Finite Group Databasebeta

← Group #100968

Character table — Group #100968

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888884444444488888888
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
χ5111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2122222222-2-2-2-22222-2-20000000022-2-2002-2000000000022-2-222-2-20000000000000000
χ2222222222-2-2-2-22222-2-20000000022-2-2002-20000000000-2-222-2-2220000000000000000
χ2322222222-2-2-2-22222-2-200000000-2-22200-220022-2-222-2-2000000000000000000000000
χ2422222222-2-2-2-22222-2-200000000-2-22200-2200-2-222-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2220000000022-2-200-22002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2220000000022-2-200-2200−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22200000000-2-222002-200000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-22200000000-2-222002-20000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ292-222-2-2-222-22-200000000002i2i−2i−2i2i−2i2i−2i2-200001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ302-222-2-2-222-22-200000000002i2i−2i−2i2i−2i2i−2i2-20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ312-222-2-2-222-22-200000000002i2i−2i−2i−2i2i−2i2i-2200001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ322-222-2-2-222-22-200000000002i2i−2i−2i−2i2i−2i2i-220000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ332-222-2-2-222-22-20000000000−2i−2i2i2i2i−2i2i−2i-2200001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ342-222-2-2-222-22-20000000000−2i−2i2i2i2i−2i2i−2i-220000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ352-222-2-2-222-22-20000000000−2i−2i2i2i−2i2i−2i2i2-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ362-222-2-2-222-22-20000000000−2i−2i2i2i−2i2i−2i2i2-20000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ372-222-2-2-22-22-220000002i2i−2i−2i00002i−2i−2i2i00002-21−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ382-222-2-2-22-22-220000002i2i−2i−2i00002i−2i−2i2i00002-2−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ392-222-2-2-22-22-220000002i2i−2i−2i0000−2i2i2i−2i0000-221+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ402-222-2-2-22-22-220000002i2i−2i−2i0000−2i2i2i−2i0000-22−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ412-222-2-2-22-22-22000000−2i−2i2i2i00002i−2i−2i2i0000-221−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ422-222-2-2-22-22-22000000−2i−2i2i2i00002i−2i−2i2i0000-22−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ432-222-2-2-22-22-22000000−2i−2i2i2i0000−2i2i2i−2i00002-21+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ442-222-2-2-22-22-22000000−2i−2i2i2i0000−2i2i2i−2i00002-2−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ452-22-222-2-2-222-22i2i−2i−2i2i−2i2i−2i2i−2i2-22-200000000000000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ462-22-222-2-2-222-22i2i−2i−2i2i−2i2i−2i2i−2i2-22-20000000000000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ472-22-222-2-2-222-22i2i−2i−2i2i−2i−2i2i−2i2i-22-2200000000000000000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ482-22-222-2-2-222-22i2i−2i−2i2i−2i−2i2i−2i2i-22-220000000000000000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ492-22-222-2-2-222-2−2i−2i2i2i−2i2i2i−2i2i−2i-22-2200000000000000000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ502-22-222-2-2-222-2−2i−2i2i2i−2i2i2i−2i2i−2i-22-220000000000000000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ512-22-222-2-2-222-2−2i−2i2i2i−2i2i−2i2i−2i2i2-22-200000000000000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ522-22-222-2-2-222-2−2i−2i2i2i−2i2i−2i2i−2i2i2-22-20000000000000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ53444-4-4-44-444-4-40000004-4-440000000000000000000000000000000000000000000000
χ54444-4-4-44-444-4-4000000-444-40000000000000000000000000000000000000000000000
χ55444-4-4-44-4-4-44400000000004i−4i−4i4i000000000000000000000000000000000000000000
χ56444-4-4-44-4-4-4440000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ5744-4-44-4-4400004i−4i4i−4i00000000000000000000000000000000000000002-22i−2i00000000
χ5844-4-44-4-4400004i−4i4i−4i0000000000000000000000000000000000000000-22−2i2i00000000
χ5944-4-44-4-440000−4i4i−4i4i00000000000000000000000000000000000000002-2−2i2i00000000
χ6044-4-44-4-440000−4i4i−4i4i0000000000000000000000000000000000000000-222i−2i00000000
χ614-44-444-4-44-4-444i4i−4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ624-44-444-4-44-4-44−4i−4i4i4i4i−4i00000000000000000000000000000000000000000000000000
χ634-4-444-44-400004-4-440000000000000000000000000000000000002i−2i2i−2i000000000000
χ644-4-444-44-400004-4-44000000000000000000000000000000000000−2i2i−2i2i000000000000
χ654-4-444-44-40000-444-40000000000000000000000000000000000002i−2i−2i2i000000000000
χ664-4-444-44-40000-444-4000000000000000000000000000000000000−2i2i2i−2i000000000000
χ6788-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8-8888000000000000000000000000000000000000000000000000000000000000

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