Finite Group Databasebeta

← Group #269641

Character table — Group #269641

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111111
χ5111111111111111111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1-1-1
χ91111111111111111-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-11111-1-11-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1111111-1-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-111-1-11111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111-1-1-1-1111-1-1-1-11
χ17222222222-2-22-222-20000-22222-222220000-2-2220000-2-200000000000000-2000000000000
χ18222222222-2-22-222-20000-22222-2-2-2-2-20000-2-2-2-2000022000000000000002000000000000
χ19222222222-2-22-222-20000-2-2-2-2-2-22222000022-2-20000-2-2000000000000002000000000000
χ20222222222-2-22-222-20000-2-2-2-2-2-2-2-2-2-20000222200002200000000000000-2000000000000
χ2122222222-222-22-2-222222-20000-2000022220000-2-22200-2-20000000000000000000-200000
χ2222222222-222-22-2-222222-20000-20000-2-2-2-20000-2-2-2-200220000000000000000000200000
χ2322222222-222-22-2-22-2-2-2-2-20000-200002222000022-2-200-2-20000000000000000000200000
χ2422222222-222-22-2-22-2-2-2-2-20000-20000-2-2-2-20000222200220000000000000000000-200000
χ2522-2-222-2-2-200202-20000002i2i−2i−2i02i2i−2i−2ii2i2−i2−i2002-2000000i2−i2000022−2−222−2−20000000000i2−i20
χ2622-2-222-2-2-200202-20000002i2i−2i−2i02i2i−2i−2i−i2−i2i2i2002-2000000−i2i20000−2−222−2−2220000000000−i2i20
χ2722-2-222-2-2-200202-20000002i2i−2i−2i0−2i−2i2i2ii2i2−i2−i200-22000000i2−i2000022−2−2−2−2220000000000−i2i20
χ2822-2-222-2-2-200202-20000002i2i−2i−2i0−2i−2i2i2i−i2−i2i2i200-22000000−i2i20000−2−22222−2−20000000000i2−i20
χ2922-2-222-2-2-200202-2000000−2i−2i2i2i02i2i−2i−2ii2i2−i2−i200-22000000i2−i20000−2−22222−2−20000000000−i2i20
χ3022-2-222-2-2-200202-2000000−2i−2i2i2i02i2i−2i−2i−i2−i2i2i200-22000000−i2i2000022−2−2−2−2220000000000i2−i20
χ3122-2-222-2-2-200202-2000000−2i−2i2i2i0−2i−2i2i2ii2i2−i2−i2002-2000000i2−i20000−2−222−2−2220000000000i2−i20
χ3222-2-222-2-2-200202-2000000−2i−2i2i2i0−2i−2i2i2i−i2−i2i2i2002-2000000−i2i2000022−2−222−2−20000000000−i2i20
χ332-2-222-2-2202-20200-222-2-20000002−22−22i−2i2i−2i0000002i−2i2−20022−2−20000i2−i2i2−i200000000i2−i2000
χ342-2-222-2-2202-20200-222-2-20000002−22−2−2i2i−2i2i000000−2i2i2−20022−2−20000−i2i2−i2i200000000−i2i2000
χ352-2-222-2-2202-20200-222-2-2000000−22−222i−2i2i−2i0000002i−2i−2200−2−2220000−i2i2−i2i200000000−i2i2000
χ362-2-222-2-2202-20200-222-2-2000000−22−22−2i2i−2i2i000000−2i2i−2200−2−2220000i2−i2i2−i200000000i2−i2000
χ372-2-222-2-2202-20200-2-2-2220000002−22−22i−2i2i−2i000000−2i2i2−200−2−2220000i2−i2i2−i200000000−i2i2000
χ382-2-222-2-2202-20200-2-2-2220000002−22−2−2i2i−2i2i0000002i−2i2−200−2−2220000−i2i2−i2i200000000i2−i2000
χ392-2-222-2-2202-20200-2-2-222000000−22−222i−2i2i−2i000000−2i2i−220022−2−20000−i2i2−i2i200000000i2−i2000
χ402-2-222-2-2202-20200-2-2-222000000−22−22−2i2i−2i2i0000002i−2i−220022−2−20000i2−i2i2−i200000000−i2i2000
χ412-2-2-2-2222222-2-22-2-2000022-22-2-2000000002-200000000002i−2i2i−2i0000000002i−2i0000000000
χ422-2-2-2-2222222-2-22-2-2000022-22-2-2000000002-20000000000−2i2i−2i2i000000000−2i2i0000000000
χ432-2-2-2-2222222-2-22-2-200002-22-22-200000000-2200000000002i−2i2i−2i000000000−2i2i0000000000
χ442-2-2-2-2222222-2-22-2-200002-22-22-200000000-220000000000−2i2i−2i2i0000000002i−2i0000000000
χ452-2-2-2-22222-2-2-222-222-22-2-22-22-2200000000-22002-2000000000000000000000002-2000000
χ462-2-2-2-22222-2-2-222-222-22-2-2-22-222000000002-2002-200000000000000000000000-22000000
χ472-2-2-2-22222-2-2-222-22-22-22-22-22-2200000000-2200-2200000000000000000000000-22000000
χ482-2-2-2-22222-2-2-222-22-22-22-2-22-222000000002-200-22000000000000000000000002-2000000
χ492-2-2-2-2222-2-2-222-2222-22-220000-2000000000000-2200000000002-22-200000002-200000000
χ502-2-2-2-2222-2-2-222-2222-22-220000-2000000000000-220000000000-22-220000000-2200000000
χ512-2-2-2-2222-2-2-222-222-22-2220000-20000000000002-200000000002-22-20000000-2200000000
χ522-2-2-2-2222-2-2-222-222-22-2220000-20000000000002-20000000000-22-2200000002-200000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-4-4404-40-40040000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ55444-4-4-4-4404-40-4004000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ56444-4-4-4-440-440400-44-4-44000000000000000000000000000000000000000000000000000
χ57444-4-4-4-440-440400-4-444-4000000000000000000000000000000000000000000000000000
χ5844-4-444-4-4400-40-440000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ5944-4-444-4-4400-40-44000000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ604-444-44-4-440040-4-40000000000000000000000000000000000022−22−222200000000000000000
χ614-444-44-4-440040-4-400000000000000000000000000000000000−222222−2200000000000000000
χ624-444-44-4-4-400-40440000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ634-444-44-4-4-400-4044000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ644-44-44-44-40000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ654-44-44-44-40000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ664-44-44-44-4000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ674-44-44-44-4000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ684-4-444-4-440-440-4004000000000022−2222−22000000000000−2222000000000000000000000000000
χ694-4-444-4-440-440-40040000000000−2222−222200000000000022−22000000000000000000000000000
χ704-4-4-4-4444-4444-4-44-40000-400004000000000000000000000000000000000000000000000
χ7188-88-8-88-8000000000000000000000000000000000000000000000000000000000000000

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