Finite Group Databasebeta

← Group #411313

Character table — Group #411313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222222444444444444444444888888888888888822444444888888882444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111-1-111-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-111-1-111-1-1
χ911111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1011111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11-1-11111-1-111-1-1
χ1211111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-111-1-1-1-111-1-111
χ1311111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1411111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1511111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111-1-1111-1-111-1-1-1-111
χ1611111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-111-1-1-111-1-11111-1-1
χ17222222222-2-2-2-222-2-222222222-2-22-2-2-2-200000000000000002-22-222-2-2000000000000000000000000
χ18222222222-2-2-2-222-2-222222222-2-22-2-2-2-20000000000000000-22-22-2-222000000000000000000000000
χ19222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-22222200000000000000002-22-2-2-222000000000000000000000000
χ20222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222220000000000000000-22-2222-2-2000000000000000000000000
χ212222-2-2-2-2222222-2-2-200000000-2-2-200002i2i2i2i−2i−2i−2i−2i000000002-2-22000000002i2i−2i−2i0000000000000000
χ222222-2-2-2-2222222-2-2-200000000-2-2-200002i2i2i2i−2i−2i−2i−2i00000000-222-200000000−2i−2i2i2i0000000000000000
χ232222-2-2-2-2222222-2-2-200000000-2-2-20000−2i−2i−2i−2i2i2i2i2i000000002-2-2200000000−2i−2i2i2i0000000000000000
χ242222-2-2-2-2222222-2-2-200000000-2-2-20000−2i−2i−2i−2i2i2i2i2i00000000-222-2000000002i2i−2i−2i0000000000000000
χ252222-2-2-2-22-2-2-2-22-2220000000022-20000000000002i2i2i2i−2i−2i−2i−2i22-2-200002i2i−2i−2i00000000000000000000
χ262222-2-2-2-22-2-2-2-22-2220000000022-20000000000002i2i2i2i−2i−2i−2i−2i-2-2220000−2i−2i2i2i00000000000000000000
χ272222-2-2-2-22-2-2-2-22-2220000000022-2000000000000−2i−2i−2i−2i2i2i2i2i22-2-20000−2i−2i2i2i00000000000000000000
χ282222-2-2-2-22-2-2-2-22-2220000000022-2000000000000−2i−2i−2i−2i2i2i2i2i-2-22200002i2i−2i−2i00000000000000000000
χ292222-2-2-2-2-22-22-2-222-22i2i2i2i−2i−2i−2i−2i2-222i2i−2i−2i0000000000000000000000000000000002-2000002i−2i000000
χ302222-2-2-2-2-22-22-2-222-22i2i2i2i−2i−2i−2i−2i2-222i2i−2i−2i000000000000000000000000000000000-2200000−2i2i000000
χ312222-2-2-2-2-22-22-2-222-2−2i−2i−2i−2i2i2i2i2i2-22−2i−2i2i2i0000000000000000000000000000000002-200000−2i2i000000
χ322222-2-2-2-2-22-22-2-222-2−2i−2i−2i−2i2i2i2i2i2-22−2i−2i2i2i000000000000000000000000000000000-22000002i−2i000000
χ332222-2-2-2-2-2-22-22-22-222i2i2i2i−2i−2i−2i−2i-222−2i−2i2i2i00000000000000000000000000000000200-20000002i−2i0000
χ342222-2-2-2-2-2-22-22-22-222i2i2i2i−2i−2i−2i−2i-222−2i−2i2i2i00000000000000000000000000000000-2002000000−2i2i0000
χ352222-2-2-2-2-2-22-22-22-22−2i−2i−2i−2i2i2i2i2i-2222i2i−2i−2i00000000000000000000000000000000200-2000000−2i2i0000
χ362222-2-2-2-2-2-22-22-22-22−2i−2i−2i−2i2i2i2i2i-2222i2i−2i−2i00000000000000000000000000000000-20020000002i−2i0000
χ372-2-2222-2-2222-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i2222i−2i2i−2i000000000000000000000000000000000000002i−2i0000002-2
χ382-2-2222-2-2222-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i2222i−2i2i−2i00000000000000000000000000000000000000−2i2i000000-22
χ392-2-2222-2-2222-2-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i222−2i2i−2i2i000000000000000000000000000000000000002i−2i000000-22
χ402-2-2222-2-2222-2-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i222−2i2i−2i2i00000000000000000000000000000000000000−2i2i0000002-2
χ412-2-2222-2-22-2-222-2-2222i2i−2i−2i2i2i−2i−2i-2-22−2i2i−2i2i0000000000000000000000000000000000002-20000002i−2i00
χ422-2-2222-2-22-2-222-2-2222i2i−2i−2i2i2i−2i−2i-2-22−2i2i−2i2i000000000000000000000000000000000000-22000000−2i2i00
