Finite Group Databasebeta

← Group #281621

Character table — Group #281621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444224444888888888888888844444444488888888888888882244888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-1111111-1-111-1-11111-1-1-1-111111111-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111-1
χ101111111111-1-1-1-1111111-1-111-1-11111-1-1-1-111111111-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-11
χ111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-111-1-111-11
χ121111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-111-1-11-1
χ131111111111-1-1-1-1111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-11
χ141111111111-1-1-1-1111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111-1
χ151111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-11-1
χ161111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111-11
χ1722222222222222-2-22-2-2222-2-2-2-20000000000000000-222-2-222-2-200000000000000000000000000
χ1822222222222222-2-22-2-2222-2-2-2-20000000000000000-2-2-222-2-22200000000000000000000000000
χ192222222222-2-2-2-2-2-22-2-22-2-2-2-2220000000000000000222-2-2-2-22200000000000000000000000000
χ202222222222-2-2-2-2-2-22-2-22-2-2-2-22200000000000000002-2-22222-2-200000000000000000000000000
χ2122222222-2-2222222-222-2-2-2-2-2222222222200000000-200000000-2-2-2-20000000000000000000000
χ2222222222-2-2222222-222-2-2-2-2-222-2-2-2-2-2-2-2-200000000-20000000022220000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i20000000000002i2i−2i−2i000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i2000000000000−2i−2i2i2i000000000000000000
χ2522222222-2-2-2-2-2-222-222-222-2-2-2-22222-2-2-2-200000000200000000-2-2220000000000000000000000
χ2622222222-2-2-2-2-2-222-222-222-2-2-2-2-2-2-2-222220000000020000000022-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i-2000000000000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i-20000000000002i2i−2i−2i000000000000000000
χ292-2222-2-2-2002i2i−2i−2i2-202-2000002i−2i22-2-22i2i−2i−2i000000000000000000000000022−2−2i2i2−i2−i20000i2−i22−200
χ302-2222-2-2-2002i2i−2i−2i2-202-2000002i−2i22-2-22i2i−2i−2i0000000000000000000000000−2−222−i2−i2i2i20000−i2i2−2200
χ312-2222-2-2-2002i2i−2i−2i2-202-2000002i−2i-2-222−2i−2i2i2i000000000000000000000000022−2−2i2i2−i2−i20000−i2i2−2200
χ322-2222-2-2-2002i2i−2i−2i2-202-2000002i−2i-2-222−2i−2i2i2i0000000000000000000000000−2−222−i2−i2i2i20000i2−i22−200
χ332-2222-2-2-200−2i−2i2i2i2-202-200000−2i2i22-2-2−2i−2i2i2i000000000000000000000000022−2−2−i2−i2i2i20000−i2i22−200
χ342-2222-2-2-200−2i−2i2i2i2-202-200000−2i2i22-2-2−2i−2i2i2i0000000000000000000000000−2−222i2i2−i2−i20000i2−i2−2200
χ352-2222-2-2-200−2i−2i2i2i2-202-200000−2i2i-2-2222i2i−2i−2i000000000000000000000000022−2−2−i2−i2i2i20000i2−i2−2200
χ362-2222-2-2-200−2i−2i2i2i2-202-200000−2i2i-2-2222i2i−2i−2i0000000000000000000000000−2−222i2i2−i2−i20000−i2i22−200
χ372-22-2-22-22222-22-200-200-22-200002−22−22−22−2i2i2−i2−i2i2i2−i2−i202i−2i002i−2i002−22−2i2−i2i2−i2000000000000000000
χ382-22-2-22-22222-22-200-200-22-200002−22−22−22−2−i2−i2i2i2−i2−i2i2i20−2i2i00−2i2i002−22−2−i2i2−i2i2000000000000000000
χ392-22-2-22-22222-22-200-200-22-20000−22−22−22−22i2i2−i2−i2i2i2−i2−i20−2i2i00−2i2i00−22−22i2−i2i2−i2000000000000000000
χ402-22-2-22-22222-22-200-200-22-20000−22−22−22−22−i2−i2i2i2−i2−i2i2i202i−2i002i−2i00−22−22−i2i2−i2i2000000000000000000
χ412-22-2-22-2222-22-2200-200-2-2200002−22−2−22−22i2i2−i2−i2i2i2−i2−i202i−2i00−2i2i002−2−22−i2i2−i2i2000000000000000000
