Finite Group Databasebeta

← Group #98179

Character table — Group #98179

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444444444444444888888888888888824444488888888
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
χ3111111111111111111111111111111-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ71111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-11-1-111ii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-11-1-111−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1ii−i−i−i−iii
χ1211111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1−i−iiiii−i−i
χ1311111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1111-1-1−i−iii−i−iii
χ1411111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1111-1-1ii−i−iii−i−i
χ1511111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1-111−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111ii−i−i−i−iii
χ1722222222222222-2-222-2-2-2-22222-2-22200-222-2-200-2-2000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2-2-22200-2-2-2220022000000000000000000000000000000
χ192222222222-2-2-2-2222222220000-2-2-2-222-2000022000000000000000000-2-2000000000000
χ202222222222-2-2-2-2222222220000-2-2-2-2-2-2-20000-2-200000000000000000022000000000000
χ212222222222-2-2-2-2-2-222-2-2-2-2000022-2-2002000000000000000000000000002-22-200000000
χ222222222222-2-2-2-2-2-222-2-2-2-2000022-2-200200000000000000000000000000-22-2200000000
χ2322222222-2-2222222-2-222-2-2222222-2-200-2-2-22200-2-2000000000000000000000000000000
χ2422222222-2-2222222-2-222-2-2-2-2-2-222-2-200-222-2-20022000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-222-2-20000-2-222002000000000000000000000000002-2-2200000000
χ2622222222-2-2-2-2-2-222-2-222-2-20000-2-22200200000000000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2220000222222-20000-2-20000000000000000002-2000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200002222-2-2-2000022000000000000000000-22000000000000
χ2922-2-22-2-220022-2-22i−2i002i−2i002i2i−2i−2i2i−2i00000002-200001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000001−i−1+i1+i−1−i0000
χ3022-2-22-2-220022-2-22i−2i002i−2i002i2i−2i−2i2i−2i00000002-20000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000−1+i1−i−1−i1+i0000
χ3122-2-22-2-220022-2-22i−2i002i−2i00−2i−2i2i2i2i−2i0000000-2200001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000−1+i1−i−1−i1+i0000
χ3222-2-22-2-220022-2-22i−2i002i−2i00−2i−2i2i2i2i−2i0000000-220000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000001−i−1+i1+i−1−i0000
χ3322-2-22-2-220022-2-2−2i2i00−2i2i002i2i−2i−2i−2i2i0000000-2200001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000−1−i1+i−1+i1−i0000
χ3422-2-22-2-220022-2-2−2i2i00−2i2i002i2i−2i−2i−2i2i0000000-220000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000001+i−1−i1−i−1+i0000
χ3522-2-22-2-220022-2-2−2i2i00−2i2i00−2i−2i2i2i−2i2i00000002-200001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000001+i−1−i1−i−1+i0000
χ3622-2-22-2-220022-2-2−2i2i00−2i2i00−2i−2i2i2i−2i2i00000002-20000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000−1−i1+i−1+i1−i0000
χ372-222-2-2-222i−2i00002i−2i2i−2i−2i2i2-2000000002-2000002i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ382-222-2-2-222i−2i00002i−2i2i−2i−2i2i2-2000000002-2000002i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ392-222-2-2-222i−2i00002i−2i2i−2i−2i2i2-200000000-2200000−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ402-222-2-2-222i−2i00002i−2i2i−2i−2i2i2-200000000-2200000−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ412-222-2-2-22−2i2i0000−2i2i−2i2i2i−2i2-2000000002-200000−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ422-222-2-2-22−2i2i0000−2i2i−2i2i2i−2i2-2000000002-200000−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ432-222-2-2-22−2i2i0000−2i2i−2i2i2i−2i2-200000000-22000002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ442-222-2-2-22−2i2i0000−2i2i−2i2i2i−2i2-200000000-22000002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ452-22-222-2-22i−2i2-22-200−2i2i00002-22-2002i−2i0002i−2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000001−i−1+i1+i−1−i
χ462-22-222-2-22i−2i2-22-200−2i2i00002-22-2002i−2i0002i−2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000−1+i1−i−1−i1+i
χ472-22-222-2-22i−2i2-22-200−2i2i0000-22-22002i−2i000−2i2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000−1+i1−i−1−i1+i
χ482-22-222-2-22i−2i2-22-200−2i2i0000-22-22002i−2i000−2i2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000001−i−1+i1+i−1−i
χ492-22-222-2-2−2i2i2-22-2002i−2i00002-22-200−2i2i000−2i2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000001+i−1−i1−i−1+i
χ502-22-222-2-2−2i2i2-22-2002i−2i00002-22-200−2i2i000−2i2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000−1−i1+i−1+i1−i
χ512-22-222-2-2−2i2i2-22-2002i−2i0000-22-2200−2i2i0002i−2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000−1−i1+i−1+i1−i
χ522-22-222-2-2−2i2i2-22-2002i−2i0000-22-2200−2i2i0002i−2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000001+i−1−i1−i−1+i
χ53444-4-4-44-444000000-4-400000000000000000000000000000002-2-222-2-2200000000000000
χ54444-4-4-44-444000000-4-40000000000000000000000000000000-222-2-222-200000000000000
χ55444-4-4-44-4-4-40000004400000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ56444-4-4-44-4-4-4000000440000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ5744-4-44-4-4400-4-4444i−4i004i−4i000000−4i4i0000000000000000000000000000000000000000000
χ5844-4-44-4-4400-4-444−4i4i00−4i4i0000004i−4i0000000000000000000000000000000000000000000
χ594-444-4-4-444i−4i0000−4i4i4i−4i4i−4i-440000000000000000000000000000000000000000000000000
χ604-444-4-4-44−4i4i00004i−4i−4i4i−4i4i-440000000000000000000000000000000000000000000000000
χ614-44-444-4-44i−4i-44-4400−4i4i0000000000−4i4i00000000000000000000000000000000000000000
χ624-44-444-4-4−4i4i-44-44004i−4i00000000004i−4i00000000000000000000000000000000000000000
χ634-4-444-44-4004-4-44000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ644-4-444-44-4004-4-4400000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ654-4-444-44-400-444-400000000000000000000000004i−4i000000000000000000000000000000
χ664-4-444-44-400-444-40000000000000000000000000−4i4i000000000000000000000000000000
χ674-4-4-4-44440000004400-4-40000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ684-4-4-4-44440000004400-4-4000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ694-4-4-4-4444000000-4-400440000000000000000000002-2-222-2-220000000000000000000000
χ704-4-4-4-4444000000-4-40044000000000000000000000-222-2-222-20000000000000000000000
χ7188-88-88-8-8000000000000000000000000000000000000000000000000000000000000000

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