Finite Group Databasebeta

← Group #13022327

Character table — Group #13022327

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222224444444455558888888888101010101010101010101010101016161616161616161616161620202020202020202020202020202020404040404040404040404040
order12222244444444510101022224488101020202020224444888888882020202020202020404040404444888888888888444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ31111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111111-1-1-1-11111111111-1-1-1-1-1-1iiii−i−i−i−i111111111111-1-1-1-1iiiiii−i−i−i−i−i−i-1-1ii−i−i-1-1ii−i−i
χ6111111111111111111-1-1-1-11111111111-1-1-1-1-1-1−i−i−i−iiiii111111111111-1-1-1-1−i−i−i−i−i−iiiiiii-1-1−i−iii-1-1−i−iii
χ7111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-1-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11−i−iii11−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−iiiiiii11ii−i−i11ii−i−i
χ91111111111-1-1-1-11111111111-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1
χ101111111111-1-1-1-11111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111
χ111111111111-1-1-1-111111111-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ121111111111-1-1-1-111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1
χ131111111111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-11111ii−i−i−i−i−i−iiiii-1-1ii−i−i11−i−iii
χ141111111111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−i−iiiiiii−i−i−i−i-1-1−i−iii11ii−i−i
χ151111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-111111111ii−i−i−i−i−i−iiiii11−i−iii-1-1ii−i−i
χ161111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-111111111−i−iiiiiii−i−i−i−i11ii−i−i-1-1−i−iii
χ171-1-111-111-1-1ii−i−i1-1-1111-1-11-1i−i1-111-1-11-1-111-1ii−i−iii−i−iii−i−i11-1-1ii−i−iii−i−ii−i11-1-1i−i11-1-11-1i−ii−ii−i1-11-1
χ181-1-111-111-1-1ii−i−i1-1-1111-1-11-1i−i1-111-1-11-1-111-1−i−iii−i−iiiii−i−i11-1-1ii−i−iii−i−i−ii-1-111−ii-1-1111-1−ii−iii−i-11-11
χ191-1-111-111-1-1ii−i−i1-1-1111-1-1-11−ii1-111-1-11-1-111-1ii−i−iii−i−iii−i−i-1-111−i−iiiii−i−ii−i11-1-1i−i11-1-1-11−ii−ii−ii-11-11
χ201-1-111-111-1-1ii−i−i1-1-1111-1-1-11−ii1-111-1-11-1-111-1−i−iii−i−iiiii−i−i-1-111−i−iiiii−i−i−ii-1-111−ii-1-111-11i−ii−i−ii1-11-1
χ211-1-111-111-1-1ii−i−i1-1-11-1-1111-1i−i1-111-1-1-111-1-1111-1-1-1-111ii−i−i11-1-1ii−i−i−i−iii1-1−i−iii-11ii−i−i-111-1-11−ii−iii−i
χ221-1-111-111-1-1ii−i−i1-1-11-1-1111-1i−i1-111-1-1-111-1-11-1-11111-1-1ii−i−i11-1-1ii−i−i−i−iii-11ii−i−i1-1−i−iii-11-111-1−iii−i−ii
χ231-1-111-111-1-1ii−i−i1-1-11-1-111-11−ii1-111-1-1-111-1-1111-1-1-1-111ii−i−i-1-111−i−iii−i−iii1-1−i−iii-11ii−i−i1-1-111-1i−ii−i−ii
χ241-1-111-111-1-1ii−i−i1-1-11-1-111-11−ii1-111-1-1-111-1-11-1-11111-1-1ii−i−i-1-111−i−iii−i−iii-11ii−i−i1-1−i−iii1-11-1-11i−i−iii−i
χ251-1-111-111-1-1−i−iii1-1-1111-1-11-1−ii1-111-1-11-1-111-1ii−i−iii−i−i−i−iii11-1-1−i−iii−i−iiii−i-1-111i−i-1-1111-1i−ii−i−ii-11-11
χ261-1-111-111-1-1−i−iii1-1-1111-1-11-1−ii1-111-1-11-1-111-1−i−iii−i−iii−i−iii11-1-1−i−iii−i−iii−ii11-1-1−ii11-1-11-1−ii−ii−ii1-11-1
χ271-1-111-111-1-1−i−iii1-1-1111-1-1-11i−i1-111-1-11-1-111-1ii−i−iii−i−i−i−iii-1-111ii−i−i−i−iiii−i-1-111i−i-1-111-11−ii−iii−i1-11-1
χ281-1-111-111-1-1−i−iii1-1-1111-1-1-11i−i1-111-1-11-1-111-1−i−iii−i−iii−i−iii-1-111ii−i−i−i−iii−ii11-1-1−ii11-1-1-11i−ii−ii−i-11-11
