Finite Group Databasebeta

← Group #119970

Character table — Group #119970

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444422444422444444444444448888888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1
χ101111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii-1-111
χ111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i-1-111
χ121111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii11-1-1
χ131111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii11-1-1
χ141111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−i-1-111
χ151111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii-1-111
χ161111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i11-1-1
χ1722222222222222-2-2222222-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ1822222222222222-2-2222222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ192222222222-2-2-2-22222-2-2-2-22222-2-2-2-222-2-2-2-222000000000000000000000000000000000000
χ202222222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000
χ2122222222-2-2222222-2-2-2-2-2-222-2-222-2-20000000000000000000000000000000000002i−2i2i−2i0000
χ2222222222-2-2222222-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000−2i2i−2i2i0000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2522222222-2-2-2-2-2-222-2-2222222-2-2-2-22200000000000000000000000022-2-2-2-222000000000000
χ2622222222-2-2-2-2-2-222-2-2222222-2-2-2-222000000000000000000000000-2-22222-2-2000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-20000000000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000000000000000-222-20000
χ2922-222-2-2-22-22i2i−2i−2i002-22i2i−2i−2i00000000002i−2i002-21+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000
χ3022-222-2-2-22-22i2i−2i−2i002-22i2i−2i−2i00000000002i−2i002-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000
χ3122-222-2-2-22-22i2i−2i−2i002-22i2i−2i−2i0000000000−2i2i00-221+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000
χ3222-222-2-2-22-22i2i−2i−2i002-22i2i−2i−2i0000000000−2i2i00-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000
χ3322-222-2-2-22-2−2i−2i2i2i002-2−2i−2i2i2i00000000002i−2i00-221−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000
χ3422-222-2-2-22-2−2i−2i2i2i002-2−2i−2i2i2i00000000002i−2i00-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000
χ3522-222-2-2-22-2−2i−2i2i2i002-2−2i−2i2i2i0000000000−2i2i002-21−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000
χ3622-222-2-2-22-2−2i−2i2i2i002-2−2i−2i2i2i0000000000−2i2i002-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000
χ372-222-22-2-2-222i−2i2i−2i002-22i−2i2i−2i000000002-2002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ382-222-22-2-2-222i−2i2i−2i002-22i−2i2i−2i000000002-2002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ392-222-22-2-2-222i−2i2i−2i002-22i−2i2i−2i00000000-2200−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ402-222-22-2-2-222i−2i2i−2i002-22i−2i2i−2i00000000-2200−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ412-222-22-2-2-22−2i2i−2i2i002-2−2i2i−2i2i000000002-200−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ422-222-22-2-2-22−2i2i−2i2i002-2−2i2i−2i2i000000002-200−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ432-222-22-2-2-22−2i2i−2i2i002-2−2i2i−2i2i00000000-22002i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ442-222-22-2-2-22−2i2i−2i2i002-2−2i2i−2i2i00000000-22002i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ452-2-22-2-222222-2-2222-2-2-222-2-2-2-222-22-200000000000000000000000000000000000000002i−2i2i−2i
χ462-2-22-2-222222-2-2222-2-2-222-2-2-2-222-22-20000000000000000000000000000000000000000−2i2i−2i2i
χ472-2-22-2-222222-2-22-2-2-2-2-222-2222-2-22-22000000000000000000000000000000002i−2i2i−2i00000000
χ482-2-22-2-222222-2-22-2-2-2-2-222-2222-2-22-2200000000000000000000000000000000−2i2i−2i2i00000000
χ492-2-22-2-22222-222-222-2-22-2-22-2-2-22-22-22000000000000000000000000000000002i−2i−2i2i00000000
χ502-2-22-2-22222-222-222-2-22-2-22-2-2-22-22-2200000000000000000000000000000000−2i2i2i−2i00000000
χ512-2-22-2-22222-222-2-2-2-2-22-2-22222-22-22-200000000000000000000000000000000000000002i−2i−2i2i
χ522-2-22-2-22222-222-2-2-2-2-22-2-22222-22-22-20000000000000000000000000000000000000000−2i2i2i−2i
χ532-2-22-2-222-2-22-2-2222222-2-22-2-22-22-2-2200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ542-2-22-2-222-2-22-2-2222222-2-22-2-22-22-2-220000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ552-2-22-2-222-2-22-2-22-2-2222-2-2222-22-222-2000000002-2-222-2-220000000000000000000000000000
χ562-2-22-2-222-2-22-2-22-2-2222-2-2222-22-222-200000000-222-2-222-20000000000000000000000000000
χ572-2-22-2-222-2-2-222-22222-222-2-2-22-2-222-2000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ582-2-22-2-222-2-2-222-22222-222-2-2-22-2-222-200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ592-2-22-2-222-2-2-222-2-2-222-222-222-222-2-2200000000000000002-2-222-2-2200000000000000000000
χ602-2-22-2-222-2-2-222-2-2-222-222-222-222-2-220000000000000000-222-2-222-200000000000000000000
χ6144-444-4-4-4-444i4i−4i−4i00-44−4i−4i4i4i0000000000000000000000000000000000000000000000000000
χ6244-444-4-4-4-44−4i−4i4i4i00-444i4i−4i−4i0000000000000000000000000000000000000000000000000000
χ6344-4-4-444-40000004i−4i0000004i−4i000000000000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000
χ6444-4-4-444-40000004i−4i0000004i−4i00000000000000000000000000000000−2−2i2+2i−2+2i2−2i00000000000000
χ6544-4-4-444-4000000−4i4i000000−4i4i000000000000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000
χ6644-4-4-444-4000000−4i4i000000−4i4i00000000000000000000000000000000−2+2i2−2i−2−2i2+2i00000000000000
χ674-444-44-4-44-44i−4i4i−4i00-44−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ684-444-44-4-44-4−4i4i−4i4i00-444i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ694-44-44-44-40000004i−4i000000−4i4i0000000000000000000000000000002+2i−2−2i00002−2i−2+2i000000000000
χ704-44-44-44-40000004i−4i000000−4i4i000000000000000000000000000000−2−2i2+2i0000−2+2i2−2i000000000000
χ714-44-44-44-4000000−4i4i0000004i−4i0000000000000000000000000000002−2i−2+2i00002+2i−2−2i000000000000
χ724-44-44-44-4000000−4i4i0000004i−4i000000000000000000000000000000−2+2i2−2i0000−2−2i2+2i000000000000
χ73888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000

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