Finite Group Databasebeta

← Group #13041363

Character table — Group #13041363

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222244444444444555588888881010101010101010101010101010101010101010161616161616161616202020202020202020202020202020202020203232404040404040404040
order12224444444588881010102222444202020204444444444448888888820202020204040404044444444444888888882020444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1
χ31111111111111111111-1-1-1-11111111-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i111111111-1-1-1ii−i−iii−i−i-1-1-1-1ii−i−i11-1-1-1iii−i−i−i
χ41111111111111111111-1-1-1-11111111-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii111111111-1-1-1−i−iii−i−iii-1-1-1-1−i−iii11-1-1-1−i−i−iiii
χ5111111111111-1-1-1-111111111-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-111-1
χ6111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-11-1-11
χ7111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1iiii−i−i−i−i-1-1−i−i−i−iiiii11111-1-1-1-1-1-1-1−i−iiiii−i−i1111−i−iii-1-1-111ii−i−i−ii
χ8111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1−i−i−i−iiiii-1-1iiii−i−i−i−i11111-1-1-1-1-1-1-1ii−i−i−i−iii1111ii−i−i-1-1-111−i−iiii−i
χ911111111-1-11111111111111-1-1-1111111111111111111111111-1-11-1-11111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1
χ1011111111-1-11111111111111-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111
χ1111111111-1-1111111111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i-1-11-1-1111111-1−i−iiiii−i−i-1-1-1-1ii−i−i-1-1111−i−i−iiii
χ1211111111-1-1111111111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii-1-11-1-1111111-1ii−i−i−i−iii-1-1-1-1−i−iii-1-1111iii−i−i−i
χ1311111111-1-111-1-1-1-11111111-1111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-111-1-11-1-11
χ1411111111-1-111-1-1-1-11111111-111111111-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-11111-111-1
χ1511111111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1iiii−i−i−i−i-1-1−i−i−i−iiiii-1-11-1-1-1-1-1-111-1ii−i−iii−i−i1111−i−iii111-1-1−i−iiii−i
χ1611111111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1−i−i−i−iiiii-1-1iiii−i−i−i−i-1-11-1-1-1-1-1-111-1−i−iii−i−iii1111ii−i−i111-1-1ii−i−i−ii
χ171111-1-11111-1111-1-11111111-11-1-1-111-1-111-1-111-1-1111111111111-1-1-111-1-111-111111-11-111-1-1-1-1-1-11-1-11-11-1-11-1-1
χ181111-1-11111-1111-1-11111111-11-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1-1-1-1-11-1111-1-111111-1-11-1-111-111
χ191111-1-11111-1111-1-1111-1-1-1-1-11-1-1-11111ii−i−i−i−iii-1-1iiii−i−i−i−i11-1-1-111-1-1-1-11ii−i−ii−i−ii-1-111−i−iii1-11-11i−i−i−iii
χ201111-1-11111-1111-1-1111-1-1-1-1-11-1-1-11111−i−iiiii−i−i-1-1−i−i−i−iiiii11-1-1-111-1-1-1-11−i−iii−iii−i-1-111ii−i−i1-11-11−iiii−i−i
χ211111-1-11111-11-1-1111111111-1-11-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-11-11-1-1-1111111-11-1-111-111-11
χ221111-1-11111-11-1-1111111111-1-11-1-111-1-1-1-111-1-111111111111111-1-1-1-1-11111-11111-11-11-1-111-1-1-1-1-11-1-11-11-1-11-1
χ231111-1-11111-11-1-111111-1-1-1-1-1-11-1-11111ii−i−i−i−iii-1-1−i−i−i−iiiii11-1-1-1-1-111-1-11−i−iiii−i−ii11-1-1ii−i−i-1111-1i−ii−ii−i
χ241111-1-11111-11-1-111111-1-1-1-1-1-11-1-11111−i−iiiii−i−i-1-1iiii−i−i−i−i11-1-1-1-1-111-1-11ii−i−i−iii−i11-1-1−i−iii-1111-1−ii−ii−ii
χ251111-1-111-1-1-1111-1-111111111-11-1-111-1-111-1-111-1-11111111111-1-1-11111-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1-111-11-111-111
χ261111-1-111-1-1-1111-1-111111111-11-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-11-1111-1-11111-111-111-1-11-1-1
χ271111-1-111-1-1-1111-1-1111-1-1-1-11-11-1-11111ii−i−i−i−iii-1-1iiii−i−i−i−i-1-1-11111-1-1111−i−iiii−i−ii-1-111−i−iii-11-11-1−iiii−i−i
