Finite Group Databasebeta

← Group #326137

Character table — Group #326137

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888844444444444488888888888888888824884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1
χ611111111111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1-11
χ711111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-111-1
χ9111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11-11-1
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-11-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1111111-1-111-1-1
χ17222222222-22-22-22-2-2-22222-2-2-2-2000022-2-200000000000000000000000000-22000000
χ18222222222-22-22-22-2-2-22222-2-2-2-20000-2-222000000000000000000000000002-2000000
χ19222222222-22-22-22-2-2-2-2-2-2-22222000022-2-2000000000000000000000000002-2000000
χ20222222222-22-22-22-2-2-2-2-2-2-222220000-2-22200000000000000000000000000-22000000
χ2122222222-22-22-22-22-2-200000000222200002222-2-2-2-2-2-2000000000000000000000000
χ2222222222-22-22-22-22-2-20000000022220000-2-2-2-22222-2-2000000000000000000000000
χ2322222222-22-22-22-22-2-200000000-2-2-2-2000022-2-2-2-22222000000000000000000000000
χ2422222222-22-22-22-22-2-200000000-2-2-2-20000-2-22222-2-222000000000000000000000000
χ2522-2-2-22-2222-2-222-2-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000002i−2i00000000000022-2-200000000
χ2622-2-2-22-2222-2-222-2-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000−2i2i000000000000-2-22200000000
χ2722-2-2-22-2222-2-222-2-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000002i−2i000000000000-2-22200000000
χ2822-2-2-22-2222-2-222-2-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000−2i2i00000000000022-2-200000000
χ2922-2-2-22-222-2-222-2-222-22i2i−2i−2i−2i−2i2i2i0000000000000000002i2i−2i−2i000000000000002-20000
χ3022-2-2-22-222-2-222-2-222-22i2i−2i−2i−2i−2i2i2i000000000000000000−2i−2i2i2i00000000000000-220000
χ3122-2-2-22-222-2-222-2-222-2−2i−2i2i2i2i2i−2i−2i0000000000000000002i2i−2i−2i00000000000000-220000
χ3222-2-2-22-222-2-222-2-222-2−2i−2i2i2i2i2i−2i−2i000000000000000000−2i−2i2i2i000000000000002-20000
χ3322-2-2-22-22-222-2-222-22-2000000002i2i−2i−2i000000000000−2i2i00002i2i−2i−2i22-2-2000000000000
χ3422-2-2-22-22-222-2-222-22-2000000002i2i−2i−2i000000000000−2i2i0000−2i−2i2i2i-2-222000000000000
χ3522-2-2-22-22-222-2-222-22-200000000−2i−2i2i2i0000000000002i−2i00002i2i−2i−2i-2-222000000000000
χ3622-2-2-22-22-222-2-222-22-200000000−2i−2i2i2i0000000000002i−2i0000−2i−2i2i2i22-2-2000000000000
χ372-222-22-2-20-20-20202002−22−22−22−22-22-2000000002i−2i2i−2i000000i2−i2i2−i2i2−i2i2−i22−22−200000000
χ382-222-22-2-20-20-20202002−22−22−22−22-22-200000000−2i2i−2i2i000000−i2i2−i2i2−i2i2−i2i22−22−200000000
χ392-222-22-2-20-20-20202002−22−22−22−2-22-22000000002i−2i−2i2i000000i2−i2i2−i2−i2i2−i2i2−22−2200000000
χ402-222-22-2-20-20-20202002−22−22−22−2-22-2200000000−2i2i2i−2i000000−i2i2−i2i2i2−i2i2−i2−22−2200000000
χ412-222-22-2-20-20-2020200−22−22−22−222-22-2000000002i−2i2i−2i000000−i2i2−i2i2−i2i2−i2i2−22−2200000000
χ422-222-22-2-20-20-2020200−22−22−22−222-22-200000000−2i2i−2i2i000000i2−i2i2−i2i2−i2i2−i2−22−2200000000
χ432-222-22-2-20-20-2020200−22−22−22−22-22-22000000002i−2i−2i2i000000−i2i2−i2i2i2−i2i2−i22−22−200000000
χ442-222-22-2-20-20-2020200−22−22−22−22-22-2200000000−2i2i2i−2i000000i2−i2i2−i2−i2i2−i2i22−22−200000000
χ452-2-2-2222-20-202020-200i2−i2−i2i2i2−i2−i2i22i−2i−2i2i00002i−2i2-200000000002−2−22−i2i2i2−i22−2−2200000000
χ462-2-2-2222-20-202020-200i2−i2−i2i2i2−i2−i2i22i−2i−2i2i0000−2i2i-220000000000−222−2i2−i2−i2i22−2−2200000000
χ472-2-2-2222-20-202020-200i2−i2−i2i2i2−i2−i2i2−2i2i2i−2i00002i−2i-2200000000002−2−22i2−i2−i2i2−222−200000000
χ482-2-2-2222-20-202020-200i2−i2−i2i2i2−i2−i2i2−2i2i2i−2i0000−2i2i2-20000000000−222−2−i2i2i2−i2−222−200000000
χ492-2-2-2222-20-202020-200−i2i2i2−i2−i2i2i2−i22i−2i−2i2i00002i−2i2-20000000000−222−2i2−i2−i2i2−222−200000000
χ502-2-2-2222-20-202020-200−i2i2i2−i2−i2i2i2−i22i−2i−2i2i0000−2i2i-2200000000002−2−22−i2i2i2−i2−222−200000000
χ512-2-2-2222-20-202020-200−i2i2i2−i2−i2i2i2−i2−2i2i2i−2i00002i−2i-220000000000−222−2−i2i2i2−i22−2−2200000000
χ522-2-2-2222-20-202020-200−i2i2i2−i2−i2i2i2−i2−2i2i2i−2i0000−2i2i2-200000000002−2−22i2−i2−i2i22−2−2200000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ54444-44-4-4-440-40-4040000000000000004-4000000000000000000000000000000000000
χ55444-44-4-4-440-40-404000000000000000-44000000000000000000000000000000000000
χ56444-44-4-4-4-404040-40000000000000000000000000000022−2222−2200000000000000000000
χ57444-44-4-4-4-404040-400000000000000000000000000000−2222−222200000000000000000000
χ5844-44-4-44-44040-40-4000000000000000004-40000000000000000000000000000000000
χ5944-44-4-44-44040-40-400000000000000000-440000000000000000000000000000000000
χ6044-44-4-44-4-40-40404000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ6144-44-4-44-4-40-4040400000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ6244-4-4-44-44-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ634-444-44-4-404040-40-40022−2222−22−2222−2222000000000000000000000000000000000000000000
χ644-444-44-4-404040-40-400−2222−222222−2222−22000000000000000000000000000000000000000000
χ654-4-4-4444-4040-40-404002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ664-4-4-4444-4040-40-40400−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ678-88-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).