Finite Group Databasebeta

← Group #309521

Character table — Group #309521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-111111111-1-1-1-11111-11-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1111-1-111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-111111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11
χ17222222222-222-2-22-20000-22222-222220000002200-2-2-2-200000000000000-2000000000000
χ18222222222-222-2-22-20000-22222-2-2-2-2-2000000-2-200-2-222000000000000002000000000000
χ19222222222-222-2-22-20000-2-2-2-2-2-22222000000-2-20022-2-2000000000000002000000000000
χ20222222222-222-2-22-20000-2-2-2-2-2-2-2-2-2-20000002200222200000000000000-2000000000000
χ2122222222-22-2-222-222222-20000-200002222-2-200220000-2-20000000000000-200000000000
χ2222222222-22-2-222-222222-20000-20000-2-2-2-2-2-200-2-20000220000000000000200000000000
χ2322222222-22-2-222-22-2-2-2-2-20000-2000022222200-2-20000-2-20000000000000200000000000
χ2422222222-22-2-222-22-2-2-2-2-20000-20000-2-2-2-22200220000220000000000000-200000000000
χ252-22-2-222-222-2-2-2-2222i2i−2i−2i22i2i−2i−2i-2000000002i−2i00002i−2i000000000000000000002-20000000
χ262-22-2-222-222-2-2-2-2222i2i−2i−2i2−2i−2i2i2i-2000000002i−2i0000−2i2i00000000000000000000-220000000
χ272-22-2-222-222-2-2-2-222−2i−2i2i2i22i2i−2i−2i-200000000−2i2i00002i−2i00000000000000000000-220000000
χ282-22-2-222-222-2-2-2-222−2i−2i2i2i2−2i−2i2i2i-200000000−2i2i0000−2i2i000000000000000000002-20000000
χ292-22-2-222-22-2-2-2222-20000-22i2i−2i−2i200000000000000−2i2i000022-2-200000000002i−2i000000000
χ302-22-2-222-22-2-2-2222-20000-22i2i−2i−2i200000000000000−2i2i0000-2-2220000000000−2i2i000000000
χ312-22-2-222-22-2-2-2222-20000-2−2i−2i2i2i2000000000000002i−2i000022-2-20000000000−2i2i000000000
χ322-22-2-222-22-2-2-2222-20000-2−2i−2i2i2i2000000000000002i−2i0000-2-22200000000002i−2i000000000
χ332-22-2-222-2-2222-2-2-222i2i−2i−2i-20000200000000−2i2i0000000000000022-2-200000000002i−2i00000
χ342-22-2-222-2-2222-2-2-222i2i−2i−2i-20000200000000−2i2i00000000000000-2-2220000000000−2i2i00000
χ352-22-2-222-2-2222-2-2-22−2i−2i2i2i-200002000000002i−2i0000000000000022-2-20000000000−2i2i00000
χ362-22-2-222-2-2222-2-2-22−2i−2i2i2i-200002000000002i−2i00000000000000-2-22200000000002i−2i00000
χ372-2-22-22-2202002-20-22i−2i2i−2i00000022−2−22i2i−2i−2i00002-2002−200i2−i2i2−i20000i2i2−i2−i2000000002−2000
χ382-2-22-22-2202002-20-22i−2i2i−2i00000022−2−2−2i−2i2i2i0000-22002−200i2−i2i2−i20000−i2−i2i2i200000000−22000
χ392-2-22-22-2202002-20-22i−2i2i−2i000000−2−2222i2i−2i−2i00002-200−2200−i2i2−i2i20000−i2−i2i2i200000000−22000
χ402-2-22-22-2202002-20-22i−2i2i−2i000000−2−222−2i−2i2i2i0000-2200−2200−i2i2−i2i20000i2i2−i2−i2000000002−2000
χ412-2-22-22-2202002-20-2−2i2i−2i2i00000022−2−22i2i−2i−2i0000-22002−200−i2i2−i2i20000i2i2−i2−i200000000−22000
χ422-2-22-22-2202002-20-2−2i2i−2i2i00000022−2−2−2i−2i2i2i00002-2002−200−i2i2−i2i20000−i2−i2i2i2000000002−2000
χ432-2-22-22-2202002-20-2−2i2i−2i2i000000−2−2222i2i−2i−2i0000-2200−2200i2−i2i2−i20000−i2−i2i2i2000000002−2000
χ442-2-22-22-2202002-20-2−2i2i−2i2i000000−2−222−2i−2i2i2i00002-200−2200i2−i2i2−i20000i2i2−i2−i200000000−22000
χ452-2-2-22-222202-200-20000002i−2i2i−2i02-22-22−22−2002i−2i0000002−20000i2−i2i2−i22−22−20000000000i2−i20
χ462-2-2-22-222202-200-20000002i−2i2i−2i02-22-2−22−22002i−2i000000−220000−i2i2−i2i2−22−220000000000−i2i20
χ472-2-2-22-222202-200-20000002i−2i2i−2i0-22-222−22−200−2i2i0000002−20000i2−i2i2−i2−22−220000000000−i2i20
χ482-2-2-22-222202-200-20000002i−2i2i−2i0-22-22−22−2200−2i2i000000−220000−i2i2−i2i22−22−20000000000i2−i20
χ492-2-2-22-222202-200-2000000−2i2i−2i2i02-22-22−22−200−2i2i0000002−20000−i2i2−i2i22−22−20000000000−i2i20
χ502-2-2-22-222202-200-2000000−2i2i−2i2i02-22-2−22−2200−2i2i000000−220000i2−i2i2−i2−22−220000000000i2−i20
χ512-2-2-22-222202-200-2000000−2i2i−2i2i0-22-222−22−2002i−2i0000002−20000−i2i2−i2i2−22−220000000000i2−i20
χ522-2-2-22-222202-200-2000000−2i2i−2i2i0-22-22−22−22002i−2i000000−220000i2−i2i2−i22−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-4-4400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ55444-4-4-4-4400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ56444-4-4-4-44000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ57444-4-4-4-44000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ5844-44-4-44-440-4400-40000004-4-440000000000000000000000000000000000000000000000
χ5944-44-4-44-440-4400-4000000-444-40000000000000000000000000000000000000000000000
χ6044-44-4-44-4-404-4004000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ6144-44-4-44-4-404-400400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ6244-4-444-4-40400-440-44-4-44000000000000000000000000000000000000000000000000000
χ6344-4-444-4-40400-440-4-444-4000000000000000000000000000000000000000000000000000
χ6444-4-444-4-40-4004-4040000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ6544-4-444-4-40-4004-404000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ664-44-4-444-4-4-44444-4-4000040000-4000000000000000000000000000000000000000000000
χ674-4-44-44-440-400-440400000000002222−22−22000000000000−2222000000000000000000000000000
χ684-4-44-44-440-400-44040000000000−22−22222200000000000022−22000000000000000000000000000
χ694-4-4-44-444-40-4400400000000000000022−2222−220000000000−22220000000000000000000000000
χ704-4-4-44-444-40-44004000000000000000−2222−2222000000000022−220000000000000000000000000
χ718-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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