Finite Group Databasebeta

← Group #13017107

Character table — Group #13017107

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size11112222444444444555588888888101010101010101010101010101010101616161616161616162020202020202020202020202020203232404040404040404040404040
order12224444458888101010222244882020202044444444444444442040404040404040404448888888888882020444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ3111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ511111111111111111-1-1-1-111111111-1-1iiii−i−i−i−iii−i−i-1-1111111111-1i−i-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i-1-1ii−i−i
χ611111111111111111-1-1-1-111111111-1-1−i−i−i−iiiii−i−iii-1-1111111111-1−ii-1-1-1-1−i−i−i−iiiii11-1-1−i−iii-1-1−i−iii
χ711111111111111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iii−i−i-1-111111-1-1-1-1-1i−i-1-1-1-1iiii−i−i−i−i-1-111−i−iii11−i−iii
χ811111111111111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−iii-1-111111-1-1-1-1-1−ii-1-1-1-1−i−i−i−iiiii-1-111ii−i−i11ii−i−i
χ91111111111-1-1-1-1111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ101111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-11111
χ111111111111-1-1-1-11111111-1-111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ121111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1
χ131111111111-1-1-1-1111-1-1-1-111-1-11111-1-1iiii−i−i−i−iii−i−i-1-11-1-1-1-1-1-1-1-1-1i−i1111−i−i−i−iiiii11-1-1ii−i−i11−i−iii
χ141111111111-1-1-1-1111-1-1-1-111-1-11111-1-1−i−i−i−iiiii−i−iii-1-11-1-1-1-1-1-1-1-1-1−ii1111iiii−i−i−i−i11-1-1−i−iii11ii−i−i
χ151111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1iiii−i−i−i−iii−i−i-1-11-1-1-1-11111-1i−i1111−i−i−i−iiiii-1-111−i−iii-1-1ii−i−i
χ161111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1−i−i−i−iiiii−i−iii-1-11-1-1-1-11111-1−ii1111iiii−i−i−i−i-1-111ii−i−i-1-1−i−iii
χ171111-1-1-1-111ii−i−i11111111-1i−i-1-1-1-1-1-111-1-111-1-11111-1-11ii−i−iii−i−i1-1-1ii−i−iii−i−iii−i−i1-11-11-11-1i−ii−ii−i
χ181111-1-1-1-111ii−i−i11111111-1i−i-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11ii−i−iii−i−i111ii−i−i−i−iii−i−iii1-11-1-11-11i−i−ii−ii
χ191111-1-1-1-111ii−i−i1111111-11−ii-1-1-1-1-1-111-1-111-1-11111-1-11ii−i−i−i−iii1-1-1ii−i−iii−i−iii−i−i-11-11-11-11−ii−ii−ii
χ201111-1-1-1-111ii−i−i1111111-11−ii-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11ii−i−i−i−iii111ii−i−i−i−iii−i−iii-11-111-11-1−iii−ii−i
χ211111-1-1-1-111ii−i−i111-1-1-1-11-1i−i-1-1-1-111ii−i−i−i−iiiii−i−i111ii−i−iii−i−i-1−ii−i−iii-1-11111-1-11-1-11i−i−ii−ii-111-1
χ221111-1-1-1-111ii−i−i111-1-1-1-11-1i−i-1-1-1-111−i−iiiii−i−i−i−iii111ii−i−iii−i−i-1i−i−i−iii11-1-1-1-1111-1-11−iii−i−ii1-1-11
χ231111-1-1-1-111ii−i−i111-1-1-1-1-11−ii-1-1-1-111ii−i−i−i−iiiii−i−i111ii−i−i−i−iii-1−ii−i−iii-1-11111-1-1-111-1−iii−ii−i1-1-11
χ241111-1-1-1-111ii−i−i111-1-1-1-1-11−ii-1-1-1-111−i−iiiii−i−i−i−iii111ii−i−i−i−iii-1i−i−i−iii11-1-1-1-111-111-1i−i−iii−i-111-1
χ251111-1-1-1-111−i−iii11111111-1−ii-1-1-1-1-1-111-1-111-1-11111-1-11−i−iii−i−iii1-1-1−i−iii−i−iii−i−iii1-11-11-11-1−ii−ii−ii
χ261111-1-1-1-111−i−iii11111111-1−ii-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11−i−iii−i−iii111−i−iiiii−i−iii−i−i1-11-1-11-11−iii−ii−i
χ271111-1-1-1-111−i−iii1111111-11i−i-1-1-1-1-1-111-1-111-1-11111-1-11−i−iiiii−i−i1-1-1−i−iii−i−iii−i−iii-11-11-11-11i−ii−ii−i
