Finite Group Databasebeta

← Group #481513

Character table — Group #481513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444448888888888888888881616161611112222224444444488888888888888888816161616
order12222244442244444424444444448888888844442222224444224444442444444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-11111111111-1-1-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ61111111111-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1111111111111-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111
χ71111111111-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1111111111111-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ81111111111-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-11111111111-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ9111111-1-1-1-111-1-1-1-111-1111-1-111-1-111-1-111-1-11-11-1111111-1-1-1-111-1-1-1-111-1111-1-111-1-111-1-111-1-11-11-1
χ10111111-1-1-1-111-1-1-1-111-1111-1-111-1-1-1-111-1-111-11-11111111-1-1-1-111-1-1-1-111-1111-1-111-1-1-1-111-1-111-11-11
χ11111111-1-1-1-111-1-1-1-111-11-1-111-1-11111-1-111-1-1-11-11111111-1-1-1-111-1-1-1-111-11-1-111-1-11111-1-111-1-1-11-11
χ12111111-1-1-1-111-1-1-1-111-11-1-111-1-111-1-111-1-1111-11-1111111-1-1-1-111-1-1-1-111-11-1-111-1-111-1-111-1-1111-11-1
χ13111111-1-1-1-1-1-11111-1-1-11ii−i−i−i−iiiii−i−i−i−iii1-1-11111111-1-1-1-1-1-11111-1-1-11ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ14111111-1-1-1-1-1-11111-1-1-11ii−i−i−i−iii−i−iiiii−i−i-111-1111111-1-1-1-1-1-11111-1-1-11ii−i−i−i−iii−i−iiiii−i−i-111-1
χ15111111-1-1-1-1-1-11111-1-1-11−i−iiiii−i−iii−i−i−i−iii-111-1111111-1-1-1-1-1-11111-1-1-11−i−iiiii−i−iii−i−i−i−iii-111-1
χ16111111-1-1-1-1-1-11111-1-1-11−i−iiiii−i−i−i−iiiii−i−i1-1-11111111-1-1-1-1-1-11111-1-1-11−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ17222222222222-2-222-2-2-2-200000000000000000000222222222222-2-222-2-2-2-200000000000000000000
χ182222222222-2-222-2-222-2-2000000000000000000002222222222-2-222-2-222-2-200000000000000000000
χ19222222-2-2-2-22222-2-2-2-22-200000000000000000000222222-2-2-2-22222-2-2-2-22-200000000000000000000
χ20222222-2-2-2-2-2-2-2-222222-200000000000000000000222222-2-2-2-2-2-2-2-222222-200000000000000000000
χ212-22-22-22i2i−2i−2i002-2002i−2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000002-22-22-22i2i−2i−2i002-2002i−2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000
χ222-22-22-22i2i−2i−2i002-2002i−2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000002-22-22-22i2i−2i−2i002-2002i−2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000
χ232-22-22-22i2i−2i−2i00-2200−2i2i001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000002-22-22-22i2i−2i−2i00-2200−2i2i001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000
χ242-22-22-22i2i−2i−2i00-2200−2i2i00−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000002-22-22-22i2i−2i−2i00-2200−2i2i00−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000
χ252-22-22-2−2i−2i2i2i002-200−2i2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000002-22-22-2−2i−2i2i2i002-200−2i2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000
χ262-22-22-2−2i−2i2i2i002-200−2i2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000002-22-22-2−2i−2i2i2i002-200−2i2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000
