Finite Group Databasebeta

← Group #305331

Character table — Group #305331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-111111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-111-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111-1-1111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-11
χ172222222222-2-2-222-22222-20000-2000022222200-2-200-2-200000000000000-2000000000000
χ182222222222-2-2-222-22222-20000-20000-2-2-2-2-2-200-2-20022000000000000002000000000000
χ192222222222-2-2-222-2-2-2-2-2-20000-200002222-2-2002200-2-2000000000000002000000000000
χ202222222222-2-2-222-2-2-2-2-2-20000-20000-2-2-2-2220022002200000000000000-2000000000000
χ2122222222-2-2222-2-220000-22222-222220000002200-2-2000000-2-200000000000-2000000000
χ2222222222-2-2222-2-220000-22222-2-2-2-2-2000000-2-200-2-200000022000000000002000000000
χ2322222222-2-2222-2-220000-2-2-2-2-2-22222000000-2-20022000000-2-2000000000002000000000
χ2422222222-2-2222-2-220000-2-2-2-2-2-2-2-2-2-20000002200220000002200000000000-2000000000
χ252-222-2-2-222-20002-2022-2-2000000i2i2−i2−i22i2i−2i−2i2i−2i000000000000i2−i2i2i2−i2−i222−2−200000000002−20
χ262-222-2-2-222-20002-2022-2-2000000i2i2−i2−i2−2i−2i2i2i−2i2i000000000000i2−i2i2i2−i2−i2−2−2220000000000−220
χ272-222-2-2-222-20002-2022-2-2000000−i2−i2i2i22i2i−2i−2i2i−2i000000000000−i2i2−i2−i2i2i2−2−2220000000000−220
χ282-222-2-2-222-20002-2022-2-2000000−i2−i2i2i2−2i−2i2i2i−2i2i000000000000−i2i2−i2−i2i2i222−2−200000000002−20
χ292-222-2-2-222-20002-20-2-222000000i2i2−i2−i22i2i−2i−2i−2i2i000000000000i2−i2−i2−i2i2i222−2−20000000000−220
χ302-222-2-2-222-20002-20-2-222000000i2i2−i2−i2−2i−2i2i2i2i−2i000000000000i2−i2−i2−i2i2i2−2−22200000000002−20
χ312-222-2-2-222-20002-20-2-222000000−i2−i2i2i22i2i−2i−2i−2i2i000000000000−i2i2i2i2−i2−i2−2−22200000000002−20
χ322-222-2-2-222-20002-20-2-222000000−i2−i2i2i2−2i−2i2i2i2i−2i000000000000−i2i2i2i2−i2−i222−2−20000000000−220
χ332-22-2-222-22222-2-2-2-22-22-2222-2-2-20000000000002-22-2000000000000000002-20000000000
χ342-22-2-222-22222-2-2-2-22-22-22-2-222-20000000000002-2-2200000000000000000-220000000000
χ352-22-2-222-22222-2-2-2-2-22-22222-2-2-2000000000000-222-200000000000000000-220000000000
χ362-22-2-222-22222-2-2-2-2-22-222-2-222-2000000000000-22-22000000000000000002-20000000000
χ372-22-2-222-222-2-22-2-222-22-2-200002000000000000-2200002i2i−2i−2i00000000000000002i−2i00000
χ382-22-2-222-222-2-22-2-222-22-2-200002000000000000-220000−2i−2i2i2i0000000000000000−2i2i00000
χ392-22-2-222-222-2-22-2-22-22-22-2000020000000000002-200002i2i−2i−2i0000000000000000−2i2i00000
χ402-22-2-222-222-2-22-2-22-22-22-2000020000000000002-20000−2i−2i2i2i00000000000000002i−2i00000
χ412-22-2-222-2-2-222-222-20000-222-2-2200000000000000-22000000002i−2i2i−2i000000002i−2i0000000
χ422-22-2-222-2-2-222-222-20000-222-2-2200000000000000-2200000000−2i2i−2i2i00000000−2i2i0000000
χ432-22-2-222-2-2-222-222-20000-2-2-2222000000000000002-2000000002i−2i2i−2i00000000−2i2i0000000
χ442-22-2-222-2-2-222-222-20000-2-2-2222000000000000002-200000000−2i2i−2i2i000000002i−2i0000000
χ452-2-2-22-222002-2200-2000002i−2i2i−2i02-22-22−22−2002i−2i00002−2i2−i2i2−i20000002−22−200000000i2−i2000
χ462-2-2-22-222002-2200-2000002i−2i2i−2i02-22-2−22−22002i−2i0000−22−i2i2−i2i2000000−22−2200000000−i2i2000
χ472-2-2-22-222002-2200-2000002i−2i2i−2i0-22-222−22−200−2i2i00002−2i2−i2i2−i2000000−22−2200000000−i2i2000
χ482-2-2-22-222002-2200-2000002i−2i2i−2i0-22-22−22−2200−2i2i0000−22−i2i2−i2i20000002−22−200000000i2−i2000
χ492-2-2-22-222002-2200-200000−2i2i−2i2i02-22-22−22−200−2i2i00002−2−i2i2−i2i20000002−22−200000000−i2i2000
χ502-2-2-22-222002-2200-200000−2i2i−2i2i02-22-2−22−2200−2i2i0000−22i2−i2i2−i2000000−22−2200000000i2−i2000
χ512-2-2-22-222002-2200-200000−2i2i−2i2i0-22-222−22−2002i−2i00002−2−i2i2−i2i2000000−22−2200000000i2−i2000
χ522-2-2-22-222002-2200-200000−2i2i−2i2i0-22-22−22−22002i−2i0000−22i2−i2i2−i20000002−22−200000000−i2i2000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-44-4-4-44-4000-4404-4-44000000000000000000000000000000000000000000000000000
χ55444-44-4-4-44-4000-440-444-4000000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-440004-40000000000000000000000000000000000022−22−222200000000000000000
χ57444-44-4-4-4-440004-400000000000000000000000000000000000−222222−2200000000000000000
χ5844-44-4-44-4004-4-4004000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ5944-44-4-44-4004-4-400400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ6044-44-4-44-400-44400-4000000000000000000000000000022−22−222200000000000000000000000
χ6144-44-4-44-400-44400-40000000000000000000000000000−222222−2200000000000000000000000
χ6244-4-4-44-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ6344-4-4-44-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ6444-4-4-44-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ6544-4-4-44-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ664-444-4-4-44-44000-44000000000002i22i2−2i2−2i2000000000000000000−2i22i2000000000000000000000
χ674-444-4-4-44-44000-4400000000000−2i2−2i22i22i20000000000000000002i2−2i2000000000000000000000
χ684-44-4-444-4-4-4-4-44444000040000-4000000000000000000000000000000000000000000000
χ694-4-4-44-44400-44-40040000000000000022−2222−2200000000−2222000000000000000000000000000
χ704-4-4-44-44400-44-400400000000000000−2222−22220000000022−22000000000000000000000000000
χ718-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000

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