χ281111-1-1-1-111−i−iii1111111-11i−i-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11−i−iiiii−i−i111−i−iiiii−i−iii−i−i-11-111-11-1i−i−ii−ii
χ291111-1-1-1-111−i−iii111-1-1-1-11-1−ii-1-1-1-111ii−i−i−i−iiiii−i−i111−i−iii−i−iii-1−iiii−i−i11-1-1-1-1111-1-11i−i−iii−i1-1-11
χ301111-1-1-1-111−i−iii111-1-1-1-11-1−ii-1-1-1-111−i−iiiii−i−i−i−iii111−i−iii−i−iii-1i−iii−i−i-1-11111-1-11-1-11−iii−ii−i-111-1
χ311111-1-1-1-111−i−iii111-1-1-1-1-11i−i-1-1-1-111ii−i−i−i−iiiii−i−i111−i−iiiii−i−i-1−iiii−i−i11-1-1-1-111-111-1−iii−i−ii-111-1
χ321111-1-1-1-111−i−iii111-1-1-1-1-11i−i-1-1-1-111−i−iiiii−i−i−i−iii111−i−iiiii−i−i-1i−iii−i−i-1-11111-1-1-111-1i−i−ii−ii1-1-11
χ3322222-22-2-220000222222200002-22-22-222-2-222-2-2-2-2-2-22-2-200000000-22200000000000000000000000000
χ3422222-22-2-220000222222200002-22-22-2-2-222-2-22222222-2-200000000-2-2-200000000000000000000000000
χ3522222-22-2-220000222-2-2-2-200002-22-2-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-22-20000000022i−2i00000000000000000000000000
χ3622222-22-2-220000222-2-2-2-200002-22-2-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-22-2000000002−2i2i00000000000000000000000000
χ372222-22-22-22000022222220000-22-22-2222222222-2-2-2-2-22-200000000-2-2-200000000000000000000000000
χ382222-22-22-22000022222220000-22-22-22-2-2-2-2-2-2-2-22222-22-200000000-22200000000000000000000000000
χ392222-22-22-220000222-2-2-2-20000-22-222-22i2i2i2i−2i−2i−2i−2i−2i−2i2i2i2-2-2000000002−2i2i00000000000000000000000000
χ402222-22-22-220000222-2-2-2-20000-22-222-2−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i2-2-20000000022i−2i00000000000000000000000000
χ4122-2-2020-2022−22−22-2-222-2-20000020-2022-22-22-22-200000-202−22−200000002−22−22−22−22−22−200000000000000
χ4222-2-2020-2022−22−22-2-222-2-20000020-202-22-22-22-2200000-202−22−200000002−22−2−22−22−22−2200000000000000
χ4322-2-2020-2022−22−22-2-2-2-2220000020-20-22i−2i2i−2i−2i2i−2i2i00000202−22−20000000−22−22i2−i2i2−i2−i2i2−i2i200000000000000
χ4422-2-2020-2022−22−22-2-2-2-2220000020-20-2−2i2i−2i2i2i−2i2i−2i00000202−22−20000000−22−22−i2i2−i2i2i2−i2i2−i200000000000000
χ4522-2-2020-202−22−222-2-222-2-20000020-2022-22-22-22-200000-20−22−220000000−22−22−22−22−22−2200000000000000
χ4622-2-2020-202−22−222-2-222-2-20000020-202-22-22-22-2200000-20−22−220000000−22−222−22−22−22−200000000000000
χ4722-2-2020-202−22−222-2-2-2-2220000020-20-22i−2i2i−2i−2i2i−2i2i0000020−22−2200000002−22−2−i2i2−i2i2i2−i2i2−i200000000000000
χ4822-2-2020-202−22−222-2-2-2-2220000020-20-2−2i2i−2i2i2i−2i2i−2i0000020−22−2200000002−22−2i2−i2i2−i2−i2i2−i2i200000000000000
χ4922-2-20-20202i2−i2−i2i22-2-222-2-200000-2020-22-2-222-2-220000020i2−i2−i2i20000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000
χ5022-2-20-20202i2−i2−i2i22-2-222-2-200000-2020-2-222-2-222-20000020i2−i2−i2i20000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000000000
χ5122-2-20-20202i2−i2−i2i22-2-2-2-22200000-202022i−2i−2i2i−2i2i2i−2i00000-20i2−i2−i2i20000000−i2i2i2−i2−222−22−2−2200000000000000
χ5222-2-20-20202i2−i2−i2i22-2-2-2-22200000-20202−2i2i2i−2i2i−2i−2i2i00000-20i2−i2−i2i20000000−i2i2i2−i22−2−22−222−200000000000000
χ5322-2-20-20202−i2i2i2−i22-2-222-2-200000-2020-22-2-222-2-220000020−i2i2i2−i20000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000
