Finite Group Databasebeta

← Group #13041473

Character table — Group #13041473

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222244444444444555588888881010101010101010101010101010101010101010161616161616161616202020202020202020202020202020202020203232404040404040404040
order12224444224588881010102222444202020204444444444448888888810102020204040404022444444444888888882020444444444
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−i111111111-1-1-1iiii−i−i−i−i-1-1-1-1ii−i−i11-1-1-1i−iii−i−i
χ41111111111111111111-1-1-1-11111111-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii111111111-1-1-1−i−i−i−iiiii-1-1-1-1−i−iii11-1-1-1−ii−i−iii
χ5111111111111-1-1-1-111111111-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ6111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1111-1-111-1-111-1-1-1-11111-1-11-1-111-1-1-1-1
χ7111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1iiii−i−i−i−i-1-1−i−i−i−iiiii11111-1-1-1-1-1-1-1ii−i−i−i−iii1111−i−iii-1-1-111−iiii−i−i
χ8111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1−i−i−i−iiiii-1-1iiii−i−i−i−i11111-1-1-1-1-1-1-1−i−iiiii−i−i1111ii−i−i-1-1-111i−i−i−iii
χ911111111-1-11111111111111-1-1-1111111111111111111111111-1-11-1-11111-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1
χ1011111111-1-11111111111111-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-1-1111111
χ1111111111-1-1111111111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i-1-11-1-1111111-1ii−i−i−i−iii-1-1-1-1ii−i−i-1-1111−ii−i−iii
χ1211111111-1-1111111111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii-1-11-1-1111111-1−i−iiiii−i−i-1-1-1-1−i−iii-1-1111i−iii−i−i
χ1311111111-1-111-1-1-1-11111111-1111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-11111-1-1-1-1
χ1411111111-1-111-1-1-1-11111111-111111111-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-11111
χ1511111111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1iiii−i−i−i−i-1-1−i−i−i−iiiii-1-11-1-1-1-1-1-111-1iiii−i−i−i−i1111−i−iii111-1-1i−i−i−iii
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−i−i−iiiii1111ii−i−i111-1-1−iiii−i−i
χ171111-1-11111-1111-1-11111111-11-1-1-111-1-111-1-111-1-1111111111111-1-1-111-1-111-11-1111-11111-1-1-1-1-1-11-1-11-1-1-11-11-1
χ181111-1-11111-1111-1-11111111-11-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-111-1-11-1-1-11-1-111-1-111111-1-11-111-11-11
χ191111-1-11111-1111-1-1111-1-1-1-1-11-1-1-11111ii−i−i−i−iii-1-1iiii−i−i−i−i11-1-1-111-1-1-1-11i−iii−ii−i−i-1-111−i−iii1-11-11−iii−i−ii
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−ii−i−ii−iii-1-111ii−i−i1-11-11i−i−iii−i
χ211111-1-11111-11-1-1111111111-1-11-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-11111-11-1-1-11-1-1-1-1-1111111-11-1-11111-11-1
χ221111-1-11111-11-1-1111111111-1-11-1-111-1-1-1-111-1-111111111111111-1-1-1-1-11111-1-1111-1111-1-111-1-1-1-1-11-1-11-1-1-11-11
χ231111-1-11111-11-1-111111-1-1-1-1-1-11-1-11111ii−i−i−i−iii-1-1−i−i−i−iiiii11-1-1-1-1-111-1-11i−i−i−i−iiii11-1-1ii−i−i-1111-1i−ii−i−ii
χ241111-1-11111-11-1-111111-1-1-1-1-1-11-1-11111−i−iiiii−i−i-1-1iiii−i−i−i−i11-1-1-1-1-111-1-11−iiiii−i−i−i11-1-1−i−iii-1111-1−ii−iii−i
χ251111-1-111-1-1-1111-1-111111111-11-1-111-1-111-1-111-1-11111111111-1-1-11111-1-1-1-1-11-1-1-11-1-1-111-1-1-1-1-1-1-111-1111-11-11
χ261111-1-111-1-1-1111-1-111111111-11-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-111111-1-11111-111-11-1-11-11-1