χ432-2-2222-2-22-2-222-2-222−2i−2i2i2i−2i−2i2i2i-2-222i−2i2i−2i0000000000000000000000000000000000002-2000000−2i2i00
χ442-2-2222-2-22-2-222-2-222−2i−2i2i2i−2i−2i2i2i-2-222i−2i2i−2i000000000000000000000000000000000000-220000002i−2i00
χ452-2-2222-2-2-22-2-22222-200000000-22-200002i2i−2i−2i2i2i−2i−2i0000000000002-22-22i−2i2i−2i00000000000000000000
χ462-2-2222-2-2-22-2-22222-200000000-22-200002i2i−2i−2i2i2i−2i−2i000000000000-22-22−2i2i−2i2i00000000000000000000
χ472-2-2222-2-2-22-2-22222-200000000-22-20000−2i−2i2i2i−2i−2i2i2i0000000000002-22-2−2i2i−2i2i00000000000000000000
χ482-2-2222-2-2-22-2-22222-200000000-22-20000−2i−2i2i2i−2i−2i2i2i000000000000-22-222i−2i2i−2i00000000000000000000
χ492-2-2222-2-2-2-222-222-22000000002-2-20000000000002i2i−2i−2i2i2i−2i−2i00002-2-2200002i−2i2i−2i0000000000000000
χ502-2-2222-2-2-2-222-222-22000000002-2-20000000000002i2i−2i−2i2i2i−2i−2i0000-222-20000−2i2i−2i2i0000000000000000
χ512-2-2222-2-2-2-222-222-22000000002-2-2000000000000−2i−2i2i2i−2i−2i2i2i00002-2-220000−2i2i−2i2i0000000000000000
χ522-2-2222-2-2-2-222-222-22000000002-2-2000000000000−2i−2i2i2i−2i−2i2i2i0000-222-200002i−2i2i−2i0000000000000000
χ532-2-22-2-222-22-2-222-2-2222-2-2-2-2222-222-2-2222-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ542-2-22-2-222-22-2-222-2-2222-2-2-2-2222-222-2-22-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ552-2-22-2-222-22-2-222-2-22-2-22222-2-22-22-222-222-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ562-2-22-2-222-22-2-222-2-22-2-22222-2-22-22-222-2-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ572-2-22-2-222-2-222-22-22-222-2-2-2-222-222-222-20000000000000000000000002-2-222-2-220000000000000000
χ582-2-22-2-222-2-222-22-22-222-2-2-2-222-222-222-2000000000000000000000000-222-2-222-20000000000000000
χ592-2-22-2-222-2-222-22-22-2-2-22222-2-2-2222-2-220000000000000000000000002-2-22-222-20000000000000000
χ602-2-22-2-222-2-222-22-22-2-2-22222-2-2-2222-2-22000000000000000000000000-222-22-2-220000000000000000
χ6144444444-44-44-4-4-4-4400000000-44-40000000000000000000000000000000000000000000000000000
χ6244444444-4-44-44-4-44-4000000004-4-40000000000000000000000000000000000000000000000000000
χ6344-4-44i−4i4i−4i0000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ6444-4-44i−4i4i−4i0000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i0000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ6544-4-44i−4i4i−4i000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ6644-4-44i−4i4i−4i000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i0000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ6744-4-4−4i4i−4i4i0000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ6844-4-4−4i4i−4i4i0000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i0000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ6944-4-4−4i4i−4i4i000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ7044-4-4−4i4i−4i4i000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i0000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ714-44-44i−4i−4i4i0000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ724-44-44i−4i−4i4i0000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ734-44-44i−4i−4i4i000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i00000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ744-44-44i−4i−4i4i000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ754-44-4−4i4i4i−4i0000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ764-44-4−4i4i4i−4i0000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ774-44-4−4i4i4i−4i000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ784-44-4−4i4i4i−4i000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ794-4-44-4-444444-4-4-444400000000-4-4-40000000000000000000000000000000000000000000000000000
χ804-4-44-4-4444-4-444-44-4-40000000044-40000000000000000000000000000000000000000000000000000

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