χ422-22-2-22-2222-22-2200-200-2-2200002−22−2−22−22−i2−i2i2i2−i2−i2i2i20−2i2i002i−2i002−2−22i2−i2i2−i2000000000000000000
χ432-22-2-22-2222-22-2200-200-2-220000−22−222−22−2i2i2−i2−i2i2i2−i2−i20−2i2i002i−2i00−222−2−i2i2−i2i2000000000000000000
χ442-22-2-22-2222-22-2200-200-2-220000−22−222−22−2−i2−i2i2i2−i2−i2i2i202i−2i00−2i2i00−222−2i2−i2i2−i2000000000000000000
χ452-22-2-22-22-2-22-22-2002002-2200002−22−22−22−222−2−2−2−2220002-2002-2−22−222−2−22000000000000000000
χ462-22-2-22-22-2-22-22-2002002-2200002−22−22−22−2−2−22222−2−2000-2200-22−22−22−222−2000000000000000000
χ472-22-2-22-22-2-22-22-2002002-220000−22−22−22−2222−2−2−2−222000-2200-222−22−22−2−22000000000000000000
χ482-22-2-22-22-2-22-22-2002002-220000−22−22−22−22−2−22222−2−20002-2002-22−22−2−222−2000000000000000000
χ492-22-2-22-22-2-2-22-220020022-200002−22−2−22−2222−2−2−2−2220002-200-22−222−2−222−2000000000000000000
χ502-22-2-22-22-2-2-22-220020022-200002−22−2−22−22−2−22222−2−2000-22002-2−222−22−2−22000000000000000000
χ512-22-2-22-22-2-2-22-220020022-20000−22−222−22−222−2−2−2−222000-22002-22−2−22−222−2000000000000000000
χ522-22-2-22-22-2-2-22-220020022-20000−22−222−22−2−2−22222−2−20002-200-222−2−222−2−22000000000000000000
χ532-2-22-2-2222-20000222-2-2-2002-200000000002i−2i2i−2i2i−2i2i−2i000000000000000002i−2i2i−2i00002-200000000
χ542-2-22-2-2222-20000222-2-2-2002-200000000002i−2i2i−2i2i−2i2i−2i00000000000000000−2i2i−2i2i0000-2200000000
χ552-2-22-2-2222-20000222-2-2-2002-20000000000−2i2i−2i2i−2i2i−2i2i000000000000000002i−2i2i−2i0000-2200000000
χ562-2-22-2-2222-20000222-2-2-2002-20000000000−2i2i−2i2i−2i2i−2i2i00000000000000000−2i2i−2i2i00002-200000000
χ572-2-22-2-222-220000-2-2-2222002-200000000002-22-2-22-220000000000000000000002-22-2002-2000000
χ582-2-22-2-222-220000-2-2-2222002-200000000002-22-2-22-22000000000000000000000-22-2200-22000000
χ592-2-22-2-222-220000-2-2-2222002-20000000000-22-222-22-20000000000000000000002-22-200-22000000
χ602-2-22-2-222-220000-2-2-2222002-20000000000-22-222-22-2000000000000000000000-22-22002-2000000
χ61444-4-4-44-4004i−4i−4i4i00000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000000
χ62444-4-4-44-4004i−4i−4i4i000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000000
χ63444-4-4-44-400−4i4i4i−4i00000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000000000
χ64444-4-4-44-400−4i4i4i−4i000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000000000
χ6544-44-44-4-40000004-40-4400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ6644-44-44-4-40000004-40-440000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ6744-44-44-4-4000000-4404-4000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ6844-44-44-4-4000000-4404-400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ6944-4-44-4-444-4000000-40040000000000000022−22−222222−22−222200000000000000000000000000000000000
χ7044-4-44-4-444-4000000-400400000000000000−222222−22−222222−2200000000000000000000000000000000000
χ7144-4-44-4-44-44000000400-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ7244-4-44-4-44-44000000400-400000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ734-4444-4-4-4004i4i−4i−4i-440-4400000−4i4i000000000000000000000000000000000000000000000000000
χ744-4444-4-4-400−4i−4i4i4i-440-44000004i−4i000000000000000000000000000000000000000000000000000
χ754-4-44-4-4444-40000-4-4444-400-4400000000000000000000000000000000000000000000000000000
χ764-4-44-4-444-44000044-4-4-4400-4400000000000000000000000000000000000000000000000000000
χ778-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000

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