Finite Group Databasebeta

← Group #481456

Character table — Group #481456

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444448888888888888888881616161611112222224444444488888888888888888816161616
order12222244442244444444888888888888888822442222224444224444444488888888888888882244
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
χ9111111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−iii−i−iii−i−i1-11-1111111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ10111111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−i−i−iii−i−iii-11-11111111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ11111111-1-1-1-11111-1-1-1-11-1−i−iii−i−iiiii−i−iii−i−i-11-11111111-1-1-1-11111-1-1-1-11-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ12111111-1-1-1-11111-1-1-1-11-1−i−iii−i−iii−i−iii−i−iii1-11-1111111-1-1-1-11111-1-1-1-11-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ13111111-1-1-1-1-1-1-1-111111-111-1-1-1-11111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111-111-1-1-1-11111-1-1-1-1111-1-11
χ14111111-1-1-1-1-1-1-1-111111-111-1-1-1-111-1-11111-1-1-111-1111111-1-1-1-1-1-1-1-111111-111-1-1-1-111-1-11111-1-1-111-1
χ15111111-1-1-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-111-111-1111111-1-1-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-111-111-1
χ16111111-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-11111-1-11-1-11111111-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-11111-1-11-1-11
χ17222222222222-2-22-2-22-2-200000000000000000000222222222222-2-22-2-22-2-200000000000000000000
χ182222222222-2-222-222-2-2-2000000000000000000002222222222-2-222-222-2-2-200000000000000000000
χ19222222-2-2-2-222-2-2-222-2-2200000000000000000000222222-2-2-2-222-2-2-222-2-2200000000000000000000
χ20222222-2-2-2-2-2-2222-2-22-2200000000000000000000222222-2-2-2-2-2-2222-2-22-2200000000000000000000
χ2122-2-22-222-2-2002i−2i02i−2i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000022-2-22-222-2-2002i−2i02i−2i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ2222-2-22-222-2-2002i−2i02i−2i00000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000022-2-22-222-2-2002i−2i02i−2i00000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ2322-2-22-222-2-200−2i2i0−2i2i000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000022-2-22-222-2-200−2i2i0−2i2i000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ2422-2-22-222-2-200−2i2i0−2i2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000022-2-22-222-2-200−2i2i0−2i2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ2522-2-22-2-2-222002i−2i0−2i2i000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i000022-2-22-2-2-222002i−2i0−2i2i000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ2622-2-22-2-2-222002i−2i0−2i2i00000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i000022-2-22-2-2-222002i−2i0−2i2i00000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ2722-2-22-2-2-22200−2i2i02i−2i000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i000022-2-22-2-2-22200−2i2i02i−2i000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ2822-2-22-2-2-22200−2i2i02i−2i00000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i000022-2-22-2-2-22200−2i2i02i−2i00000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ2922-2-2-222-22-22-200200-200i2−i2i2−i2i2−i2i2−i200000000000022-2-2-222-22-22-200200-200i2−i2i2−i2i2−i2i2−i2000000000000
χ3022-2-2-222-22-22-200200-200−i2i2−i2i2−i2i2−i2i200000000000022-2-2-222-22-22-200200-200−i2i2−i2i2−i2i2−i2i2000000000000
χ3122-2-2-222-22-2-2200-2002002−22−2−22−2200000000000022-2-2-222-22-2-2200-2002002−22−2−22−22000000000000
χ3222-2-2-222-22-2-2200-200200−22−222−22−200000000000022-2-2-222-22-2-2200-200200−22−222−22−2000000000000
χ3322-2-2-22-22-222-200-2002002−2−222−2−2200000000000022-2-2-22-22-222-200-2002002−2−222−2−22000000000000
χ3422-2-2-22-22-222-200-200200−222−2−222−200000000000022-2-2-22-22-222-200-200200−222−2−222−2000000000000
χ3522-2-2-22-22-22-2200200-200i2−i2−i2i2−i2i2i2−i200000000000022-2-2-22-22-22-2200200-200i2−i2−i2i2−i2i2i2−i2000000000000
χ3622-2-2-22-22-22-2200200-200−i2i2i2−i2i2−i2−i2i200000000000022-2-2-22-22-22-2200200-200−i2i2i2−i2i2−i2−i2i2000000000000
χ374444-4-44-4-440000000000000000000000000000004444-4-44-4-44000000000000000000000000000000
χ384444-4-4-444-40000000000000000000000000000004444-4-4-444-4000000000000000000000000000000
