Finite Group Databasebeta

← Group #117120

Character table — Group #117120

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444224444444444224444444444444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ121111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ131111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ141111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ151111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-20000000022-2-222-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-200000000-2-222-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-222-2-20000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-222-2-2220000000000000000
χ2322222222-2-2-2-22222-2-2-2-22-22-22-22-200000000000000000000000000002i−2i2i−2i00000000
χ2422222222-2-2-2-22222-2-2-2-22-22-22-22-20000000000000000000000000000−2i2i−2i2i00000000
χ2522222222-2-2-2-22222-2-2-2-2-22-22-22-220000000000000000000000002-22-2000000000000
χ2622222222-2-2-2-22222-2-2-2-2-22-22-22-22000000000000000000000000-22-22000000000000
χ2722222222-2-2-2-2-2-2-2-222222-22-2-22-220000000000000000000000000000000000002-22-2
χ2822222222-2-2-2-2-2-2-2-222222-22-2-22-22000000000000000000000000000000000000-22-22
χ2922222222-2-2-2-2-2-2-2-22222-22-222-22-2000000000000000000000000000000002-22-20000
χ3022222222-2-2-2-2-2-2-2-22222-22-222-22-200000000000000000000000000000000-22-220000
χ312222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2220000000022-2-2-2-222000000000000000000000000
χ322222-2-2-2-222-2-222-2-2-2-22222-2-2-2-22200000000-2-22222-2-2000000000000000000000000
χ332222-2-2-2-222-2-2-2-22222-2-222-2-222-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ342222-2-2-2-222-2-2-2-22222-2-222-2-222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ352222-2-2-2-222-2-2-2-22222-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ362222-2-2-2-222-2-2-2-22222-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ372222-2-2-2-2-2-22222-2-222-2-22-2-22-222-20000000000000000000000002-2-22000000000000
χ382222-2-2-2-2-2-22222-2-222-2-22-2-22-222-2000000000000000000000000-222-2000000000000
χ392222-2-2-2-2-2-22222-2-222-2-2-222-22-2-2200000000000000000000000000002i−2i−2i2i00000000
χ402222-2-2-2-2-2-22222-2-222-2-2-222-22-2-220000000000000000000000000000−2i2i2i−2i00000000
χ412222-2-2-2-2-2-222-2-222-2-2222-2-222-2-22000000000000000000000000000000002i−2i−2i2i0000
χ422222-2-2-2-2-2-222-2-222-2-2222-2-222-2-2200000000000000000000000000000000−2i2i2i−2i0000
χ432222-2-2-2-2-2-222-2-222-2-222-222-2-222-20000000000000000000000000000000000002i−2i−2i2i
χ442222-2-2-2-2-2-222-2-222-2-222-222-2-222-2000000000000000000000000000000000000−2i2i2i−2i
χ452-22-22i2i−2i−2i2-22i−2i2-22i−2i2i−2i2-2000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i002i−2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ462-22-22i2i−2i−2i2-22i−2i2-22i−2i2i−2i2-2000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2i2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ472-22-22i2i−2i−2i2-22i−2i2-22i−2i2i−2i2-200000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002i−2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ482-22-22i2i−2i−2i2-22i−2i2-22i−2i2i−2i2-200000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2i2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ492-22-22i2i−2i−2i2-22i−2i-22−2i2i−2i2i-22000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i2i−2i002-2001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ502-22-22i2i−2i−2i2-22i−2i-22−2i2i−2i2i-22000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−2i2i00-2200−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ512-22-22i2i−2i−2i2-22i−2i-22−2i2i−2i2i-2200000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i2i−2i002-200−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ522-22-22i2i−2i−2i2-22i−2i-22−2i2i−2i2i-2200000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2i2i00-22001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ532-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i−2i2i2-2000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i002i−2i00-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ542-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i−2i2i2-2000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2i2i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ552-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i−2i2i2-200000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i002i−2i00-221+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ562-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i−2i2i2-200000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2i2i002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ572-22-2−2i−2i2i2i2-2−2i2i-222i−2i2i−2i-22000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i2i−2i00-2200−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ582-22-2−2i−2i2i2i2-2−2i2i-222i−2i2i−2i-22000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−2i2i002-2001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ592-22-2−2i−2i2i2i2-2−2i2i-222i−2i2i−2i-2200000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i2i−2i00-22001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ602-22-2−2i−2i2i2i2-2−2i2i-222i−2i2i−2i-2200000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−2i2i002-200−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ614-44-44i4i−4i−4i-44−4i4i4-44i−4i−4i4i-44000000000000000000000000000000000000000000000000
χ624-44-44i4i−4i−4i-44−4i4i-44−4i4i4i−4i4-4000000000000000000000000000000000000000000000000
χ634-44-4−4i−4i4i4i-444i−4i4-4−4i4i4i−4i-44000000000000000000000000000000000000000000000000
χ644-44-4−4i−4i4i4i-444i−4i-444i−4i−4i4i4-4000000000000000000000000000000000000000000000000
χ6588-8-88-88-8000000000000000000000000000000000000000000000000000000000000
χ6688-8-8-88-88000000000000000000000000000000000000000000000000000000000000
χ678-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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