Finite Group Databasebeta

← Group #93033

Character table — Group #93033

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order122222222222444444444488888888448888161616161616161616161616161616164444444488888888
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
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ91-1-1-1111-111-1-11-1-111-111-1-1-1-1-1-111111-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101-1-1-1111-111-1-11-1-111-111-1-1-1-1-1-111111-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111-1-1-1111-111-1-11-1-111-111-1-1-1-1-1-111111-111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121-1-1-1111-111-1-11-1-111-111-1-1-1-1-1-111111-111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131-1-1-1111-111-1-11-1-111-1-1-1111111-1-1-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-1
χ141-1-1-1111-111-1-11-1-111-1-1-1111111-1-1-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-111
χ151-1-1-1111-111-1-11-1-111-1-1-1111111-1-1-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii11-1-1-1-111
χ161-1-1-1111-111-1-11-1-111-1-1-1111111-1-1-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-11111-1-1
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-222222222-2-2-2-2-2-200000000000000000000000000000000
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
χ21222222222222-2-2-2-2-2-2-2-2-2-200000000220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-200000000220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ2322222222-2-2-2-2-2-2-2-22200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ2422222222-2-2-2-2-2-2-2-22200002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ2522222222-2-2-2-2-2-2-2-2220000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ2622222222-2-2-2-2-2-2-2-2220000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ27222-22-2-2-22-2-220000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2002−22−2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000000000
χ28222-22-2-2-22-2-220000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2002−22−2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000000000
χ29222-22-2-2-22-2-220000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200−22−22ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000000000
χ30222-22-2-2-22-2-220000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200−22−22−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000000000
χ31222-22-2-2-22-2-22000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200−22−22ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000000000
χ32222-22-2-2-22-2-22000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200−22−22−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000000000
χ33222-22-2-2-22-2-22000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2002−22−2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000000000
χ34222-22-2-2-22-2-22000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2002−22−2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000000000
χ352-2-222-2-222-22-20000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i200−222−2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000000000
χ362-2-222-2-222-22-20000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i200−222−2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000000000
χ372-2-222-2-222-22-20000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2002−2−22ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000000000
χ382-2-222-2-222-22-20000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2002−2−22−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000000000
χ392-2-222-2-222-22-2000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2002−2−22ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000000000
χ402-2-222-2-222-22-2000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2002−2−22−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000000000
χ412-2-222-2-222-22-2000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i200−222−2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000000000
χ422-2-222-2-222-22-2000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i200−222−2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000000000
χ432-2-2-2222-222-2-22-2-222-222-2-22222-2-2-2-22-2-2-22200000000000000000000000000000000
χ442-2-2-2222-222-2-22-2-222-2-2-222-2-2-2-22222-22-2-22200000000000000000000000000000000
χ452-2-2-2222-222-2-2-222-2-2222-2-200000000-22000022−2−2−2−22222−2−2−2−2220000000000000000
χ462-2-2-2222-222-2-2-222-2-2222-2-200000000-220000−2−22222−2−2−2−22222−2−20000000000000000
χ472-2-2-2222-222-2-2-222-2-22-2-222000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ482-2-2-2222-222-2-2-222-2-22-2-222000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ492-2-2-2222-2-2-222-222-22-200002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i
χ502-2-2-2222-2-2-222-222-22-200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i
χ512-2-2-2222-2-2-222-222-22-20000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i
χ522-2-2-2222-2-2-222-222-22-20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i
χ5344444444-4-4-4-44444-4-400000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-444-4000000000022−22−222222−22−222200000000000000000000000000000000000000
χ55444-44-4-4-4-444-40000000000−222222−22−222222−2200000000000000000000000000000000000000
χ5644-44-44-4-4000044-4-400000000000000000000000000000000000000002-22-200000000
χ5744-44-44-4-4000044-4-40000000000000000000000000000000000000000-22-2200000000
χ5844-44-44-4-40000-4-4440000000000000000000000000000000000002i−2i2i−2i000000000000
χ5944-44-44-4-40000-4-444000000000000000000000000000000000000−2i2i−2i2i000000000000
χ604-44-4-44-4400004-44-400000000000000000000000000000000000000002i−2i−2i2i00000000
χ614-44-4-44-4400004-44-40000000000000000000000000000000000000000−2i2i2i−2i00000000
χ624-44-4-44-440000-44-440000000000000000000000000000000000002-2-22000000000000
χ634-44-4-44-440000-44-44000000000000000000000000000000000000-222-2000000000000
χ644-4-444-4-44-44-44000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ654-4-444-4-44-44-440000000000−222222−2222−22−222200000000000000000000000000000000000000
χ664-4-4-4444-4-4-4444-4-44-4400000000000000000000000000000000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-888-8-88-8000000000000000000000000000000000000000000000000000000000000

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