χ272-22-22-2−2i−2i2i2i00-22002i−2i001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000002-22-22-2−2i−2i2i2i00-22002i−2i001+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000
χ282-22-22-2−2i−2i2i2i00-22002i−2i00−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000002-22-22-2−2i−2i2i2i00-22002i−2i00−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000
χ292-22-2-222i−2i2i−2i2-2002i−2i0000000000002−2i2−i22−2i2−i200002-22-2-222i−2i2i−2i2-2002i−2i0000000000002−2i2−i22−2i2−i20000
χ302-22-2-222i−2i2i−2i2-2002i−2i000000000000−22−i2i2−22−i2i200002-22-2-222i−2i2i−2i2-2002i−2i000000000000−22−i2i2−22−i2i20000
χ312-22-2-222i−2i2i−2i-2200−2i2i000000000000i2−i2−22−i2i22−200002-22-2-222i−2i2i−2i-2200−2i2i000000000000i2−i2−22−i2i22−20000
χ322-22-2-222i−2i2i−2i-2200−2i2i000000000000−i2i22−2i2−i2−2200002-22-2-222i−2i2i−2i-2200−2i2i000000000000−i2i22−2i2−i2−220000
χ332-22-2-22−2i2i−2i2i2-200−2i2i0000000000002−2−i2i22−2−i2i200002-22-2-22−2i2i−2i2i2-200−2i2i0000000000002−2−i2i22−2−i2i20000
χ342-22-2-22−2i2i−2i2i2-200−2i2i000000000000−22i2−i2−22i2−i200002-22-2-22−2i2i−2i2i2-200−2i2i000000000000−22i2−i2−22i2−i20000
χ352-22-2-22−2i2i−2i2i-22002i−2i000000000000i2−i22−2−i2i2−2200002-22-2-22−2i2i−2i2i-22002i−2i000000000000i2−i22−2−i2i2−220000
χ362-22-2-22−2i2i−2i2i-22002i−2i000000000000−i2i2−22i2−i22−200002-22-2-22−2i2i−2i2i-22002i−2i000000000000−i2i2−22i2−i22−20000
χ374444-4-44-4-440000000000000000000000000000004444-4-44-4-44000000000000000000000000000000
χ384444-4-4-444-40000000000000000000000000000004444-4-4-444-4000000000000000000000000000000
χ3988-8-800000000000000000000000000000000000088-8-8000000000000000000000000000000000000
χ408-8-880000000000000000000000000000000000008-8-88000000000000000000000000000000000000
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ421111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ4311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ4411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ451111111111-1-1-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111
χ461111111111-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1
χ471111111111-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1
χ481111111111-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111
χ49111111-1-1-1-111-1-1-1-111-1111-1-111-1-111-1-111-1-11-11-1-1-1-1-1-1-11111-1-11111-1-11-1-1-111-1-111-1-111-1-111-11-11
χ50111111-1-1-1-111-1-1-1-111-1111-1-111-1-1-1-111-1-111-11-11-1-1-1-1-1-11111-1-11111-1-11-1-1-111-1-11111-1-111-1-11-11-1
χ51111111-1-1-1-111-1-1-1-111-11-1-111-1-11111-1-111-1-1-11-11-1-1-1-1-1-11111-1-11111-1-11-111-1-111-1-1-1-111-1-1111-11-1
χ52111111-1-1-1-111-1-1-1-111-11-1-111-1-111-1-111-1-1111-11-1-1-1-1-1-1-11111-1-11111-1-11-111-1-111-1-111-1-111-1-1-11-11
χ53111111-1-1-1-1-1-11111-1-1-11ii−i−i−i−iiiii−i−i−i−iii1-1-11-1-1-1-1-1-1111111-1-1-1-1111-1−i−iiiii−i−i−i−iiiii−i−i-111-1
χ54111111-1-1-1-1-1-11111-1-1-11ii−i−i−i−iii−i−iiiii−i−i-111-1-1-1-1-1-1-1111111-1-1-1-1111-1−i−iiiii−i−iii−i−i−i−iii1-1-11
χ55111111-1-1-1-1-1-11111-1-1-11−i−iiiii−i−iii−i−i−i−iii-111-1-1-1-1-1-1-1111111-1-1-1-1111-1ii−i−i−i−iii−i−iiiii−i−i1-1-11
χ56111111-1-1-1-1-1-11111-1-1-11−i−iiiii−i−i−i−iiiii−i−i1-1-11-1-1-1-1-1-1111111-1-1-1-1111-1ii−i−i−i−iiiii−i−i−i−iii-111-1