χ291-1-111-111-1-1−i−iii1-1-11-1-1111-1−ii1-111-1-1-111-1-1111-1-1-1-111−i−iii11-1-1−i−iiiii−i−i1-1ii−i−i-11−i−iii-111-1-11i−ii−i−ii
χ301-1-111-111-1-1−i−iii1-1-11-1-1111-1−ii1-111-1-1-111-1-11-1-11111-1-1−i−iii11-1-1−i−iiiii−i−i-11−i−iii1-1ii−i−i-11-111-1i−i−iii−i
χ311-1-111-111-1-1−i−iii1-1-11-1-111-11i−i1-111-1-1-111-1-1111-1-1-1-111−i−iii-1-111ii−i−iii−i−i1-1ii−i−i-11−i−iii1-1-111-1−ii−iii−i
χ321-1-111-111-1-1−i−iii1-1-11-1-111-11i−i1-111-1-1-111-1-11-1-11111-1-1−i−iii-1-111ii−i−iii−i−i-11−i−iii1-1ii−i−i1-11-1-11−iii−i−ii
χ33222222-2-2-2-2000022222222000022-2-2-2-222-2-2-2-2000000000000000000000000002i−2i2i−2i002i−2i2i−2i000000000000
χ34222222-2-2-2-2000022222222000022-2-2-2-222-2-2-2-200000000000000000000000000−2i2i−2i2i00−2i2i−2i2i000000000000
χ35222222-2-2-2-200002222-2-2-2-2000022-2-2-2-2-2-22222000000000000000000000000002-22-200-22-22000000000000
χ36222222-2-2-2-200002222-2-2-2-2000022-2-2-2-2-2-2222200000000000000000000000000-22-22002-22-2000000000000
χ372222-2-22-22-20000222222220000-2-22-22-2-2-2-22-22222222220000000000000000-2-20000-2-20000000000000000
χ382222-2-22-22-20000222222220000-2-22-22-2-2-2-22-22-2-2-2-2-2-2-2-20000000000000000220000220000000000000000
χ392222-2-22-22-200002222-2-2-2-20000-2-22-22-2222-22-22i2i2i2i−2i−2i−2i−2i0000000000000000−2i−2i00002i2i0000000000000000
χ402222-2-22-22-200002222-2-2-2-20000-2-22-22-2222-22-2−2i−2i−2i−2i2i2i2i2i00000000000000002i2i0000−2i−2i0000000000000000
χ412222-2-2-22-222-22-2222222220000-2-2-22-22-2-22-22-2000000002-22-2000000002-22-2000000000000000000000000
χ422222-2-2-22-222-22-22222-2-2-2-20000-2-2-22-2222-22-22000000002-22-200000000-22-22000000000000000000000000
χ432222-2-2-22-22-22-22222222220000-2-2-22-22-2-22-22-200000000-22-2200000000-22-22000000000000000000000000
χ442222-2-2-22-22-22-222222-2-2-2-20000-2-2-22-2222-22-2200000000-22-22000000002-22-2000000000000000000000000
χ452-2-222-2-2-22200002-2-2222-2-200002-2-2-2222-22-2-22000000000000000000000000002i−2i−2i2i002i−2i−2i2i000000000000
χ462-2-222-2-2-22200002-2-2222-2-200002-2-2-2222-22-2-2200000000000000000000000000−2i2i2i−2i00−2i2i2i−2i000000000000
χ472-2-222-2-2-22200002-2-22-2-22200002-2-2-222-22-222-2000000000000000000000000002-2-2200-222-2000000000000
χ482-2-222-2-2-22200002-2-22-2-22200002-2-2-222-22-222-200000000000000000000000000-222-2002-2-22000000000000
χ492-2-22-222-2-2200002-2-2222-2-20000-222-2-22-2222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000−2i2i0000−2i2i0000000000000000
χ502-2-22-222-2-2200002-2-2222-2-20000-222-2-22-2222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000002i−2i00002i−2i0000000000000000
χ512-2-22-222-2-2200002-2-22-2-2220000-222-2-222-2-2-22222-2-2-2-2220000000000000000-2200002-20000000000000000
χ522-2-22-222-2-2200002-2-22-2-2220000-222-2-222-2-2-222-2-22222-2-200000000000000002-20000-220000000000000000
χ532-2-22-22-222-22i−2i−2i2i2-2-2222-2-20000-22-222-2-22-2-222000000002i−2i−2i2i000000002i−2i−2i2i000000000000000000000000
χ542-2-22-22-222-22i−2i−2i2i2-2-22-2-2220000-22-222-22-222-2-2000000002i−2i−2i2i00000000−2i2i2i−2i000000000000000000000000
χ552-2-22-22-222-2−2i2i2i−2i2-2-2222-2-20000-22-222-2-22-2-22200000000−2i2i2i−2i00000000−2i2i2i−2i000000000000000000000000