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-1-1-11111-1-1111i−i−i−i−iiii-1-111−i−iii-11-11-1i−i−iii−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-1-1-11111-1-1111−iiiii−i−i−i-1-111ii−i−i-11-11-1−iii−i−ii
χ291111-1-111-1-1-11-1-111111111111-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11-1111-111-1-11111111-111-1-1-1-11-11
χ301111-1-111-1-1-11-1-111111111111-1-1-111-1-1-1-111-1-1111111111111-1-1-111-1-111-1-1-1-11-1-1-11-1-1-1-111-1-1-1-11-111-1111-11-1
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-1-1-111-1-111111i−iii−ii−i−i11-1-1ii−i−i1-1-1-11−ii−iii−i
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−ii−i−ii−iii11-1-1−i−iii1-1-1-11i−ii−i−ii
χ33222222-2-200-220000222222200022-2-22222222222-2-20000000000-200000000-2-2-200-2-2000000000000000000000
χ34222222-2-200-220000222222200022-2-222-2-2-2-2-2-2-2-2-2-20000000000-200000000-2220022000000000000000000000
χ35222222-2-200-220000222-2-2-2-200022-2-2-2-22i2i2i2i−2i−2i−2i−2i220000000000-2000000002−2i−2i002i2i000000000000000000000
χ36222222-2-200-220000222-2-2-2-200022-2-2-2-2−2i−2i−2i−2i2i2i2i2i220000000000-20000000022i2i00−2i−2i000000000000000000000
χ372222-2-2-2-2002200002222222000-2-2-2-2-2-222-2-222-2-2-2-200000000002000000002-2200-22000000000000000000000
χ382222-2-2-2-2002200002222222000-2-2-2-2-2-2-2-222-2-222-2-2000000000020000000022-2002-2000000000000000000000
χ392222-2-2-2-200220000222-2-2-2-2000-2-2-2-2222i2i−2i−2i−2i−2i2i2i220000000000200000000-2−2i2i002i−2i000000000000000000000
χ402222-2-2-2-200220000222-2-2-2-2000-2-2-2-222−2i−2i2i2i2i2i−2i−2i220000000000200000000-22i−2i00−2i2i000000000000000000000
χ412-22-22-2000002i2−i2i2−i2-22-22-2-220002-2002-22-22-22-22-200i2i2−i2−i2i2i2−i2−i200000i2−i2i2−i200000000000i2−i2i2−i2i2−i2i2−i200000000000
χ422-22-22-2000002i2−i2i2−i2-22-22-2-220002-2002-2-22-22-22-2200−i2−i2i2i2−i2−i2i2i200000i2−i2i2−i200000000000i2−i2i2−i2−i2i2−i2i200000000000
χ432-22-22-2000002i2−i2i2−i2-22-2-222-20002-200-222i−2i2i−2i−2i2i−2i2i00−2−22222−2−200000i2−i2i2−i200000000000−i2i2−i2i2−222−200000000000
χ442-22-22-2000002i2−i2i2−i2-22-2-222-20002-200-22−2i2i−2i2i2i−2i2i−2i0022−2−2−2−22200000i2−i2i2−i200000000000−i2i2−i2i22−2−2200000000000
χ452-22-22-2000002−i2i2−i2i2-22-22-2-220002-2002-22-22-22-22-200−i2−i2i2i2−i2−i2i2i200000−i2i2−i2i200000000000−i2i2−i2i2−i2i2−i2i200000000000
χ462-22-22-2000002−i2i2−i2i2-22-22-2-220002-2002-2-22-22-22-2200i2i2−i2−i2i2i2−i2−i200000−i2i2−i2i200000000000−i2i2−i2i2i2−i2i2−i200000000000
χ472-22-22-2000002−i2i2−i2i2-22-2-222-20002-200-222i−2i2i−2i−2i2i−2i2i0022−2−2−2−22200000−i2i2−i2i200000000000i2−i2i2−i22−2−2200000000000
χ482-22-22-2000002−i2i2−i2i2-22-2-222-20002-200-22−2i2i−2i2i2i−2i2i−2i00−2−22222−2−200000−i2i2−i2i200000000000i2−i2i2−i2−222−200000000000
χ492-22-2-22000002i2−i2−i2i2-22-22-2-22000-2200-222-2-222-2-2200i2i2−i2−i2i2i2−i2−i200000i2−i2−i2i200000000000i2−i2−i2i2−i2i2−i2i200000000000
χ502-22-2-22000002i2−i2−i2i2-22-22-2-22000-2200-22-222-2-222-200−i2−i2i2i2−i2−i2i2i200000i2−i2−i2i200000000000i2−i2−i2i2i2−i2i2−i200000000000
χ512-22-2-22000002i2−i2−i2i2-22-2-222-2000-22002-22i−2i−2i2i−2i2i2i−2i00−2−22222−2−200000i2−i2−i2i200000000000−i2i2i2−i22−2−2200000000000
χ522-22-2-22000002i2−i2−i2i2-22-2-222-2000-22002-2−2i2i2i−2i2i−2i−2i2i0022−2−2−2−22200000i2−i2−i2i200000000000−i2i2i2−i2−222−200000000000
