Finite Group Databasebeta

← Group #98167

Character table — Group #98167

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444444444444444888888888888888822444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-111-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111-1-111-1-1111-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1111ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1iiii−i−i−i−i−i−i−i−iiiii111-1-1-1ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1−i−i−i−iiiiiiiii−i−i−i−i111-1-1-1−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111iiii−i−i−i−iiiii−i−i−i−i11-11-1-1−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111−i−i−i−iiiii−i−i−i−iiiii11-11-1-1ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii-1-11-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i-1-11-111ii−i−i−i−iii
χ1722222222222222-2-222-2-2-2-2222222-2-22200-2-200-2-2-2000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-222-2-2-2-2002200-222000000000000000000000000000000
χ19222222222222-2-222-2-222-2-22222-2-222-2-200-2-200-222000000000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-2-2-2-22222002200-2-2-2000000000000000000000000000000
χ2122222222-2-2-2-222222222220000-2-2-2-200220022-200000000000000000000-2-20000000000
χ2222222222-2-2-2-222222222220000-2-2-2-200-2-200-2-2-200000000000000000000220000000000
χ2322222222-2-2-2-222-2-222-2-2-2-20000-2-2220000000020000000000000000002-2002-200000000
χ2422222222-2-2-2-222-2-222-2-2-2-20000-2-222000000002000000000000000000-2200-2200000000
χ2522222222-2-2-2-2-2-222-2-222-2-2000022-2-20000000020000000000000000002-200-2200000000
χ2622222222-2-2-2-2-2-222-2-222-2-2000022-2-2000000002000000000000000000-22002-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22200002222002200-2-2-2000000000000000000002-20000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200-2-20022-200000000000000000000-220000000000
χ2922-2-2-222-200002i−2i2i−2i2i−2i2i−2i2-200000000002i−2i002-20001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ3022-2-2-222-200002i−2i2i−2i2i−2i2i−2i2-200000000002i−2i002-2000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ3122-2-2-222-200002i−2i2i−2i2i−2i2i−2i2-20000000000−2i2i00-220001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ3222-2-2-222-200002i−2i2i−2i2i−2i2i−2i2-20000000000−2i2i00-22000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ3322-2-2-222-20000−2i2i−2i2i−2i2i−2i2i2-200000000002i−2i00-220001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ3422-2-2-222-20000−2i2i−2i2i−2i2i−2i2i2-200000000002i−2i00-22000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ3522-2-2-222-20000−2i2i−2i2i−2i2i−2i2i2-20000000000−2i2i002-20001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ3622-2-2-222-20000−2i2i−2i2i−2i2i−2i2i2-20000000000−2i2i002-2000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ372-222-22-2-222-2-2002i−2i00−2i2i0022-2-2002i−2i0000000002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000001−i−1+i1+i−1−i0000
χ382-222-22-2-222-2-2002i−2i00−2i2i0022-2-2002i−2i0000000002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000−1+i1−i−1−i1+i0000
χ392-222-22-2-222-2-2002i−2i00−2i2i00-2-222002i−2i000000000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000−1+i1−i−1−i1+i0000
χ402-222-22-2-222-2-2002i−2i00−2i2i00-2-222002i−2i000000000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000001−i−1+i1+i−1−i0000
χ412-222-22-2-222-2-200−2i2i002i−2i0022-2-200−2i2i000000000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000001+i−1−i1−i−1+i0000
χ422-222-22-2-222-2-200−2i2i002i−2i0022-2-200−2i2i000000000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000−1−i1+i−1+i1−i0000
χ432-222-22-2-222-2-200−2i2i002i−2i00-2-22200−2i2i0000000002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000−1−i1+i−1+i1−i0000
χ442-222-22-2-222-2-200−2i2i002i−2i00-2-22200−2i2i0000000002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000001+i−1−i1−i−1+i0000
χ452-22-22-22-22-22-22i−2i00−2i2i00002i−2i2i−2i2i−2i002-2000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000001−i−1+i1+i−1−i
χ462-22-22-22-22-22-22i−2i00−2i2i00002i−2i2i−2i2i−2i002-200000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000−1+i1−i−1−i1+i
χ472-22-22-22-22-22-22i−2i00−2i2i0000−2i2i−2i2i2i−2i00-22000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000−1+i1−i−1−i1+i
χ482-22-22-22-22-22-22i−2i00−2i2i0000−2i2i−2i2i2i−2i00-2200000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000001−i−1+i1+i−1−i
χ492-22-22-22-22-22-2−2i2i002i−2i00002i−2i2i−2i−2i2i00-22000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000−1−i1+i−1+i1−i
χ502-22-22-22-22-22-2−2i2i002i−2i00002i−2i2i−2i−2i2i00-2200000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000001+i−1−i1−i−1+i
χ512-22-22-22-22-22-2−2i2i002i−2i0000−2i2i−2i2i−2i2i002-2000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000001+i−1−i1−i−1+i
χ522-22-22-22-22-22-2−2i2i002i−2i0000−2i2i−2i2i−2i2i002-200000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000−1−i1+i−1+i1−i
χ53444-4-4-4-444-4-4400000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ54444-4-4-4-444-4-440000000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ55444-4-4-4-44-444-400000000000000000000004i−4i00000000000000000000000000000000000
χ56444-4-4-4-44-444-40000000000000000000000−4i4i00000000000000000000000000000000000
χ5744-4-4-444-400004i−4i−4i4i4i−4i−4i4i-440000000000000000000000000000000000000000000000000
χ5844-4-4-444-40000−4i4i4i−4i−4i4i4i−4i-440000000000000000000000000000000000000000000000000
χ594-444-44-4-4-4-444004i−4i00−4i4i00000000−4i4i00000000000000000000000000000000000000000
χ604-444-44-4-4-4-44400−4i4i004i−4i000000004i−4i00000000000000000000000000000000000000000
χ614-44-44-44-4-44-444i−4i00−4i4i00000000−4i4i0000000000000000000000000000000000000000000
χ624-44-44-44-4-44-44−4i4i004i−4i000000004i−4i0000000000000000000000000000000000000000000
χ634-4-44-4-44400004400-4-400000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ644-4-44-4-44400004400-4-40000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ654-4-44-4-4440000-4-4004400000000000000000000000000000002-2-222-2-2200000000000000
χ664-4-44-4-4440000-4-400440000000000000000000000000000000-222-2-222-200000000000000
χ674-4-4-444-440000004400-4-40000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ684-4-4-444-440000004400-4-4000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ694-4-4-444-44000000-4-400440000000000000000000002-2-222-2-220000000000000000000000
χ704-4-4-444-44000000-4-40044000000000000000000000-222-2-222-20000000000000000000000
χ7188-888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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