χ57222222222222-2-222-2-2-2-200000000000000000000-2-2-2-2-2-2-2-2-2-2-2-222-2-2222200000000000000000000
χ582222222222-2-222-2-222-2-200000000000000000000-2-2-2-2-2-2-2-2-2-222-2-222-2-22200000000000000000000
χ59222222-2-2-2-22222-2-2-2-22-200000000000000000000-2-2-2-2-2-22222-2-2-2-22222-2200000000000000000000
χ60222222-2-2-2-2-2-2-2-222222-200000000000000000000-2-2-2-2-2-222222222-2-2-2-2-2200000000000000000000
χ612-22-22-22i2i−2i−2i002-2002i−2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000-22-22-22−2i−2i2i2i00-2200−2i2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000
χ622-22-22-22i2i−2i−2i002-2002i−2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000-22-22-22−2i−2i2i2i00-2200−2i2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000
χ632-22-22-22i2i−2i−2i00-2200−2i2i001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000-22-22-22−2i−2i2i2i002-2002i−2i00−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000
χ642-22-22-22i2i−2i−2i00-2200−2i2i00−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000-22-22-22−2i−2i2i2i002-2002i−2i001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000
χ652-22-22-2−2i−2i2i2i002-200−2i2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000-22-22-222i2i−2i−2i00-22002i−2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000
χ662-22-22-2−2i−2i2i2i002-200−2i2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000-22-22-222i2i−2i−2i00-22002i−2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000
χ672-22-22-2−2i−2i2i2i00-22002i−2i001+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000-22-22-222i2i−2i−2i002-200−2i2i00−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000
χ682-22-22-2−2i−2i2i2i00-22002i−2i00−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000-22-22-222i2i−2i−2i002-200−2i2i001+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000
χ692-22-2-222i−2i2i−2i2-2002i−2i0000000000002−2i2−i22−2i2−i20000-22-222-2−2i2i−2i2i-2200−2i2i000000000000−22−i2i2−22−i2i20000
χ702-22-2-222i−2i2i−2i2-2002i−2i000000000000−22−i2i2−22−i2i20000-22-222-2−2i2i−2i2i-2200−2i2i0000000000002−2i2−i22−2i2−i20000
χ712-22-2-222i−2i2i−2i-2200−2i2i000000000000i2−i2−22−i2i22−20000-22-222-2−2i2i−2i2i2-2002i−2i000000000000−i2i22−2i2−i2−220000
χ722-22-2-222i−2i2i−2i-2200−2i2i000000000000−i2i22−2i2−i2−220000-22-222-2−2i2i−2i2i2-2002i−2i000000000000i2−i2−22−i2i22−20000
χ732-22-2-22−2i2i−2i2i2-200−2i2i0000000000002−2−i2i22−2−i2i20000-22-222-22i−2i2i−2i-22002i−2i000000000000−22i2−i2−22i2−i20000
χ742-22-2-22−2i2i−2i2i2-200−2i2i000000000000−22i2−i2−22i2−i20000-22-222-22i−2i2i−2i-22002i−2i0000000000002−2−i2i22−2−i2i20000
χ752-22-2-22−2i2i−2i2i-22002i−2i000000000000i2−i22−2−i2i2−220000-22-222-22i−2i2i−2i2-200−2i2i000000000000−i2i2−22i2−i22−20000
χ762-22-2-22−2i2i−2i2i-22002i−2i000000000000−i2i2−22i2−i22−20000-22-222-22i−2i2i−2i2-200−2i2i000000000000i2−i22−2−i2i2−220000
χ774444-4-44-4-44000000000000000000000000000000-4-4-4-444-444-4000000000000000000000000000000
χ784444-4-4-444-4000000000000000000000000000000-4-4-4-4444-4-44000000000000000000000000000000
χ7988-8-8000000000000000000000000000000000000-8-888000000000000000000000000000000000000
χ808-8-88000000000000000000000000000000000000-888-8000000000000000000000000000000000000

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