Finite Group Databasebeta

← Group #98182

Character table — Group #98182

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
χ311111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-1-1-1111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ711111111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ811111111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-111ii−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-111−i−iii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1ii−i−i−i−iii
χ1211111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1−i−iiiii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1111-1-1−i−iii−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1111-1-1ii−i−iii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111ii−i−i−i−iii
χ17222222222222-2-2-2-22222000022-2-2-2-20000-22200220000000000000000-2-2000000000000
χ18222222222222-2-2-2-22222000022-2-2-2-20000-2-2-200-2-2000000000000000022000000000000
χ192222222222-2-2222222-2-22222-2-222-2-222-2-2-200-2-200000000000000000000000000000000
χ202222222222-2-2222222-2-2-2-2-2-2-2-222-2-2-2-222-2002200000000000000000000000000000000
χ212222222222-2-2-2-2-2-222-2-20000-2-2-2-222000020000000000000000000000002-22-200000000
χ222222222222-2-2-2-2-2-222-2-20000-2-2-2-22200002000000000000000000000000-22-2200000000
χ2322222222-2-2222222-2-2222222-2-2-2-222-2-222-200-2-200000000000000000000000000000000
χ2422222222-2-2222222-2-222-2-2-2-2-2-2-2-22222-2-2-2002200000000000000000000000000000000
χ2522222222-2-222-2-2-2-2-2-2220000-2-222-2-2000020000000000000000000000002-2-2200000000
χ2622222222-2-222-2-2-2-2-2-2220000-2-222-2-200002000000000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200002222220000-22200-2-200000000000000002-2000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200002222220000-2-2-200220000000000000000-22000000000000
χ2922-22-2-2-22002i−2i22-2-2002i−2i2i2i−2i−2i00002i−2i002-200000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000001−i−1+i1+i−1−i0000
χ3022-22-2-2-22002i−2i22-2-2002i−2i2i2i−2i−2i00002i−2i002-20000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000−1+i1−i−1−i1+i0000
χ3122-22-2-2-22002i−2i22-2-2002i−2i−2i−2i2i2i00002i−2i00-2200000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000−1+i1−i−1−i1+i0000
χ3222-22-2-2-22002i−2i22-2-2002i−2i−2i−2i2i2i00002i−2i00-220000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000001−i−1+i1+i−1−i0000
χ3322-22-2-2-2200−2i2i22-2-200−2i2i2i2i−2i−2i0000−2i2i00-2200000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000−1−i1+i−1+i1−i0000
χ3422-22-2-2-2200−2i2i22-2-200−2i2i2i2i−2i−2i0000−2i2i00-220000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000001+i−1−i1−i−1+i0000
χ3522-22-2-2-2200−2i2i22-2-200−2i2i−2i−2i2i2i0000−2i2i002-200000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000001+i−1−i1−i−1+i0000
χ3622-22-2-2-2200−2i2i22-2-200−2i2i−2i−2i2i2i0000−2i2i002-20000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000−1−i1+i−1+i1−i0000
χ372-22-22-2-222i−2i002-22-22i−2i002i−2i2i−2i002i−2i002-2000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000001+i−1−i1−i−1+i
χ382-22-22-2-222i−2i002-22-22i−2i002i−2i2i−2i002i−2i002-200000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−1−i1+i−1+i1−i
χ392-22-22-2-222i−2i002-22-22i−2i00−2i2i−2i2i002i−2i00-22000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−1−i1+i−1+i1−i
χ402-22-22-2-222i−2i002-22-22i−2i00−2i2i−2i2i002i−2i00-2200000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000001+i−1−i1−i−1+i
χ412-22-22-2-22−2i2i002-22-2−2i2i002i−2i2i−2i00−2i2i00-22000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−1+i1−i−1−i1+i
χ422-22-22-2-22−2i2i002-22-2−2i2i002i−2i2i−2i00−2i2i00-2200000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000001−i−1+i1+i−1−i
χ432-22-22-2-22−2i2i002-22-2−2i2i00−2i2i−2i2i00−2i2i002-2000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000001−i−1+i1+i−1−i
χ442-22-22-2-22−2i2i002-22-2−2i2i00−2i2i−2i2i00−2i2i002-200000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−1+i1−i−1−i1+i
χ452-2-222-22-22i−2i−2i2i0000−2i2i2i−2i00002-20000000002-2002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ462-2-222-22-22i−2i−2i2i0000−2i2i2i−2i00002-20000000002-2002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ472-2-222-22-22i−2i−2i2i0000−2i2i2i−2i00002-2000000000-2200−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ482-2-222-22-22i−2i−2i2i0000−2i2i2i−2i00002-2000000000-2200−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ492-2-222-22-2−2i2i2i−2i00002i−2i−2i2i00002-20000000002-200−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ502-2-222-22-2−2i2i2i−2i00002i−2i−2i2i00002-20000000002-200−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ512-2-222-22-2−2i2i2i−2i00002i−2i−2i2i00002-2000000000-22002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ522-2-222-22-2−2i2i2i−2i00002i−2i−2i2i00002-2000000000-22002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ5344-44-4-4-44004i−4i-4-444004i−4i00000000−4i4i00000000000000000000000000000000000000000
χ5444-44-4-4-4400−4i4i-4-44400−4i4i000000004i−4i00000000000000000000000000000000000000000
χ5544-4-444-4-444000000-4-400000000000000000000000000000002-2-222-2-2200000000000000
χ5644-4-444-4-444000000-4-40000000000000000000000000000000-222-2-222-200000000000000
χ5744-4-444-4-4-4-40000004400000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ5844-4-444-4-4-4-4000000440000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ594-444-44-4-40044000000-4-40000000000000000000002-2-222-2-220000000000000000000000
χ604-444-44-4-40044000000-4-4000000000000000000000-222-2-222-20000000000000000000000
χ614-444-44-4-400-4-4000000440000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ624-444-44-4-400-4-400000044000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ634-44-44-4-444i−4i00-44-444i−4i00000000−4i4i0000000000000000000000000000000000000000000
χ644-44-44-4-44−4i4i00-44-44−4i4i000000004i−4i0000000000000000000000000000000000000000000
χ654-4-444-44-44i−4i4i−4i0000−4i4i−4i4i0000-44000000000000000000000000000000000000000000000
χ664-4-444-44-4−4i4i−4i4i00004i−4i4i−4i0000-44000000000000000000000000000000000000000000000
χ674-4-4-4-444400004-4-4400004-4-4400000000000000000000000000000000000000000000000
χ684-4-4-4-444400004-4-440000-444-400000000000000000000000000000000000000000000000
χ694-4-4-4-44440000-444-40000000000000000000004-400000000000000000000000000000000
χ704-4-4-4-44440000-444-4000000000000000000000-4400000000000000000000000000000000
χ71888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000

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