4i4i0000000000002−2i−2+2i2+2i−2−2i0000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ654-44-44i−4i−4i4i000000000000−2+2i2−2i−2−2i2+2i00002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ664-44-44i−4i−4i4i000000000000−2+2i2−2i−2−2i2+2i0000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ674-44-4−4i4i4i−4i0000000000002+2i−2−2i2−2i−2+2i00002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ684-44-4−4i4i4i−4i0000000000002+2i−2−2i2−2i−2+2i0000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ694-44-4−4i4i4i−4i000000000000−2−2i2+2i−2+2i2−2i00002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ704-44-4−4i4i4i−4i000000000000−2−2i2+2i−2+2i2−2i0000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ714-4-4444-4-44-4-44-44-4-4-4444000000000000000000000000000000000000000000000000000000
χ724-4-4444-4-4-4-44-444-444-44-4000000000000000000000000000000000000000000000000000000
χ734-4-44-4-444444-4-4-4-44-444-4000000000000000000000000000000000000000000000000000000
χ744-4-44-4-4444-4-44-44444-4-4-4000000000000000000000000000000000000000000000000000000

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