χ562-2-22-22-222-2−2i2i2i−2i2-2-22-2-2220000-22-222-22-222-2-200000000−2i2i2i−2i000000002i−2i−2i2i000000000000000000000000
χ5744444444444444-1-1-1-100004444-1-1-1-1-1-100000000000000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ5844444444444444-1-1-1-10000-4-4-4-4-1-1-1-1-1-100000000000000-1-1-1-1111111110000000000000000000000000000
χ594444444444-4-4-4-4-1-1-1-1000044-4-4-1-1-1-1-1-1000000000000001111-1-1-1-111110000000000000000000000000000
χ604444444444-4-4-4-4-1-1-1-10000-4-444-1-1-1-1-1-10000000000000011111111-1-1-1-10000000000000000000000000000
χ614444-4-4-44-444-44-4-1-1-1-100000000111-11-100000000000000-11-115−55−55−55−50000000000000000000000000000
χ624444-4-4-44-444-44-4-1-1-1-100000000111-11-100000000000000-11-11−55−55−55−550000000000000000000000000000
χ634444-4-4-44-44-44-44-1-1-1-100000000111-11-1000000000000001-11-15−55−5−55−550000000000000000000000000000
χ644444-4-4-44-44-44-44-1-1-1-100000000111-11-1000000000000001-11-1−55−555−55−50000000000000000000000000000
χ6544-4-4000000000044-4-44-44-4000000000000000022−2222−2222−2222−220000000000000000000000000000000000000000
χ6644-4-4000000000044-4-44-44-40000000000000000−2222−2222−2222−22220000000000000000000000000000000000000000
χ6744-4-4000000000044-4-4-44-4400000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ6844-4-4000000000044-4-4-44-440000000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ694-44-400000000004-44-44-4-4400000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ704-44-400000000004-44-44-4-440000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ714-44-400000000004-44-4-444-4000000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ724-44-400000000004-44-4-444-40000000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ734-4-444-444-4-44i4i−4i−4i-111-100004-44i−4i-11-1-11100000000000000−i−iii-1-111−i−iii0000000000000000000000000000
χ744-4-444-444-4-44i4i−4i−4i-111-10000-44−4i4i-11-1-11100000000000000−i−iii11-1-1ii−i−i0000000000000000000000000000
χ754-4-444-444-4-4−4i−4i4i4i-111-100004-4−4i4i-11-1-11100000000000000ii−i−i-1-111ii−i−i0000000000000000000000000000
χ764-4-444-444-4-4−4i−4i4i4i-111-10000-444i−4i-11-1-11100000000000000ii−i−i11-1-1−i−iii0000000000000000000000000000
χ774-4-44-44-444-44i−4i−4i4i-111-1000000001-11-1-1100000000000000−iii−i5−5−55i5−i5−i5i50000000000000000000000000000
χ784-4-44-44-444-44i−4i−4i4i-111-1000000001-11-1-1100000000000000−iii−i−555−5−i5i5i5−i50000000000000000000000000000
χ794-4-44-44-444-4−4i4i4i−4i-111-1000000001-11-1-1100000000000000i−i−ii5−5−55−i5i5i5−i50000000000000000000000000000
χ804-4-44-44-444-4−4i4i4i−4i-111-1000000001-11-1-1100000000000000i−i−ii−555−5i5−i5−i5i50000000000000000000000000000
χ81888888-8-8-8-80000-2-2-2-200000000-2-22222000000000000000000000000000000000000000000000000000000
χ828888-8-88-88-80000-2-2-2-20000000022-22-22000000000000000000000000000000000000000000000000000000
χ838-8-888-8-8-8880000-222-200000000-2222-2-2000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-880000-222-2000000002-2-222-2000000000000000000000000000000000000000000000000000000
χ851616-16-160000000000-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ8616-1616-160000000000-44-4400000000000000000000000000000000000000000000000000000000000000000000

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