Finite Group Databasebeta

← Group #287302

Character table — Group #287302

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444488888888888888884444444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-111-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-111-1-111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1-1-111-1-1111-1
χ121111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-111-1-1-11
χ131111111111111111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-1-1-111-11
χ141111111111111111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-111-1-111-1-1-1-1-1-111-1-111-1-11111-1-11-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-11111-1-1-1-1111-1
χ17222222222-222-2-22-22222-2-2-2-22222222200000000-2000000000000-2-2-2-200000000000000
χ18222222222-222-2-22-22222-2-2-2-2-2-2-2-2-2-2-2-200000000-2000000000000222200000000000000
χ19222222222-222-2-22-2-2-2-2-222-2-22222-2-2-2-2000000002000000000000-2-22200000000000000
χ20222222222-222-2-22-2-2-2-2-222-2-2-2-2-2-2222200000000200000000000022-2-200000000000000
χ2122222222-22-2-222-2222-2-222-2-20000000000000000-22222-2-2-2-20000000000000000000000
χ2222222222-22-2-222-2222-2-222-2-20000000000000000-2-2-2-2-222220000000000000000000000
χ2322222222-22-2-222-22-2-222-2-2-2-20000000000000000222-2-2-2-2220000000000000000000000
χ2422222222-22-2-222-22-2-222-2-2-2-200000000000000002-2-22222-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-222000000002i2i2i2i−2i−2i−2i−2i2000000002i2i−2i−2i000000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i200000000−2i−2i2i2i000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i-200000000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i-2000000002i2i−2i−2i000000000000000000
χ2922-22-2-2-222-22-22-2-220000002-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000002-2002i−2i000000
χ3022-22-2-2-222-22-22-2-220000002-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000000-2200−2i2i000000
χ3122-22-2-2-222-22-22-2-220000002-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000002-200−2i2i000000
χ3222-22-2-2-222-22-22-2-220000002-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000-22002i−2i000000
χ3322-22-2-2-22-22-22-222-20000002-20000000022-2-2-2-222000000000000000002i−2i002i−2i00000000
χ3422-22-2-2-22-22-22-222-20000002-20000000022-2-2-2-22200000000000000000−2i2i00−2i2i00000000
χ3522-22-2-2-22-22-22-222-20000002-200000000-2-22222-2-2000000000000000002i−2i00−2i2i00000000
χ3622-22-2-2-22-22-22-222-20000002-200000000-2-22222-2-200000000000000000−2i2i002i−2i00000000
χ372-2-2222-2-20200-2-2022-2002-200i2i2−i2−i2i2i2−i2−i22−22−22−22−2000002i−2i2i−2i2−22−2i2−i2i2−i200000000000000
χ382-2-2222-2-20200-2-2022-2002-200i2i2−i2−i2i2i2−i2−i2−22−22−22−2200000−2i2i−2i2i−22−22i2−i2i2−i200000000000000
χ392-2-2222-2-20200-2-2022-2002-200−i2−i2i2i2−i2−i2i2i22−22−22−22−200000−2i2i−2i2i2−22−2−i2i2−i2i200000000000000
χ402-2-2222-2-20200-2-2022-2002-200−i2−i2i2i2−i2−i2i2i2−22−22−22−22000002i−2i2i−2i−22−22−i2i2−i2i200000000000000
χ412-2-2222-2-20200-2-202-2200-2200i2i2−i2−i2−i2−i2i2i22−22−22−22−2000002i−2i−2i2i−22−22i2−i2−i2i200000000000000
χ422-2-2222-2-20200-2-202-2200-2200i2i2−i2−i2−i2−i2i2i2−22−22−22−2200000−2i2i2i−2i2−22−2i2−i2−i2i200000000000000
χ432-2-2222-2-20200-2-202-2200-2200−i2−i2i2i2i2i2−i2−i22−22−22−22−200000−2i2i2i−2i−22−22−i2i2i2−i200000000000000
χ442-2-2222-2-20200-2-202-2200-2200−i2−i2i2i2i2i2−i2−i2−22−22−22−22000002i−2i−2i2i2−22−2−i2i2i2−i200000000000000
χ452-2-2222-2-20-200220-22-200-2200i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i202-22-20000i2−i2−i2i2−i2i2−i2i200000000000000
χ462-2-2222-2-20-200220-22-200-2200i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i20-22-220000−i2i2i2−i2−i2i2−i2i200000000000000
χ472-2-2222-2-20-200220-22-200-2200−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i20-22-220000i2−i2−i2i2i2−i2i2−i200000000000000
χ482-2-2222-2-20-200220-22-200-2200−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i202-22-20000−i2i2i2−i2i2−i2i2−i200000000000000
χ492-2-2222-2-20-200220-2-22002-200i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i202-2-220000−i2i2i2−i2−i2i2i2−i200000000000000
χ502-2-2222-2-20-200220-2-22002-200i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i20-222-20000i2−i2−i2i2−i2i2i2−i200000000000000
χ512-2-2222-2-20-200220-2-22002-200−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i20-222-20000−i2i2i2−i2i2−i2−i2i200000000000000
χ522-2-2222-2-20-200220-2-22002-200−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i202-2-220000i2−i2−i2i2i2−i2−i2i200000000000000
χ53444-44-4-4-440-4-4004000000000000000000000000000000000000000000000000000022−2200
χ54444-44-4-4-440-4-40040000000000000000000000000000000000000000000000000000−222200
χ55444-44-4-4-4-404400-40000000000000000000000000000000000000000000000000022−220000
χ56444-44-4-4-4-404400-400000000000000000000000000000000000000000000000000−22220000
χ5744-44-4-4-44444-4-44-4-4000000-4400000000000000000000000000000000000000000000000
χ5844-44-4-4-44-4-4-444-444000000-4400000000000000000000000000000000000000000000000
χ5944-4-4-444-440-4400-40000000004-44-40000000000000000000000000000000000000000000
χ6044-4-4-444-440-4400-4000000000-44-440000000000000000000000000000000000000000000
χ6144-4-4-444-4-404-400400000000000004i−4i4i−4i000000000000000000000000000000000000000
χ6244-4-4-444-4-404-40040000000000000−4i4i−4i4i000000000000000000000000000000000000000
χ634-444-4-44-404004-40-4000000000000000022−22−2222−222222−220000000000000000000000000000000
χ644-444-4-44-404004-40-40000000000000000−222222−2222−22−22220000000000000000000000000000000
χ654-444-4-44-40-400-440400000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000
χ664-444-4-44-40-400-44040000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000
χ674-44-4-44-4400000000004i−4i00002i2−2i2−2i22i222−22−2222000000000000000000000000000000000000000
χ684-44-4-44-4400000000004i−4i0000−2i22i22i2−2i2−222222−22000000000000000000000000000000000000000
χ694-44-4-44-440000000000−4i4i00002i2−2i2−2i22i2−222222−22000000000000000000000000000000000000000
χ704-44-4-44-440000000000−4i4i0000−2i22i22i2−2i222−22−2222000000000000000000000000000000000000000
χ718-8-8-88-888000000000000000000000000000000000000000000000000000000000000000

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