Finite Group Databasebeta

← Group #136142

Character table — Group #136142

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order122222222222444444444488888888448888161616161616161616161616161616162244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911-11-11-1-11-1-111-11-11-1ii−i−i11-1-111-1-1i−iii−i−iiiii−i−i−i−i1111-1-1-1-11-11-1i−ii−iii−i−i11-1-1
χ1011-11-11-1-11-1-111-11-11-1ii−i−i11-1-111-1-1i−iii−i−iiiii−i−i−i−i1111-1-1-1-1-11-11−ii−ii−i−iii-1-111
χ1111-11-11-1-11-1-111-11-11-1ii−i−i11-1-111-1-1i−iii−i−i−i−i−i−iiiii-1-1-1-111111-11-1i−ii−i−i−iii-1-111
χ1211-11-11-1-11-1-111-11-11-1ii−i−i11-1-111-1-1i−iii−i−i−i−i−i−iiiii-1-1-1-11111-11-11−ii−iiii−i−i11-1-1
χ1311-11-11-1-11-1-111-11-11-1−i−iii11-1-111-1-1−ii−i−iiiiiii−i−i−i−i-1-1-1-111111-11-1−ii−iiii−i−i-1-111
χ1411-11-11-1-11-1-111-11-11-1−i−iii11-1-111-1-1−ii−i−iiiiiii−i−i−i−i-1-1-1-11111-11-11i−ii−i−i−iii11-1-1
χ1511-11-11-1-11-1-111-11-11-1−i−iii11-1-111-1-1−ii−i−iii−i−i−i−iiiii1111-1-1-1-11-11-1−ii−ii−i−iii11-1-1
χ1611-11-11-1-11-1-111-11-11-1−i−iii11-1-111-1-1−ii−i−iii−i−i−i−iiiii1111-1-1-1-1-11-11i−ii−iii−i−i-1-111
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2222200000000-2-2000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222222-2-2-2-2-2-2222200000000-2-20000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-22222-2-2000022-2-2-2-222000000000000000000000022-2-2000000000000
χ2422222222-2-2-2-22222-2-2000022-2-2-2-2220000000000000000000000-2-222000000000000
χ2522222222-2-2-2-22222-2-20000-2-22222-2-20000000000000000000000000022-2-200000000
χ2622222222-2-2-2-22222-2-20000-2-22222-2-200000000000000000000000000-2-22200000000
χ2722-22-22-2-22-2-222-22-22-22i2i−2i−2i-2-222-2-2222i−2i−2i−2i2i2i00000000000000000000000000000000
χ2822-22-22-2-22-2-222-22-22-2−2i−2i2i2i-2-222-2-222−2i2i2i2i−2i−2i00000000000000000000000000000000
χ2922-22-22-2-22-2-22-22-22-222i2i−2i−2i00000000−2i2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ3022-22-22-2-22-2-22-22-22-222i2i−2i−2i00000000−2i2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ3122-22-22-2-22-2-22-22-22-22−2i−2i2i2i000000002i−2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ3222-22-22-2-22-2-22-22-22-22−2i−2i2i2i000000002i−2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ3322-22-22-2-2-222-22-22-2-2200002222-2-2-2-200000000000000000000002-2-22000000000000
χ3422-22-22-2-2-222-22-22-2-2200002222-2-2-2-20000000000000000000000-222-2000000000000
χ3522-22-22-2-2-222-22-22-2-220000-2-2-2-22222000000000000000000000000002i−2i−2i2i00000000
χ3622-22-22-2-2-222-22-22-2-220000-2-2-2-2222200000000000000000000000000−2i2i2i−2i00000000
χ372-22-222-2-2-22-220000002i−2i2i−2i2−22−22−22−200i2−i2i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ382-22-222-2-2-22-220000002i−2i2i−2i2−22−22−22−200i2−i2i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ392-22-222-2-2-22-220000002i−2i2i−2i−22−22−22−2200−i2i2−i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ402-22-222-2-2-22-220000002i−2i2i−2i−22−22−22−2200−i2i2−i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ412-22-222-2-2-22-22000000−2i2i−2i2i2−22−22−22−200−i2i2−i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ422-22-222-2-2-22-22000000−2i2i−2i2i2−22−22−22−200−i2i2−i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ432-22-222-2-2-22-22000000−2i2i−2i2i−22−22−22−2200i2−i2i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ442-22-222-2-2-22-22000000−2i2i−2i2i−22−22−22−2200i2−i2i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ452-2-2-2-2222-2-2220000002-2-222−2−222−2−22002−2−22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ462-2-2-2-2222-2-2220000002-2-222−2−222−2−22002−2−22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ472-2-2-2-2222-2-2220000002-2-22−222−2−222−200−222−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ482-2-2-2-2222-2-2220000002-2-22−222−2−222−200−222−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ492-2-2-2-2222-2-222000000-222-22−2−222−2−2200−222−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ502-2-2-2-2222-2-222000000-222-22−2−222−2−2200−222−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ512-2-2-2-2222-2-222000000-222-2−222−2−222−2002−2−22ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ522-2-2-2-2222-2-222000000-222-2−222−2−222−2002−2−22−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ5444-44-44-4-4-444-4-44-444-400000000000000000000000000000000000000000000000000
χ554-444-4-44-4000044-4-40000000000000000000000000000000000000000000000002-22-2
χ564-444-4-44-4000044-4-4000000000000000000000000000000000000000000000000-22-22
χ574-444-4-44-40000-4-444000000000000000000000000000000000000000000002i−2i2i−2i0000
χ584-444-4-44-40000-4-44400000000000000000000000000000000000000000000−2i2i−2i2i0000
χ594-44-444-4-44-44-4000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ604-44-444-4-44-44-40000000000−222222−2222−22−222200000000000000000000000000000000000000
χ614-4-444-4-4400004-4-440000000000000000000000000000000000000000000000002-2-22
χ624-4-444-4-4400004-4-44000000000000000000000000000000000000000000000000-222-2
χ634-4-444-4-440000-444-4000000000000000000000000000000000000000000002-2-220000
χ644-4-444-4-440000-444-400000000000000000000000000000000000000000000-222-20000
χ654-4-4-4-444444-4-4000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ664-4-4-4-444444-4-40000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ6888-8-88-88-8000000000000000000000000000000000000000000000000000000000000

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