χ532-22-2-22000002−i2i2i2−i2-22-22-2-22000-2200-222-2-222-2-2200−i2−i2i2i2−i2−i2i2i200000−i2i2i2−i200000000000−i2i2i2−i2i2−i2i2−i200000000000
χ542-22-2-22000002−i2i2i2−i2-22-22-2-22000-2200-22-222-2-222-200i2i2−i2−i2i2i2−i2−i200000−i2i2i2−i200000000000−i2i2i2−i2−i2i2−i2i200000000000
χ552-22-2-22000002−i2i2i2−i2-22-2-222-2000-22002-22i−2i−2i2i−2i2i2i−2i0022−2−2−2−22200000−i2i2i2−i200000000000i2−i2−i2i2−222−200000000000
χ562-22-2-22000002−i2i2i2−i2-22-2-222-2000-22002-2−2i2i2i−2i2i−2i−2i2i00−2−22222−2−200000−i2i2i2−i200000000000i2−i2−i2i22−2−2200000000000
χ572-2-2200-222-2020000-2-2222-2-200000-2200000000002-22i−2i2i−2i2i−2i2i−2i2-200000002-20002i−2i002i−2i0000000000000000000
χ582-2-2200-222-2020000-2-2222-2-200000-2200000000002-2−2i2i−2i2i−2i2i−2i2i2-200000002-2000−2i2i00−2i2i0000000000000000000
χ592-2-2200-222-2020000-2-22-2-22200000-220000000000-222-22-2-22-222-20000000-220002-200-220000000000000000000
χ602-2-2200-222-2020000-2-22-2-22200000-220000000000-22-22-222-22-22-20000000-22000-22002-20000000000000000000
χ612-2-2200-22-22020000-2-2222-2-200000-2200000000002-22i−2i2i−2i2i−2i2i−2i-220000000-22000−2i2i00−2i2i0000000000000000000
χ622-2-2200-22-22020000-2-2222-2-200000-2200000000002-2−2i2i−2i2i−2i2i−2i2i-220000000-220002i−2i002i−2i0000000000000000000
χ632-2-2200-22-22020000-2-22-2-22200000-220000000000-222-22-2-22-22-2200000002-2000-22002-20000000000000000000
χ642-2-2200-22-22020000-2-22-2-22200000-220000000000-22-22-222-22-2-2200000002-20002-200-220000000000000000000
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
χ7344-4-40000000400004-4-44-44-4000000000000000000022−22−222222−22−2222000000000000000000000000000000000000000
χ7444-4-40000000400004-4-44-44-40000000000000000000−222222−22−222222−22000000000000000000000000000000000000000
χ7544-4-40000000400004-4-4-44-4400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ7644-4-40000000400004-4-4-44-440000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ774-4-44004-400040000-4-4444-4-4000004-40000000000-4400000000000000000000000000000000000000000000000
χ784-4-44004-400040000-4-44-4-444000004-400000000004-400000000000000000000000000000000000000000000000
χ79888888-8-800-8-20000-2-2-20000000-2-22200000000000000000000002000000000000000000000000000000000000
χ808888-8-8-8-8008-20000-2-2-2000000022220000000000000000000000-2000000000000000000000000000000000000
χ818-88-88-800000-24i2−4i24i2−4i22-220000000-22000000000000000000000000000−i2i2−i2i2000000000000000000000000000000
χ828-88-88-800000-2−4i24i2−4i24i22-220000000-22000000000000000000000000000i2−i2i2−i2000000000000000000000000000000
χ838-88-8-8800000-24i2−4i2−4i24i22-2200000002-2000000000000000000000000000−i2i2i2−i2000000000000000000000000000000
χ848-88-8-8800000-2−4i24i24i2−4i22-2200000002-2000000000000000000000000000i2−i2−i2i2000000000000000000000000000000
χ858-8-88008-8000-2000022-2000000000-22000000000000000000000002i5−2i50000000000000000000000000000000000
χ868-8-88008-8000-2000022-2000000000-2200000000000000000000000−2i52i50000000000000000000000000000000000
χ878-8-8800-888-80-2000022-20000000002-200000000000000000000-220000000000000000000000000000000000000
χ888-8-8800-88-880-2000022-20000000002-2000000000000000000002-20000000000000000000000000000000000000
χ891616-16-160000000-40000-4440000000000000000000000000000000000000000000000000000000000000000000000

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