Finite Group Databasebeta

← Group #481455

Character table — Group #481455

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444448888888888888888881616161611112222224444444488888888888888888816161616
order12222222224444444444888888888888888824442222222222444444444488888888888888882444
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
χ911111-1-1-1-111111-1-1-1-11-1ii−i−iii−i−iii−i−iii−i−i1-11-111111-1-1-1-111111-1-1-1-11-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ1011111-1-1-1-111111-1-1-1-11-1ii−i−iii−i−i−i−iii−i−iii-11-1111111-1-1-1-111111-1-1-1-11-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ1111111-1-1-1-111111-1-1-1-11-1−i−iii−i−iiiii−i−iii−i−i-11-1111111-1-1-1-111111-1-1-1-11-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ1211111-1-1-1-111111-1-1-1-11-1−i−iii−i−iii−i−iii−i−iii1-11-111111-1-1-1-111111-1-1-1-11-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ1311111-1-1-1-11-1-1-1-111111-111-1-1-1-11111-1-1-1-1111-1-1111111-1-1-1-11-1-1-1-111111-111-1-1-1-11111-1-1-1-1111-1-11
χ1411111-1-1-1-11-1-1-1-111111-111-1-1-1-111-1-11111-1-1-111-111111-1-1-1-11-1-1-1-111111-111-1-1-1-111-1-11111-1-1-111-1
χ1511111-1-1-1-11-1-1-1-111111-1-1-11111-1-111-1-1-1-111-111-111111-1-1-1-11-1-1-1-111111-1-1-11111-1-111-1-1-1-111-111-1
χ1611111-1-1-1-11-1-1-1-111111-1-1-11111-1-1-1-11111-1-11-1-1111111-1-1-1-11-1-1-1-111111-1-1-11111-1-1-1-11111-1-11-1-11
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
χ1922222-2-2-2-2222-2-2-222-2-220000000000000000000022222-2-2-2-2222-2-2-222-2-2200000000000000000000
χ2022222-2-2-2-22-2-2222-2-22-220000000000000000000022222-2-2-2-22-2-2222-2-22-2200000000000000000000
χ212-22-2222-2-2-2002i−2i02i−2i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002-22-2222-2-2-2002i−2i02i−2i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ222-22-2222-2-2-2002i−2i02i−2i00000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002-22-2222-2-2-2002i−2i02i−2i00000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ232-22-2222-2-2-200−2i2i0−2i2i000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002-22-2222-2-2-200−2i2i0−2i2i000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ242-22-2222-2-2-200−2i2i0−2i2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002-22-2222-2-2-200−2i2i0−2i2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ252-22-22-2-222-2002i−2i0−2i2i000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00002-22-22-2-222-2002i−2i0−2i2i000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ262-22-22-2-222-2002i−2i0−2i2i00000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00002-22-22-2-222-2002i−2i0−2i2i00000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ272-22-22-2-222-200−2i2i02i−2i000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00002-22-22-2-222-200−2i2i02i−2i000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ282-22-22-2-222-200−2i2i02i−2i00000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00002-22-22-2-222-200−2i2i02i−2i00000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ292-22-2-22-22-222-200200-200i2−i2i2−i2i2−i2i2−i20000000000002-22-2-22-22-222-200200-200i2−i2i2−i2i2−i2i2−i2000000000000
χ302-22-2-22-22-222-200200-200−i2i2−i2i2−i2i2−i2i20000000000002-22-2-22-22-222-200200-200−i2i2−i2i2−i2i2−i2i2000000000000
χ312-22-2-22-22-22-2200-2002002−22−2−22−220000000000002-22-2-22-22-22-2200-2002002−22−2−22−22000000000000
χ322-22-2-22-22-22-2200-200200−22−222−22−20000000000002-22-2-22-22-22-2200-200200−22−222−22−2000000000000
χ332-22-2-2-22-2222-200-2002002−2−222−2−220000000000002-22-2-2-22-2222-200-2002002−2−222−2−22000000000000
χ342-22-2-2-22-2222-200-200200−222−2−222−20000000000002-22-2-2-22-2222-200-200200−222−2−222−2000000000000
χ352-22-2-2-22-222-2200200-200i2−i2−i2i2−i2i2i2−i20000000000002-22-2-2-22-222-2200200-200i2−i2−i2i2−i2i2i2−i2000000000000
χ362-22-2-2-22-222-2200200-200−i2i2i2−i2i2−i2−i2i20000000000002-22-2-2-22-222-2200200-200−i2i2i2−i2i2−i2−i2i2000000000000
χ374444-44-4-44-40000000000000000000000000000004444-44-4-44-4000000000000000000000000000000
χ384444-4-444-4-40000000000000000000000000000004444-4-444-4-4000000000000000000000000000000
