Finite Group Databasebeta

← Group #291021

Character table — Group #291021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444224444444444444444488888888888888888888888844444424
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ311111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-11-1-1-1-1
χ411111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ5111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111
χ6111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-1-1-1-1-1
χ7111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ8111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ91111111111111-1-1-1-1111-1-1-1-111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11111-1
χ101111111111111-1-1-1-1111-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1111-11
χ111111111111111-1-1-1-1111-1-1-1-111-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-11
χ121111111111111-1-1-1-1111-1-1-1-111-111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ131111111111111-1-1-1-1111-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-1
χ141111111111111-1-1-1-1111-1-1-1-111-1-1-11111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-11
χ151111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-111-11
χ161111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1111-1
χ1722222222222-2-22222-2-2222-2-2-2-2-22200220000000000000000000000000000000-20-20000
χ1822222222222-2-22222-2-2222-2-2-2-2-2-2-200-2-200000000000000000000000000000002020000
χ1922222222222-2-2-2-2-2-2-2-22-2-222-2-222200-2-2000000000000000000000000000000020-20000
χ2022222222222-2-2-2-2-2-2-2-22-2-222-2-22-2-200220000000000000000000000000000000-2020000
χ2122222222-2-2-222222222-2-2-222-2-2-2002200220000000000000000000000000000-20-200000
χ2222222222-2-2-222222222-2-2-222-2-2-200-2-200-2-2000000000000000000000000000020200000
χ2322222222-2-2-222-2-2-2-222-222-2-2-2-22002200-2-20000000000000000000000000000-20200000
χ2422222222-2-2-222-2-2-2-222-222-2-2-2-2200-2-20022000000000000000000000000000020-200000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-22220000000022-2-200000000000000000000000000002-200
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-222200000000-2-2220000000000000000000000000000-2200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000022-2-20000000000000000000000000000-2200
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000-2-22200000000000000000000000000002-200
χ292-222-22-2-20002-22i2i−2i−2i2-20002i−2i000002-2002i−2i00000000000022−2−2i2i2−i2−i222−2−2i2i2−i2−i200000000
χ302-222-22-2-20002-22i2i−2i−2i2-20002i−2i000002-2002i−2i000000000000−2−222−i2−i2i2i2−2−222−i2−i2i2i200000000
χ312-222-22-2-20002-22i2i−2i−2i2-20002i−2i00000-2200−2i2i00000000000022−2−2i2i2−i2−i2−2−222−i2−i2i2i200000000
χ322-222-22-2-20002-22i2i−2i−2i2-20002i−2i00000-2200−2i2i000000000000−2−222−i2−i2i2i222−2−2i2i2−i2−i200000000
χ332-222-22-2-20002-2−2i−2i2i2i2-2000−2i2i000002-200−2i2i00000000000022−2−2−i2−i2i2i222−2−2−i2−i2i2i200000000
χ342-222-22-2-20002-2−2i−2i2i2i2-2000−2i2i000002-200−2i2i000000000000−2−222i2i2−i2−i2−2−222i2i2−i2−i200000000
χ352-222-22-2-20002-2−2i−2i2i2i2-2000−2i2i00000-22002i−2i00000000000022−2−2−i2−i2i2i2−2−222i2i2−i2−i200000000
χ362-222-22-2-20002-2−2i−2i2i2i2-2000−2i2i00000-22002i−2i000000000000−2−222i2i2−i2−i222−2−2−i2−i2i2i200000000
χ372-22-22-22-222-2-2-2000022-200002-20000000002i−2i2i−2i000022-2-22i−2i2i−2i00000000000000000000
χ382-22-22-22-222-2-2-2000022-200002-20000000002i−2i2i−2i0000-2-222−2i2i−2i2i00000000000000000000
χ392-22-22-22-222-2-2-2000022-200002-2000000000−2i2i−2i2i000022-2-2−2i2i−2i2i00000000000000000000
χ402-22-22-22-222-2-2-2000022-200002-2000000000−2i2i−2i2i0000-2-2222i−2i2i−2i00000000000000000000
χ412-22-22-22-2-2-22220000-2-2200002-20000000002i−2i−2i2i2i2i−2i−2i000000002-22-20000000000000000
χ422-22-22-22-2-2-22220000-2-2200002-20000000002i−2i−2i2i−2i−2i2i2i00000000-22-220000000000000000
χ432-22-22-22-2-2-22220000-2-2200002-2000000000−2i2i2i−2i2i2i−2i−2i00000000-22-220000000000000000
χ442-22-22-22-2-2-22220000-2-2200002-2000000000−2i2i2i−2i−2i−2i2i2i000000002-22-20000000000000000
χ452-2-2-222-222-22002-22-200-22-2000002i−2i002i−2i000000i2−i2i2−i2i2−i2i2−i2000000002−22−22−22−200000000
χ462-2-2-222-222-22002-22-200-22-2000002i−2i002i−2i000000−i2i2−i2i2−i2i2−i2i200000000−22−22−22−2200000000
χ472-2-2-222-222-22002-22-200-22-200000−2i2i00−2i2i000000i2−i2i2−i2i2−i2i2−i200000000−22−22−22−2200000000
χ482-2-2-222-222-22002-22-200-22-200000−2i2i00−2i2i000000−i2i2−i2i2−i2i2−i2i2000000002−22−22−22−200000000
χ492-2-2-222-222-2200-22-2200-2-22000002i−2i00−2i2i000000i2−i2i2−i2−i2i2−i2i2000000002−22−2−22−2200000000
χ502-2-2-222-222-2200-22-2200-2-22000002i−2i00−2i2i000000−i2i2−i2i2i2−i2i2−i200000000−22−222−22−200000000
χ512-2-2-222-222-2200-22-2200-2-2200000−2i2i002i−2i000000i2−i2i2−i2−i2i2−i2i200000000−22−222−22−200000000
χ522-2-2-222-222-2200-22-2200-2-2200000−2i2i002i−2i000000−i2i2−i2i2i2−i2i2−i2000000002−22−2−22−2200000000
χ53444-4-4-4-440004-40000-44000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ54444-4-4-4-440004-40000-4400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ55444-4-4-4-44000-4400004-400000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ56444-4-4-4-44000-4400004-40000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ5744-444-4-4-44-4-4000000004000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ5844-444-4-4-44-4-400000000400000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ5944-444-4-4-4-44400000000-4000000000000000000022−22−22220000000000000000000000000000
χ6044-444-4-4-4-44400000000-40000000000000000000−222222−220000000000000000000000000000
χ6144-4-4-444-4000004i−4i−4i4i000000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ6244-4-4-444-4000004i−4i−4i4i00000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ6344-4-4-444-400000−4i4i4i−4i000000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ6444-4-4-444-400000−4i4i4i−4i00000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ654-444-44-4-4000-444i4i−4i−4i-44000−4i4i00000000000000000000000000000000000000000000000
χ664-444-44-4-4000-44−4i−4i4i4i-440004i−4i00000000000000000000000000000000000000000000000
χ674-44-44-44-444-4440000-4-4-40000-44000000000000000000000000000000000000000000000
χ684-44-44-44-4-4-44-4-400004440000-44000000000000000000000000000000000000000000000
χ694-4-4-444-44-44-4004-44-4004-440000000000000000000000000000000000000000000000000
χ704-4-4-444-44-44-400-44-440044-40000000000000000000000000000000000000000000000000
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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