χ398-88-80000000000000000000000000000000000008-88-8000000000000000000000000000000000000
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
χ49111111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−iii−i−iii−i−i1-11-1-1-1-1-1-1-11111-1-1-1-11111-11−i−iii−i−iii−i−iii−i−iii-11-11
χ50111111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−i−i−iii−i−iii-11-11-1-1-1-1-1-11111-1-1-1-11111-11−i−iii−i−iiiii−i−iii−i−i1-11-1
χ51111111-1-1-1-11111-1-1-1-11-1−i−iii−i−iiiii−i−iii−i−i-11-11-1-1-1-1-1-11111-1-1-1-11111-11ii−i−iii−i−i−i−iii−i−iii1-11-1
χ52111111-1-1-1-11111-1-1-1-11-1−i−iii−i−iii−i−iii−i−iii1-11-1-1-1-1-1-1-11111-1-1-1-11111-11ii−i−iii−i−iii−i−iii−i−i-11-11
χ53111111-1-1-1-1-1-1-1-111111-111-1-1-1-11111-1-1-1-1111-1-11-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-111-1
χ54111111-1-1-1-1-1-1-1-111111-111-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-111-1-1-1-1111-1-11
χ55111111-1-1-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-111-111-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1-111-1-11111-1-11-1-11
χ56111111-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-11111-1-11-1-11-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1-11111-1-1-1-111-111-1
χ57222222222222-2-22-2-22-2-200000000000000000000-2-2-2-2-2-2-2-2-2-2-2-222-222-22200000000000000000000
χ582222222222-2-222-222-2-2-200000000000000000000-2-2-2-2-2-2-2-2-2-222-2-22-2-222200000000000000000000
χ59222222-2-2-2-222-2-2-222-2-2200000000000000000000-2-2-2-2-2-22222-2-2222-2-222-200000000000000000000
χ60222222-2-2-2-2-2-2222-2-22-2200000000000000000000-2-2-2-2-2-2222222-2-2-222-22-200000000000000000000
χ6122-2-22-222-2-2002i−2i02i−2i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000-2-222-22-2-22200−2i2i0−2i2i00000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ6222-2-22-222-2-2002i−2i02i−2i00000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000-2-222-22-2-22200−2i2i0−2i2i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ6322-2-22-222-2-200−2i2i0−2i2i000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000-2-222-22-2-222002i−2i02i−2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ6422-2-22-222-2-200−2i2i0−2i2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000-2-222-22-2-222002i−2i02i−2i000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ6522-2-22-2-2-222002i−2i0−2i2i000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000-2-222-2222-2-200−2i2i02i−2i00000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ6622-2-22-2-2-222002i−2i0−2i2i00000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000-2-222-2222-2-200−2i2i02i−2i000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ6722-2-22-2-2-22200−2i2i02i−2i000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000-2-222-2222-2-2002i−2i0−2i2i00000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ6822-2-22-2-2-22200−2i2i02i−2i00000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000-2-222-2222-2-2002i−2i0−2i2i000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ6922-2-2-222-22-22-200200-200i2−i2i2−i2i2−i2i2−i2000000000000-2-2222-2-22-22-2200-200200−i2i2−i2i2−i2i2−i2i2000000000000
χ7022-2-2-222-22-22-200200-200−i2i2−i2i2−i2i2−i2i2000000000000-2-2222-2-22-22-2200-200200i2−i2i2−i2i2−i2i2−i2000000000000
χ7122-2-2-222-22-2-2200-2002002−22−2−22−22000000000000-2-2222-2-22-222-200200-200−22−222−22−2000000000000
χ7222-2-2-222-22-2-2200-200200−22−222−22−2000000000000-2-2222-2-22-222-200200-2002−22−2−22−22000000000000
χ7322-2-2-22-22-222-200-2002002−2−222−2−22000000000000-2-2222-22-22-2-2200200-200−222−2−222−2000000000000
χ7422-2-2-22-22-222-200-200200−222−2−222−2000000000000-2-2222-22-22-2-2200200-2002−2−222−2−22000000000000
χ7522-2-2-22-22-22-2200200-200i2−i2−i2i2−i2i2i2−i2000000000000-2-2222-22-22-22-200-200200−i2i2i2−i2i2−i2−i2i2000000000000
χ7622-2-2-22-22-22-2200200-200−i2i2i2−i2i2−i2−i2i2000000000000-2-2222-22-22-22-200-200200i2−i2−i2i2−i2i2i2−i2000000000000
χ774444-4-44-4-44000000000000000000000000000000-4-4-4-444-444-4000000000000000000000000000000
χ784444-4-4-444-4000000000000000000000000000000-4-4-4-4444-4-44000000000000000000000000000000
χ798-88-8000000000000000000000000000000000000-88-88000000000000000000000000000000000000
χ808-8-88000000000000000000000000000000000000-888-8000000000000000000000000000000000000

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