Finite Group Databasebeta

← Group #269771

Character table — Group #269771

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888882244444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-111-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111
χ5111111111111111111111-1-1-1-1111111111-1-11111-1-11111-1-1-1-111111111-1-11-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1111-1-1-1-111-1
χ91111111111111111-1-1-1-11111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111111-111-1-111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1111111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-11
χ17222222222-2-22-222-22222-20000-2222200000022-2-20000-2-200000000000000-20000000000
χ18222222222-2-22-222-22222-20000-2-2-2-2-2000000-2-2-2-20000220000000000000020000000000
χ19222222222-2-22-222-2-2-2-2-2-20000-22222000000-2-2220000-2-20000000000000020000000000
χ20222222222-2-22-222-2-2-2-2-2-20000-2-2-2-2-2000000222200002200000000000000-20000000000
χ2122222222-222-22-2-220000-22222-200002222220000-2-2-2-200000000000000000-2000000000
χ2222222222-222-22-2-220000-22222-20000-2-2-2-2-2-20000-2-222000000000000000002000000000
χ2322222222-222-22-2-220000-2-2-2-2-2-200002222-2-2000022-2-2000000000000000002000000000
χ2422222222-222-22-2-220000-2-2-2-2-2-20000-2-2-2-2220000222200000000000000000-2000000000
χ252-222-2-2-2202-20200-2000002i2i−2i−2i022−2−22i2i−2i−2i2-2000000002−2i2i2−i2−i20000i2i2−i2−i2000000002−2000
χ262-222-2-2-2202-20200-2000002i2i−2i−2i022−2−2−2i−2i2i2i-22000000002−2i2i2−i2−i20000−i2−i2i2i200000000−22000
χ272-222-2-2-2202-20200-2000002i2i−2i−2i0−2−2222i2i−2i−2i2-200000000−22−i2−i2i2i20000−i2−i2i2i200000000−22000
χ282-222-2-2-2202-20200-2000002i2i−2i−2i0−2−222−2i−2i2i2i-2200000000−22−i2−i2i2i20000i2i2−i2−i2000000002−2000
χ292-222-2-2-2202-20200-200000−2i−2i2i2i022−2−22i2i−2i−2i-22000000002−2−i2−i2i2i20000i2i2−i2−i200000000−22000
χ302-222-2-2-2202-20200-200000−2i−2i2i2i022−2−2−2i−2i2i2i2-2000000002−2−i2−i2i2i20000−i2−i2i2i2000000002−2000
χ312-222-2-2-2202-20200-200000−2i−2i2i2i0−2−2222i2i−2i−2i-2200000000−22i2i2−i2−i20000−i2−i2i2i2000000002−2000
χ322-222-2-2-2202-20200-200000−2i−2i2i2i0−2−222−2i−2i2i2i2-200000000−22i2i2−i2−i20000i2i2−i2−i200000000−22000
χ332-22-222-2-2200-20-22022-2-20000002i−2i2i−2ii2−i2i2−i2002i−2i0000i2−i2000000i2i2−i2−i22−22−200000000002−20
χ342-22-222-2-2200-20-22022-2-20000002i−2i2i−2i−i2i2−i2i2002i−2i0000−i2i2000000−i2−i2i2i2−22−220000000000−220
χ352-22-222-2-2200-20-22022-2-2000000−2i2i−2i2ii2−i2i2−i200−2i2i0000i2−i2000000i2i2−i2−i2−22−220000000000−220
χ362-22-222-2-2200-20-22022-2-2000000−2i2i−2i2i−i2i2−i2i200−2i2i0000−i2i2000000−i2−i2i2i22−22−200000000002−20
χ372-22-222-2-2200-20-220-2-2220000002i−2i2i−2ii2−i2i2−i200−2i2i0000i2−i2000000−i2−i2i2i22−22−20000000000−220
χ382-22-222-2-2200-20-220-2-2220000002i−2i2i−2i−i2i2−i2i200−2i2i0000−i2i2000000i2i2−i2−i2−22−2200000000002−20
χ392-22-222-2-2200-20-220-2-222000000−2i2i−2i2ii2−i2i2−i2002i−2i0000i2−i2000000−i2−i2i2i2−22−2200000000002−20
χ402-22-222-2-2200-20-220-2-222000000−2i2i−2i2i−i2i2−i2i2002i−2i0000−i2i2000000i2i2−i2−i22−22−20000000000−220
χ412-2-2-22-222222-2-22-2-22-22-220000-20000000000002-20000002i−2i2i−2i0000000000002i−2i0000000
χ422-2-2-22-222222-2-22-2-22-22-220000-20000000000002-2000000−2i2i−2i2i000000000000−2i2i0000000
χ432-2-2-22-222222-2-22-2-2-22-2220000-2000000000000-220000002i−2i2i−2i000000000000−2i2i0000000
χ442-2-2-22-222222-2-22-2-2-22-2220000-2000000000000-22000000−2i2i−2i2i0000000000002i−2i0000000
χ452-2-2-22-2222-2-2-222-222-22-2-22-22-22000000000000-222-200000000000000000000002-200000
χ462-2-2-22-2222-2-2-222-222-22-2-2-22-222000000000000-22-220000000000000000000000-2200000
χ472-2-2-22-2222-2-2-222-22-22-22-22-22-220000000000002-22-20000000000000000000000-2200000
χ482-2-2-22-2222-2-2-222-22-22-22-2-22-2220000000000002-2-2200000000000000000000002-200000
χ492-2-2-22-222-2-2-222-222000022-22-2-200000000000000-22000000002-22-200002-200000000000
χ502-2-2-22-222-2-2-222-222000022-22-2-200000000000000-2200000000-22-220000-2200000000000
χ512-2-2-22-222-2-2-222-22200002-22-22-2000000000000002-2000000002-22-20000-2200000000000
χ522-2-2-22-222-2-2-222-22200002-22-22-2000000000000002-200000000-22-2200002-200000000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-44-40000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ55444-4-4-44-40000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ56444-4-4-44-4000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ57444-4-4-44-4000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ5844-444-4-4-440040-4-404-4-44000000000000000000000000000000000000000000000000000
χ5944-444-4-4-440040-4-40-444-4000000000000000000000000000000000000000000000000000
χ6044-444-4-4-4-400-4044000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ6144-444-4-4-4-400-404400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ6244-4-4-44-4404-40-400400000000000000000000000000000022−22−2222000000000000000000000
χ6344-4-4-44-4404-40-4004000000000000000000000000000000−222222−22000000000000000000000
χ6444-4-4-44-440-440400-4000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ6544-4-4-44-440-440400-400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ664-444-4-4-440-440-400400000000002222−22−2200000000000000−22220000000000000000000000000
χ674-444-4-4-440-440-40040000000000−22−2222220000000000000022−220000000000000000000000000
χ684-44-444-4-4-400404-40000000000000002i2−2i22i2−2i200000000−2i22i2000000000000000000000000000
χ694-44-444-4-4-400404-4000000000000000−2i22i2−2i22i2000000002i2−2i2000000000000000000000000000
χ704-4-4-44-444-4444-4-44-40000-400004000000000000000000000000000000000000000000000
χ718-8-88-888-8000000000000000000000000000000000000000000000000000000000000000

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