Finite Group Databasebeta

← Group #511561

Character table — Group #511561

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444444488888888888888161616161616161632323232
order12222222444488888888444444448888161616161616161616161616161616164488881616161616161616444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ8111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ911111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-1111111-1-1-1-1-11
χ1011111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-1-1-1-1-111111-1
χ1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-111111111-1-111-1-11-1
χ1211111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-11111-1-1-1-111-1-111-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1111111-1-11111-11-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-111-1-1-1-11-111
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1111111-1-1-1-111-1-1-1-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1111111-1-1-1-1-1-11111111-1-1-1
χ17222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-2-2-200000000000000000000
χ18222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000-2-2222200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222200000000000000002-2-2-22200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-2222-2-200000000000000000000
χ2122222222-2-2-2-20000000022-2-2222200002222−2−2−2−22222−2−2−2−2-2-2000022−2−222−2−2000000000000
χ2222222222-2-2-2-20000000022-2-222220000−2−2−2−22222−2−2−2−22222-2-20000−2−222−2−222000000000000
χ2322222222-2-2-2-20000000022-2-2-2-2-2-200002222−2−2−2−22222−2−2−2−2220000−2−222−2−222000000000000
χ2422222222-2-2-2-20000000022-2-2-2-2-2-20000−2−2−2−22222−2−2−2−2222222000022−2−222−2−2000000000000
χ2522222222-2-2-2-200000000-2-22222-2-200002222−2−2−2−2−2−2−2−22222-22000022−2−2−2−222000000000000
χ2622222222-2-2-2-200000000-2-22222-2-20000−2−2−2−222222222−2−2−2−2-220000−2−22222−2−2000000000000
χ2722222222-2-2-2-200000000-2-222-2-22200002222−2−2−2−2−2−2−2−222222-20000−2−22222−2−2000000000000
χ2822222222-2-2-2-200000000-2-222-2-2220000−2−2−2−222222222−2−2−2−22-2000022−2−2−2−222000000000000
χ2922-222-2-2-22-22-22222-2-2-2-20000000000000000000022-2-222-2-200000000000000002-2002-20000
χ3022-222-2-2-22-22-22222-2-2-2-20000000000000000000022-2-222-2-20000000000000000-2200-220000
χ3122-222-2-2-22-22-22222-2-2-2-200000000000000000000-2-222-2-22200000000000000002-200-220000
χ3222-222-2-2-22-22-22222-2-2-2-200000000000000000000-2-222-2-2220000000000000000-22002-20000
χ3322-2-2-222-200002−22−22−22−22-2002i−2i2i−2i22−2−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500i2−i2i2−i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ3422-2-2-222-200002−22−22−22−22-2002i−2i2i−2i22−2−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500i2−i2i2−i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ3522-2-2-222-200002−22−22−22−22-200−2i2i−2i2i22−2−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500−i2i2−i2i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ3622-2-2-222-200002−22−22−22−22-200−2i2i−2i2i22−2−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500−i2i2−i2i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ3722-2-2-222-200002−22−22−22−2-22002i−2i−2i2i−2−222ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500i2−i2−i2i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ3822-2-2-222-200002−22−22−22−2-22002i−2i−2i2i−2−222−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500i2−i2−i2i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ3922-2-2-222-200002−22−22−22−2-2200−2i2i2i−2i−2−222ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500−i2i2i2−i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ4022-2-2-222-200002−22−22−22−2-2200−2i2i2i−2i−2−222−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500−i2i2i2−i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ4122-2-2-222-20000−22−22−22−222-2002i−2i2i−2i−2−222ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700−i2i2−i2i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4222-2-2-222-20000−22−22−22−222-2002i−2i2i−2i−2−222−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700−i2i2−i2i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4322-2-2-222-20000−22−22−22−222-200−2i2i−2i2i−2−222ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700i2−i2i2−i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4422-2-2-222-20000−22−22−22−222-200−2i2i−2i2i−2−222−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700i2−i2i2−i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4522-2-2-222-20000−22−22−22−22-22002i−2i−2i2i22−2−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700−i2i2i2−i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4622-2-2-222-20000−22−22−22−22-22002i−2i−2i2i22−2−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700−i2i2i2−i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4722-2-2-222-20000−22−22−22−22-2200−2i2i2i−2i22−2−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700i2−i2−i2i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4822-2-2-222-20000−22−22−22−22-2200−2i2i2i−2i22−2−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700i2−i2−i2i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ492-222-22-2-2-222-222-2-222-2-20000000000002-22-22-22-200000000000000000000002-2002-2000000
χ502-222-22-2-2-222-222-2-222-2-20000000000002-22-22-22-20000000000000000000000-2200-22000000
χ512-222-22-2-2-222-222-2-222-2-2000000000000-22-22-22-2200000000000000000000002-200-22000000
χ522-222-22-2-2-222-222-2-222-2-2000000000000-22-22-22-220000000000000000000000-22002-2000000
χ53444-4-4-4-44000022−2222−22−2222−2222000000000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000
χ54444-4-4-4-44000022−2222−22−2222−222200000000000000000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000
χ55444-4-4-4-440000−2222−222222−2222−22000000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ700000000000000000000000000
χ56444-4-4-4-440000−2222−222222−2222−2200000000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ700000000000000000000000000
χ5744-444-4-4-44-44-4-4-4-4-44444000000000000000000000000000000000000000000000000000000
χ5844-444-4-4-4-44-4400000000000000000000000000002222−22−22−22−22222200000000000000000000000000
χ5944-444-4-4-4-44-440000000000000000000000000000−22−2222222222−22−2200000000000000000000000000
χ604-444-44-4-44-4-440000000000000000000022−2222−22−2222−22220000000000000000000000000000000000
χ614-444-44-4-44-4-4400000000000000000000−2222−222222−2222−220000000000000000000000000000000000
χ624-444-44-4-4-444-4-4-444-4-444000000000000000000000000000000000000000000000000000000
χ634-44-44-44-4000022−22−2222−222222−22004i−4i00002i2−2i22i2−2i2000000000000000000000000000000000000000000
χ644-44-44-44-4000022−22−2222−222222−2200−4i4i0000−2i22i2−2i22i2000000000000000000000000000000000000000000
χ654-44-44-44-40000−222222−2222−22−2222004i−4i0000−2i22i2−2i22i2000000000000000000000000000000000000000000
χ664-44-44-44-40000−222222−2222−22−222200−4i4i00002i2−2i22i2−2i2000000000000000000000000000000000000000000
χ674-4-44-4-44444-4-400000000000000004i−4i−4i4i000000000000000000000000000000000000000000
χ684-4-44-4-44444-4-40000000000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ694-4-44-4-444-4-44444-4-4-4-444000000000000000000000000000000000000000000000000000000
χ704-4-44-4-444-4-444-4-44444-4-4000000000000000000000000000000000000000000000000000000
χ714-4-4-444-44000022−22−222222−22−22220000000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000000000
χ724-4-4-444-44000022−22−222222−22−2222000000000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000000000
χ734-4-4-444-440000−222222−22−222222−220000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ70000000000000000000000000000000000
χ744-4-4-444-440000−222222−22−222222−22000000000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ70000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.