Finite Group Databasebeta

← Group #309554

Character table — Group #309554

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
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
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1111-1-111-1-111-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-111111111-1-1-1-11111-11-1-1-1-1-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-111111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11
χ17222222222-2-222-2-22-200002222-20000222200-2-2220000-2-20000000000000-200000000000
χ18222222222-2-222-2-22-200002222-20000-2-2-2-200-2-2-2-20000220000000000000200000000000
χ19222222222-2-222-2-22-20000-2-2-2-2-2000022220022-2-20000-2-20000000000000200000000000
χ20222222222-2-222-2-22-20000-2-2-2-2-20000-2-2-2-20022220000220000000000000-200000000000
χ2122222222-222-2-222-2-222220000-222220000220000-2-2-2-200000000000000-2000000000000
χ2222222222-222-2-222-2-222220000-2-2-2-2-20000-2-20000-2-222000000000000002000000000000
χ2322222222-222-2-222-2-2-2-2-2-20000-222220000-2-2000022-2-2000000000000002000000000000
χ2422222222-222-2-222-2-2-2-2-2-20000-2-2-2-2-20000220000222200000000000000-2000000000000
χ2522-2-22-22-2-2002-2002000002i2i−2i−2i022−2−22i2i−2i−2i00002-2002−200i2i2−i2−i20000i2i2−i2−i2000000002−2000
χ2622-2-22-22-2-2002-2002000002i2i−2i−2i022−2−2−2i−2i2i2i0000-22002−200i2i2−i2−i20000−i2−i2i2i200000000−22000
χ2722-2-22-22-2-2002-2002000002i2i−2i−2i0−2−2222i2i−2i−2i00002-200−2200−i2−i2i2i20000−i2−i2i2i200000000−22000
χ2822-2-22-22-2-2002-2002000002i2i−2i−2i0−2−222−2i−2i2i2i0000-2200−2200−i2−i2i2i20000i2i2−i2−i2000000002−2000
χ2922-2-22-22-2-2002-200200000−2i−2i2i2i022−2−22i2i−2i−2i0000-22002−200−i2−i2i2i20000i2i2−i2−i200000000−22000
χ3022-2-22-22-2-2002-200200000−2i−2i2i2i022−2−2−2i−2i2i2i00002-2002−200−i2−i2i2i20000−i2−i2i2i2000000002−2000
χ3122-2-22-22-2-2002-200200000−2i−2i2i2i0−2−2222i2i−2i−2i0000-2200−2200i2i2−i2−i20000−i2−i2i2i2000000002−2000
χ3222-2-22-22-2-2002-200200000−2i−2i2i2i0−2−222−2i−2i2i2i00002-200−2200i2i2−i2−i20000i2i2−i2−i200000000−22000
χ332-222-2-22-2222-2-2-2-22-200002i−2i2i−2i200000000002i−2i00000000000022-2-200000000002i−2i00000
χ342-222-2-22-2222-2-2-2-22-200002i−2i2i−2i200000000002i−2i000000000000-2-2220000000000−2i2i00000
χ352-222-2-22-2222-2-2-2-22-20000−2i2i−2i2i20000000000−2i2i00000000000022-2-20000000000−2i2i00000
χ362-222-2-22-2222-2-2-2-22-20000−2i2i−2i2i20000000000−2i2i000000000000-2-22200000000002i−2i00000
χ372-222-2-22-22-2-2-2-222222i2i−2i−2i2i−2i2i−2i-20000000000−2i2i002i−2i000000000000000000002-20000000
χ382-222-2-22-22-2-2-2-222222i2i−2i−2i−2i2i−2i2i-200000000002i−2i002i−2i00000000000000000000-220000000
χ392-222-2-22-22-2-2-2-22222−2i−2i2i2i2i−2i2i−2i-20000000000−2i2i00−2i2i00000000000000000000-220000000
χ402-222-2-22-22-2-2-2-22222−2i−2i2i2i−2i2i−2i2i-200000000002i−2i00−2i2i000000000000000000002-20000000
χ412-222-2-22-2-2-2-22222-2-22i2i−2i−2i0000200000000000000−2i2i00002-22-200000000002i−2i000000000
χ422-222-2-22-2-2-2-22222-2-22i2i−2i−2i0000200000000000000−2i2i0000-22-220000000000−2i2i000000000
χ432-222-2-22-2-2-2-22222-2-2−2i−2i2i2i00002000000000000002i−2i00002-22-20000000000−2i2i000000000
χ442-222-2-22-2-2-2-22222-2-2−2i−2i2i2i00002000000000000002i−2i0000-22-2200000000002i−2i000000000
χ452-22-22-2-2202-2002-2002i−2i2i−2i000002i−2i2i−2ii2−i2i2−i22-200000000i2−i200002−22−22−22−20000000000i2−i20
χ462-22-22-2-2202-2002-2002i−2i2i−2i000002i−2i2i−2i−i2i2−i2i22-200000000−i2i20000−22−22−22−220000000000−i2i20
χ472-22-22-2-2202-2002-2002i−2i2i−2i00000−2i2i−2i2ii2−i2i2−i2-2200000000i2−i200002−22−2−22−220000000000−i2i20
χ482-22-22-2-2202-2002-2002i−2i2i−2i00000−2i2i−2i2i−i2i2−i2i2-2200000000−i2i20000−22−222−22−20000000000i2−i20
χ492-22-22-2-2202-2002-200−2i2i−2i2i000002i−2i2i−2ii2−i2i2−i2-2200000000i2−i20000−22−222−22−20000000000−i2i20
χ502-22-22-2-2202-2002-200−2i2i−2i2i000002i−2i2i−2i−i2i2−i2i2-2200000000−i2i200002−22−2−22−220000000000i2−i20
χ512-22-22-2-2202-2002-200−2i2i−2i2i00000−2i2i−2i2ii2−i2i2−i22-200000000i2−i20000−22−22−22−220000000000i2−i20
χ522-22-22-2-2202-2002-200−2i2i−2i2i00000−2i2i−2i2i−i2i2−i2i22-200000000−i2i200002−22−22−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-44-4-404-400-440000000000000000000000000000000000022−22−222200000000000000000
χ55444-4-44-4-404-400-4400000000000000000000000000000000000−222222−2200000000000000000
χ56444-4-44-4-40-44004-4004-4-4400000000000000000000000000000000000000000000000000
χ57444-4-44-4-40-44004-400-444-400000000000000000000000000000000000000000000000000
χ5844-4-44-44-4400-4400-400000000002222−22−22000000000000−2222000000000000000000000000000
χ5944-4-44-44-4400-4400-40000000000−22−22222200000000000022−22000000000000000000000000000
χ604-444-4-44-4-44444-4-4-4400000000-4000000000000000000000000000000000000000000000
χ614-44-44-4-440-4400-440000000000000002i2−2i22i2−2i20000000000−2i22i20000000000000000000000000
χ624-44-44-4-440-4400-44000000000000000−2i22i2−2i22i200000000002i2−2i20000000000000000000000000
χ634-4-4444-4-40000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ644-4-4444-4-40000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ654-4-4444-4-4000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ664-4-4444-4-4000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ674-4-4-4-44444004-400-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ684-4-4-4-44444004-400-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ694-4-4-4-4444-400-44004000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-4-4444-400-4400400000-444-40000000000000000000000000000000000000000000000
χ7188-88-8-8-88000000000000000000000000000000000000000000000000000000000000000

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