χ5422-2-20-20202−i2i2i2−i22-2-222-2-200000-2020-2-222-2-222-20000020−i2i2i2−i20000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000000000
χ5522-2-20-20202−i2i2i2−i22-2-2-2-22200000-202022i−2i−2i2i−2i2i2i−2i00000-20−i2i2i2−i20000000i2−i2−i2i22−2−22−222−200000000000000
χ5622-2-20-20202−i2i2i2−i22-2-2-2-22200000-20202−2i2i2i−2i2i−2i−2i2i00000-20−i2i2i2−i20000000i2−i2−i2i2−222−22−2−2200000000000000
χ57444444444-14444-1-1-100004444-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1000000000000000-1-1000000000000
χ58444444444-14444-1-1-10000-4-4-4-4-1-1-1-10000000000000000-1-1-1-1-1111100000000000000011000000000000
χ59444444444-1-4-4-4-4-1-1-1000044-4-4-1-1-1-10000000000000000-111111111000000000000000-1-1000000000000
χ60444444444-1-4-4-4-4-1-1-10000-4-444-1-1-1-10000000000000000-11111-1-1-1-100000000000000011000000000000
χ614444-4-4-4-44-14i4i−4i−4i-1-1-100004-44i−4i11110000000000000000-1−i−iii−i−iii000000000000000-11000000000000
χ624444-4-4-4-44-14i4i−4i−4i-1-1-10000-44−4i4i11110000000000000000-1−i−iiiii−i−i0000000000000001-1000000000000
χ634444-4-4-4-44-1−4i−4i4i4i-1-1-100004-4−4i4i11110000000000000000-1ii−i−iii−i−i000000000000000-11000000000000
χ644444-4-4-4-44-1−4i−4i4i4i-1-1-10000-444i−4i11110000000000000000-1ii−i−i−i−iii0000000000000001-1000000000000
χ654-44-440-40040000-44-44-44-4000040-40-400000000000004000000000000000000000000000000000000000
χ664-44-440-40040000-44-4-44-44000040-4040000000000000-4000000000000000000000000000000000000000
χ674-44-4-4040040000-44-44-44-40000-404040000000000000-4000000000000000000000000000000000000000
χ684-44-4-4040040000-44-4-44-440000-4040-400000000000004000000000000000000000000000000000000000
χ694-4-440000040000-4-444-4-440000000000000000004-44-40000000000000000000000000000000000000000
χ704-4-440000040000-4-444-4-44000000000000000000-44-440000000000000000000000000000000000000000
χ714-4-440000040000-4-44-444-40000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ724-4-440000040000-4-44-444-4000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ7388888-88-8-8-20000-2-2-200000000-22-22000000000000000020000000000000000000000000000000000000
χ748888-88-88-8-20000-2-2-2000000002-22-2000000000000000020000000000000000000000000000000000000
χ7588-8-8080-80-242−4242−42-222000000000-20200000000000000000−22−22000000000000000000000000000000000
χ7688-8-8080-80-2−4242−4242-222000000000-202000000000000000002−22−2000000000000000000000000000000000
χ7788-8-80-8080-24i2−4i2−4i24i2-22200000000020-200000000000000000−i2i2i2−i2000000000000000000000000000000000
χ7888-8-80-8080-2−4i24i24i2−4i2-22200000000020-200000000000000000i2−i2−i2i2000000000000000000000000000000000
χ798-88-880-800-200002-2200000000-202000000000000000000000010−1010−1000000000000000000000000000000
χ808-88-880-800-200002-2200000000-2020000000000000000000000−1010−101000000000000000000000000000000
χ818-88-8-80800-200002-220000000020-20000000000000000000000i10−i10−i10i1000000000000000000000000000000
χ828-88-8-80800-200002-220000000020-20000000000000000000000−i10i10i10−i1000000000000000000000000000000
χ8316-16-161600000-4000044-4000000000000000000000000000000000000000000000000000000000000000000

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