χ281111-1-111-1-1-1111-1-1111-1-1-1-11-11-1-11111−i−iiiii−i−i-1-1−i−i−i−iiiii-1-1-11111-1-1111ii−i−i−iii−i-1-111ii−i−i-11-11-1i−i−i−iii
χ291111-1-111-1-1-11-1-111111111111-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111111-11-1-1-11111111-111-1-11-1-11-1
χ301111-1-111-1-1-11-1-111111111111-1-1-111-1-1-1-111-1-1111111111111-1-1-111-1-111-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11-111-11-111-11
χ311111-1-111-1-1-11-1-111111-1-1-1-111-1-1-11111ii−i−i−i−iii-1-1−i−i−i−iiiii-1-1-111-1-111111ii−i−ii−i−ii11-1-1ii−i−i1-1-1-11−ii−ii−ii
χ321111-1-111-1-1-11-1-111111-1-1-1-111-1-1-11111−i−iiiii−i−i-1-1iiii−i−i−i−i-1-1-111-1-111111−i−iii−iii−i11-1-1−i−iii1-1-1-11i−ii−ii−i
χ33222222-2-200-220000222222200022-2-22222222222-2-20000000000-200000000-20000-2-2-2-20000000000000000000
χ34222222-2-200-220000222222200022-2-222-2-2-2-2-2-2-2-2-2-20000000000-200000000-2000022220000000000000000000
χ35222222-2-200-220000222-2-2-2-200022-2-2-2-22i2i2i2i−2i−2i−2i−2i220000000000-20000000020000−2i−2i2i2i0000000000000000000
χ36222222-2-200-220000222-2-2-2-200022-2-2-2-2−2i−2i−2i−2i2i2i2i2i220000000000-200000000200002i2i−2i−2i0000000000000000000
χ372222-2-2-2-2002200002222222000-2-2-2-2-2-222-2-222-2-2-2-2000000000020000000020000-22-220000000000000000000
χ382222-2-2-2-2002200002222222000-2-2-2-2-2-2-2-222-2-222-2-20000000000200000000200002-22-20000000000000000000
χ392222-2-2-2-200220000222-2-2-2-2000-2-2-2-2222i2i−2i−2i−2i−2i2i2i220000000000200000000-20000−2i2i2i−2i0000000000000000000
χ402222-2-2-2-200220000222-2-2-2-2000-2-2-2-222−2i−2i2i2i2i2i−2i−2i220000000000200000000-200002i−2i−2i2i0000000000000000000
χ4122-2-22-20000022−22−22-2-222-2-20002-2002-22-22-22-22-20022−2−222−2−2000002−22−2000000000002−22−22−22−200000000000
χ4222-2-22-20000022−22−22-2-222-2-20002-2002-2-22-22-22-2200−2−222−2−222000002−22−2000000000002−22−2−22−2200000000000
χ4322-2-22-20000022−22−22-2-2-2-2220002-200-222i−2i2i−2i−2i2i−2i2i00i2i2−i2−i2−i2−i2i2i2000002−22−200000000000−22−22i2−i2−i2i200000000000
χ4422-2-22-20000022−22−22-2-2-2-2220002-200-22−2i2i−2i2i2i−2i2i−2i00−i2−i2i2i2i2i2−i2−i2000002−22−200000000000−22−22−i2i2i2−i200000000000
χ4522-2-22-2000002−22−222-2-222-2-20002-2002-22-22-22-22-200−2−222−2−22200000−22−2200000000000−22−22−22−2200000000000
χ4622-2-22-2000002−22−222-2-222-2-20002-2002-2-22-22-22-220022−2−222−2−200000−22−2200000000000−22−222−22−200000000000
χ4722-2-22-2000002−22−222-2-2-2-2220002-200-222i−2i2i−2i−2i2i−2i2i00−i2−i2i2i2i2i2−i2−i200000−22−22000000000002−22−2−i2i2i2−i200000000000
χ4822-2-22-2000002−22−222-2-2-2-2220002-200-22−2i2i−2i2i2i−2i2i−2i00i2i2−i2−i2−i2−i2i2i200000−22−22000000000002−22−2i2−i2−i2i200000000000
χ4922-2-2-220000022−2−222-2-222-2-2000-2200-222-2-222-2-220022−2−222−2−2000002−2−22000000000002−2−22−22−2200000000000
χ5022-2-2-220000022−2−222-2-222-2-2000-2200-22-222-2-222-200−2−222−2−222000002−2−22000000000002−2−222−22−200000000000
χ5122-2-2-220000022−2−222-2-2-2-222000-22002-22i−2i−2i2i−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2000002−2−2200000000000−222−2−i2i2i2−i200000000000
χ5222-2-2-220000022−2−222-2-2-2-222000-22002-2−2i2i2i−2i2i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2000002−2−2200000000000−222−2i2−i2−i2i200000000000
χ5322-2-2-22000002−222−22-2-222-2-2000-2200-222-2-222-2-2200−2−222−2−22200000−222−200000000000−222−22−22−200000000000
χ5422-2-2-22000002−222−22-2-222-2-2000-2200-22-222-2-222-20022−2−222−2−200000−222−200000000000−222−2−22−2200000000000
χ5522-2-2-22000002−222−22-2-2-2-222000-22002-22i−2i−2i2i−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i200000−222−2000000000002−2−22i2−i2−i2i200000000000
χ5622-2-2-22000002−222−22-2-2-2-222000-22002-2−2i2i2i−2i2i−2i−2i2i00i2i2−i2−i2−i2−i2i2i200000−222−2000000000002−2−22−i2i2i2−i200000000000
