Finite Group Databasebeta

← Group #116332

Character table — Group #116332

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444444448888888888888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ91-1-111-1-111111-1-1-1-11-1-1111-1-1111-1-1-11-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1ii−i−i1-1
χ101-1-111-1-111111-1-1-1-11-1-1111-1-1111-1-1-11-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11−i−iii-11
χ111-1-111-1-111111-1-1-1-11-1-1111-1-1111-1-1-11-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1−i−iii1-1
χ121-1-111-1-111111-1-1-1-11-1-1111-1-1111-1-1-11-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11ii−i−i-11
χ131-1-111-1-111111-1-1-1-11-1-1111-1-1111-1-1-11-1-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-11−i−iii-11
χ141-1-111-1-111111-1-1-1-11-1-1111-1-1111-1-1-11-1-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii1-1ii−i−i1-1
χ151-1-111-1-111111-1-1-1-11-1-1111-1-1111-1-1-11-1-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-11ii−i−i-11
χ161-1-111-1-111111-1-1-1-11-1-1111-1-1111-1-1-11-1-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i1-1−i−iii1-1
χ17222222222222222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000000000000000
χ18222222222222222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-222-22-2-2-220000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ202222222222222222-2-2-2-2-2-2-2-222-22-2-2-22000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-22-2222-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-22-2222-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-22-2222-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-22-2222-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-2-22-2-2-222222-2-222-2-20000000000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-2-22-2-2-2222-2-222-2-2220000000000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-22-222-20000000000000000000000000000000000000000002-22-200
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-22-222-2000000000000000000000000000000000000000000-22-2200
χ2922222222-2-2-2-2-2-2-2-2-2-2-2-22222-222-22-2-220000000000000000000000000000000000000000220000-2-2
χ3022222222-2-2-2-2-2-2-2-2-2-2-2-22222-222-22-2-220000000000000000000000000000000000000000-2-2000022
χ31222-2-2-2-2222-2-222-2-222-2-22-2-2200000000000000002i−2i2i−2i000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000
χ32222-2-2-2-2222-2-222-2-222-2-22-2-2200000000000000002i−2i2i−2i000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000
χ33222-2-2-2-2222-2-222-2-222-2-22-2-220000000000000000−2i2i−2i2i000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000
χ34222-2-2-2-2222-2-222-2-222-2-22-2-220000000000000000−2i2i−2i2i000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000
χ35222-2-2-2-2222-2-222-2-2-2-222-222-2000000000000000000002i−2i2i−2i000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i200000000
χ36222-2-2-2-2222-2-222-2-2-2-222-222-2000000000000000000002i−2i2i−2i00000000−222−2−222−2−i2i2i2−i2−i2i2i2−i200000000
χ37222-2-2-2-2222-2-222-2-2-2-222-222-200000000000000000000−2i2i−2i2i000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i200000000
χ38222-2-2-2-2222-2-222-2-2-2-222-222-200000000000000000000−2i2i−2i2i00000000−222−2−222−2i2−i2−i2i2i2−i2−i2i200000000
χ392-2-222-2-222222-2-2-2-22-2-2222-2-2-2-2-2222-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ402-2-222-2-222222-2-2-2-22-2-2222-2-2-2-2-2222-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ412-2-222-2-222222-2-2-2-2-222-2-2-22222-2-222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ422-2-222-2-222222-2-2-2-2-222-2-2-22222-2-222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ432-2-222-2-222222-2-2-2-2-222-2-2-222-2-222-2-2220000000000000000000000000000000022-2-2-2-22200000000
