Finite Group Databasebeta

← Group #142180

Character table — Group #142180

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-222-2-2-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-222-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2222222-2-222-2-222-2-200000000000000000000000000000000
χ2122-22-22-2-222-2-20000002-22200002-2-2-22-20000000022-2-2000022-2-20000000000000000
χ2222-22-22-2-222-2-20000002-22200002-2-2-22-200000000-2-2220000-2-2220000000000000000
χ2322-22-22-2-222-2-20000002-2-2-200002-222-2200002i2i−2i−2i00002i2i−2i−2i00000000000000000000
χ2422-22-22-2-222-2-20000002-2-2-200002-222-220000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000
χ2522-22-22-2-222-2-2000000-22220000-22-2-2-22000022-2-20000-2-22200000000000000000000
χ2622-22-22-2-222-2-2000000-22220000-22-2-2-220000-2-222000022-2-200000000000000000000
χ2722-22-22-2-222-2-2000000-22-2-20000-22222-2000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ2822-22-22-2-222-2-2000000-22-2-20000-22222-200000000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ292-222-2-2-222-22-22i2i−2i−2i2i−2i002i−2i0000002i−2i00002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ302-222-2-2-222-22-22i2i−2i−2i2i−2i002i−2i0000002i−2i00002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ312-222-2-2-222-22-22i2i−2i−2i2i−2i00−2i2i000000−2i2i0000-221−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i0000000000000000
χ322-222-2-2-222-22-22i2i−2i−2i2i−2i00−2i2i000000−2i2i0000-22−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i0000000000000000
χ332-222-2-2-222-22-2−2i−2i2i2i−2i2i002i−2i0000002i−2i0000-221+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i0000000000000000
χ342-222-2-2-222-22-2−2i−2i2i2i−2i2i002i−2i0000002i−2i0000-22−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i0000000000000000
χ352-222-2-2-222-22-2−2i−2i2i2i−2i2i00−2i2i000000−2i2i00002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ362-222-2-2-222-22-2−2i−2i2i2i−2i2i00−2i2i000000−2i2i00002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ372-222-2-2-22-22-222i2i−2i−2i−2i2i2-2002i2i−2i−2i-2200000000000000000000000000000000i2−i22−2i2−i22−2
χ382-222-2-2-22-22-222i2i−2i−2i−2i2i2-2002i2i−2i−2i-2200000000000000000000000000000000−i2i2−22−i2i2−22
χ392-222-2-2-22-22-222i2i−2i−2i−2i2i-2200−2i−2i2i2i2-2000000000000000000000000000000002−2−i2i2−22i2−i2
χ402-222-2-2-22-22-222i2i−2i−2i−2i2i-2200−2i−2i2i2i2-200000000000000000000000000000000−22i2−i22−2−i2i2
χ412-222-2-2-22-22-22−2i−2i2i2i2i−2i2-200−2i−2i2i2i-2200000000000000000000000000000000i2−i2−22i2−i2−22
χ422-222-2-2-22-22-22−2i−2i2i2i2i−2i2-200−2i−2i2i2i-2200000000000000000000000000000000−i2i22−2−i2i22−2
χ432-222-2-2-22-22-22−2i−2i2i2i2i−2i-22002i2i−2i−2i2-2000000000000000000000000000000002−2i2−i2−22−i2i2
χ442-222-2-2-22-22-22−2i−2i2i2i2i−2i-22002i2i−2i−2i2-200000000000000000000000000000000−22−i2i22−2i2−i2
χ452-2-222-22-22-2-22000000002i−2i2-22-200−2i2i002i−2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ462-2-222-22-22-2-22000000002i−2i2-22-200−2i2i002i−2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ472-2-222-22-22-2-22000000002i−2i-22-2200−2i2i00−2i2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ482-2-222-22-22-2-22000000002i−2i-22-2200−2i2i00−2i2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ492-2-222-22-22-2-2200000000−2i2i2-22-2002i−2i00−2i2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ502-2-222-22-22-2-2200000000−2i2i2-22-2002i−2i00−2i2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ512-2-222-22-22-2-2200000000−2i2i-22-22002i−2i002i−2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ522-2-222-22-22-2-2200000000−2i2i-22-22002i−2i002i−2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ5344444444-4-4-4-44444-4-400000000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ55444-44-4-4-400004-44-400000000000000000000000000000000000000002-22-200000000
χ56444-44-4-4-400004-44-40000000000000000000000000000000000000000-22-2200000000
χ57444-44-4-4-40000-44-4400000000000000000000000000000000000000002-2-2200000000
χ58444-44-4-4-40000-44-440000000000000000000000000000000000000000-222-200000000
χ5944-44-44-4-4-4-44400000000004i−4i−4i4i000000000000000000000000000000000000000000
χ6044-44-44-4-4-4-4440000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ614-44-4-444-400004i−4i−4i4i0000000000000000000000000000000000002-22i−2i000000000000
χ624-44-4-444-400004i−4i−4i4i000000000000000000000000000000000000-22−2i2i000000000000
χ634-44-4-444-40000−4i4i4i−4i0000000000000000000000000000000000002-2−2i2i000000000000
χ644-44-4-444-40000−4i4i4i−4i000000000000000000000000000000000000-222i−2i000000000000
χ654-4-444-44-4-444-400000044000000-4-40000000000000000000000000000000000000000
χ664-4-444-44-4-444-4000000-4-4000000440000000000000000000000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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