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
χ4911111-1-1-1-111111-1-1-1-11-1ii−i−iii−i−iii−i−iii−i−i1-11-1-1-1-1-1-11111-1-1-1-1-11111-11−i−iii−i−iii−i−iii−i−iii-11-11
χ5011111-1-1-1-111111-1-1-1-11-1ii−i−iii−i−i−i−iii−i−iii-11-11-1-1-1-1-11111-1-1-1-1-11111-11−i−iii−i−iiiii−i−iii−i−i1-11-1
χ5111111-1-1-1-111111-1-1-1-11-1−i−iii−i−iiiii−i−iii−i−i-11-11-1-1-1-1-11111-1-1-1-1-11111-11ii−i−iii−i−i−i−iii−i−iii1-11-1
χ5211111-1-1-1-111111-1-1-1-11-1−i−iii−i−iii−i−iii−i−iii1-11-1-1-1-1-1-11111-1-1-1-1-11111-11ii−i−iii−i−iii−i−iii−i−i-11-11
χ5311111-1-1-1-11-1-1-1-111111-111-1-1-1-11111-1-1-1-1111-1-11-1-1-1-1-11111-11111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-111-1
χ5411111-1-1-1-11-1-1-1-111111-111-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-11111-11111-1-1-1-1-11-1-11111-1-111-1-1-1-1111-1-11
χ5511111-1-1-1-11-1-1-1-111111-1-1-11111-1-111-1-1-1-111-111-1-1-1-1-1-11111-11111-1-1-1-1-1111-1-1-1-111-1-11111-1-11-1-11
χ5611111-1-1-1-11-1-1-1-111111-1-1-11111-1-1-1-11111-1-11-1-11-1-1-1-1-11111-11111-1-1-1-1-1111-1-1-1-11111-1-1-1-111-111-1
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
χ5922222-2-2-2-2222-2-2-222-2-2200000000000000000000-2-2-2-2-22222-2-2-2222-2-222-200000000000000000000
χ6022222-2-2-2-22-2-2222-2-22-2200000000000000000000-2-2-2-2-22222-222-2-2-222-22-200000000000000000000
χ612-22-2222-2-2-2002i−2i02i−2i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000-22-22-2-2-222200−2i2i0−2i2i00000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ622-22-2222-2-2-2002i−2i02i−2i00000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000-22-22-2-2-222200−2i2i0−2i2i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ632-22-2222-2-2-200−2i2i0−2i2i000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000-22-22-2-2-2222002i−2i02i−2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ642-22-2222-2-2-200−2i2i0−2i2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000-22-22-2-2-2222002i−2i02i−2i000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ652-22-22-2-222-2002i−2i0−2i2i000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000-22-22-222-2-2200−2i2i02i−2i00000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ662-22-22-2-222-2002i−2i0−2i2i00000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000-22-22-222-2-2200−2i2i02i−2i000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ672-22-22-2-222-200−2i2i02i−2i000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000-22-22-222-2-22002i−2i0−2i2i00000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ682-22-22-2-222-200−2i2i02i−2i00000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000-22-22-222-2-22002i−2i0−2i2i000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ692-22-2-22-22-222-200200-200i2−i2i2−i2i2−i2i2−i2000000000000-22-222-22-22-2-2200-200200−i2i2−i2i2−i2i2−i2i2000000000000
χ702-22-2-22-22-222-200200-200−i2i2−i2i2−i2i2−i2i2000000000000-22-222-22-22-2-2200-200200i2−i2i2−i2i2−i2i2−i2000000000000
χ712-22-2-22-22-22-2200-2002002−22−2−22−22000000000000-22-222-22-22-22-200200-200−22−222−22−2000000000000
χ722-22-2-22-22-22-2200-200200−22−222−22−2000000000000-22-222-22-22-22-200200-2002−22−2−22−22000000000000
χ732-22-2-2-22-2222-200-2002002−2−222−2−22000000000000-22-2222-22-2-2-2200200-200−222−2−222−2000000000000
χ742-22-2-2-22-2222-200-200200−222−2−222−2000000000000-22-2222-22-2-2-2200200-2002−2−222−2−22000000000000
χ752-22-2-2-22-222-2200200-200i2−i2−i2i2−i2i2i2−i2000000000000-22-2222-22-2-22-200-200200−i2i2i2−i2i2−i2−i2i2000000000000
χ762-22-2-2-22-222-2200200-200−i2i2i2−i2i2−i2−i2i2000000000000-22-2222-22-2-22-200-200200i2−i2−i2i2−i2i2i2−i2000000000000
χ774444-44-4-44-4000000000000000000000000000000-4-4-4-44-444-44000000000000000000000000000000
χ784444-4-444-4-4000000000000000000000000000000-4-4-4-444-4-444000000000000000000000000000000
χ7988-8-8000000000000000000000000000000000000-8-888000000000000000000000000000000000000
χ808-8-88000000000000000000000000000000000000-888-8000000000000000000000000000000000000

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