χ442-2-222-2-222222-2-2-2-2-222-2-2-222-2-222-2-22200000000000000000000000000000000-2-22222-2-200000000
χ452-2-222-2-22-2-2-2-222222-2-22-2-2222-22-2-22-22000000000000000022-2-2-2-222000000000000000000000000
χ462-2-222-2-22-2-2-2-222222-2-22-2-2222-22-2-22-220000000000000000-2-22222-2-2000000000000000000000000
χ472-2-222-2-22-2-2-2-222222-2-22-2-222-22-222-22-222-2-2-2-2220000000000000000000000000000000000000000
χ482-2-222-2-22-2-2-2-222222-2-22-2-222-22-222-22-2-2-22222-2-20000000000000000000000000000000000000000
χ492-2-222-2-22-2-2-2-22222-222-222-2-22-2-2-22-2220000000000000000000000000000000000000000002i−2i−2i2i00
χ502-2-222-2-22-2-2-2-22222-222-222-2-22-2-2-22-222000000000000000000000000000000000000000000−2i2i2i−2i00
χ512-2-222-2-22-2-2-2-22222-222-222-2-2-2222-22-2-200000000000000000000000000000000000000002-20000-22
χ522-2-222-2-22-2-2-2-22222-222-222-2-2-2222-22-2-20000000000000000000000000000000000000000-2200002-2
χ532-2-2-2-222222-2-2-2-2222-22-22-22-200000000000000002-2-22000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ542-2-2-2-222222-2-2-2-2222-22-22-22-200000000000000002-2-22000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ552-2-2-2-222222-2-2-2-2222-22-22-22-20000000000000000-222-2000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ562-2-2-2-222222-2-2-2-2222-22-22-22-20000000000000000-222-2000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ572-2-2-2-222222-2-2-2-222-22-22-22-22000000000000000000002-2-22000000002−2−22−222−22−2−22−222−200000000
χ582-2-2-2-222222-2-2-2-222-22-22-22-22000000000000000000002-2-2200000000−222−22−2−22−222−22−2−2200000000
χ592-2-2-2-222222-2-2-2-222-22-22-22-2200000000000000000000-222-2000000002−2−22−222−2−222−22−2−2200000000
χ602-2-2-2-222222-2-2-2-222-22-22-22-2200000000000000000000-222-200000000−222−22−2−222−2−22−222−200000000
χ61444-4-4-4-44-4-444-4-44444-4-4-444-400000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-4-444-4-444-4-4444-4-4400000000000000000000000000000000000000000000000000000000
χ6344-44-44-4-44i−4i4i−4i4i−4i4i−4i00000000000000002-22i−2i2-22i−2i0000000000000000000000000000000000000000
χ6444-44-44-4-44i−4i4i−4i4i−4i4i−4i0000000000000000-22−2i2i-22−2i2i0000000000000000000000000000000000000000
χ6544-44-44-4-4−4i4i−4i4i−4i4i−4i4i00000000000000002-2−2i2i2-2−2i2i0000000000000000000000000000000000000000
χ6644-44-44-4-4−4i4i−4i4i−4i4i−4i4i0000000000000000-222i−2i-222i−2i0000000000000000000000000000000000000000
χ6744-4-44-44-44i−4i−4i4i4i−4i−4i4i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ6844-4-44-44-44i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ6944-4-44-44-4−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ7044-4-44-44-4−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ714-444-4-44-44i−4i4i−4i−4i4i−4i4i00000000000000002-22i−2i-22−2i2i0000000000000000000000000000000000000000
χ724-444-4-44-44i−4i4i−4i−4i4i−4i4i0000000000000000-22−2i2i2-22i−2i0000000000000000000000000000000000000000
χ734-444-4-44-4−4i4i−4i4i4i−4i4i−4i00000000000000002-2−2i2i-222i−2i0000000000000000000000000000000000000000
χ744-444-4-44-4−4i4i−4i4i4i−4i4i−4i0000000000000000-222i−2i2-2−2i2i0000000000000000000000000000000000000000
χ754-44-444-4-44i−4i−4i4i−4i4i4i−4i000000000000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ000000000000000000000000
χ764-44-444-4-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ000000000000000000000000
χ774-44-444-4-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3000000000000000000000000
χ784-44-444-4-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3000000000000000000000000
χ794-4-4-4-4444-4-44444-4-44-44-4-44-4400000000000000000000000000000000000000000000000000000000
χ804-4-4-4-4444-4-44444-4-4-44-444-44-400000000000000000000000000000000000000000000000000000000

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