χ572-22-2002-22-2020000-22-22-22-2000002-200000000002-22-22-22-22-22-200000002-202-22-200000000000000000000000
χ582-22-2002-22-2020000-22-22-22-2000002-200000000002-2-22-22-22-222-200000002-20-22-2200000000000000000000000
χ592-22-2002-22-2020000-22-2-22-22000002-20000000000-222i−2i2i−2i−2i2i−2i2i2-20000000-2202i−2i−2i2i00000000000000000000000
χ602-22-2002-22-2020000-22-2-22-22000002-20000000000-22−2i2i−2i2i2i−2i2i−2i2-20000000-220−2i2i2i−2i00000000000000000000000
χ612-22-2002-2-22020000-22-22-22-2000002-200000000002-22-22-22-22-2-220000000-220-22-2200000000000000000000000
χ622-22-2002-2-22020000-22-22-22-2000002-200000000002-2-22-22-22-22-220000000-2202-22-200000000000000000000000
χ632-22-2002-2-22020000-22-2-22-22000002-20000000000-222i−2i2i−2i−2i2i−2i2i-2200000002-20−2i2i2i−2i00000000000000000000000
χ642-22-2002-2-22020000-22-2-22-22000002-20000000000-22−2i2i−2i2i2i−2i2i−2i-2200000002-202i−2i−2i2i00000000000000000000000
χ6544444444444-14444-1-1-10000444-1-1-1-100000000000000000000-1-1-1-1-1-1-1-1-10000000000000000000-1-1000000000
χ6644444444444-1-4-4-4-4-1-1-100004-4-4-1-1-1-100000000000000000000-1-1-1-1-11111000000000000000000011000000000
χ6744444444-4-44-14444-1-1-10000-4-4-4-1-1-1-10000000000000000000011-111-1-1-1-1000000000000000000011000000000
χ6844444444-4-44-1-4-4-4-4-1-1-10000-444-1-1-1-10000000000000000000011-11111110000000000000000000-1-1000000000
χ694444-4-44444-4-144-4-4-1-1-10000-44-411-1-100000000000000000000-1-1111-1-1110000000000000000000-11000000000
χ704444-4-44444-4-1-4-444-1-1-10000-4-4411-1-100000000000000000000-1-111111-1-100000000000000000001-1000000000
χ714444-4-444-4-4-4-144-4-4-1-1-100004-4411-1-100000000000000000000111-1-1-1-11100000000000000000001-1000000000
χ724444-4-444-4-4-4-1-4-444-1-1-1000044-411-1-100000000000000000000111-1-111-1-10000000000000000000-11000000000
χ734-44-400-4400040000-44-44-44-400000-440000000000-4400000000000000000000000000000000000000000000000
χ744-44-400-4400040000-44-4-44-4400000-4400000000004-400000000000000000000000000000000000000000000000
χ754-4-44000000040000-4-444-4-44000000000000000000022−22−222222−22−2222000000000000000000000000000000000000000
χ764-4-44000000040000-4-444-4-440000000000000000000−222222−22−222222−22000000000000000000000000000000000000000
χ774-4-44000000040000-4-44-444-400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ784-4-44000000040000-4-44-444-40000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ79888888-8-800-8-20000-2-2-20000000-2-22200000000000000000000002000000000000000000000000000000000000
χ808888-8-8-8-8008-20000-2-2-2000000022220000000000000000000000-2000000000000000000000000000000000000
χ8188-8-88-800000-242−4242−42-2220000000-22000000000000000000000000000−22−22000000000000000000000000000000
χ8288-8-88-800000-2−4242−4242-2220000000-220000000000000000000000000002−22−2000000000000000000000000000000
χ8388-8-8-8800000-242−42−4242-22200000002-2000000000000000000000000000−222−2000000000000000000000000000000
χ8488-8-8-8800000-2−424242−42-22200000002-20000000000000000000000000002−2−22000000000000000000000000000000
χ858-88-8008-88-80-200002-22000000000-2200000000000000000000-220000000000000000000000000000000000000
χ868-88-8008-8-880-200002-22000000000-22000000000000000000002-20000000000000000000000000000000000000
χ878-88-800-88000-200002-220000000002-2000000000000000000000002i5−2i50000000000000000000000000000000000
χ888-88-800-88000-200002-220000000002-200000000000000000000000−2i52i50000000000000000000000000000000000
χ8916-16-16160000000-4000044-40000000000000000000000000000000000000000000000000000000000000000000000

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