Finite Group Databasebeta

← Group #72262927

Character table — Group #72262927

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85
size1122244444488888816161616161616161616161616161616163232323232323232323232323232323232646464646464646464646464646464646464128128128128128128128128128128128128128128128128
order1222222222222222222222224444444444222224444444444444444444444444444444488888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1111111111-1-11-1-1-1-11111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111-1-11111-1-11-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111-1-11111-1-11-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ711111111111111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111
χ811111111111111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111-1-11-1-111-1-1-11-111111-1-1111-1-1-1-1-111-11-1111-11-1111-1-1-1-1-11-1-11ii−i−i1-111-1-1ii−i−ii−i11-1-1i−iii−i−iii−i−i
χ1011111-1-11-1-111-1-1-11-111111-1-1111-1-1-1-1-111-11-1111-11-1111-1-1-1-1-11-1-11−i−iii1-111-1-1−i−iii−ii11-1-1−ii−i−iii−i−iii
χ1111111-1-11-1-111-1-1-11-111111-1-1111-1-1-1-1-111-11-1-1-11-11-1111-1-111-1-111-1ii−i−i-1111-1-1ii−i−ii−i-1-111i−i−i−iii−i−iii
χ1211111-1-11-1-111-1-1-11-111111-1-1111-1-1-1-1-111-11-1-1-11-11-1111-1-111-1-111-1−i−iii-1111-1-1−i−iii−ii-1-111−iiii−i−iii−i−i
χ1311111-1-11-1-111-1-1-11-111111-1-1111-1-1-1-1-111-1-11111-1-111-1-111-1-1-11-1-11ii−i−i1-1-1-111ii−i−i−ii-1-111−iiii−i−i−i−iii
χ1411111-1-11-1-111-1-1-11-111111-1-1111-1-1-1-1-111-1-11111-1-111-1-111-1-1-11-1-11−i−iii1-1-1-111−i−iiii−i-1-111i−i−i−iiiii−i−i
χ1511111-1-11-1-111-1-1-11-111111-1-1111-1-1-1-1-111-1-11-1-11-1-111-1-11111-1-111-1ii−i−i-11-1-111ii−i−i−ii11-1-1−ii−i−iiiii−i−i
χ1611111-1-11-1-111-1-1-11-111111-1-1111-1-1-1-1-111-1-11-1-11-1-111-1-11111-1-111-1−i−iii-11-1-111−i−iiii−i11-1-1i−iii−i−i−i−iii
χ17222222222222222222222-22-2-2-2-2-2-2-2-2-2-2-2200002200-2000000-20000000000000000000000000000002i−2i2i−2i
χ18222222222222222222222-22-2-2-2-2-2-2-2-2-2-2-2200002200-2000000-2000000000000000000000000000000−2i2i−2i2i
χ192222222222222222222-2-22222-2-2222-2-222-22200-2-222-2222200-20000000000-2-2-2-200000000000000000000
χ202222222222222222222-2-22222-2-2222-2-222-2-2-200-2-2-2-2-2-2-2-2-200-20000000000222200000000000000000000
χ212222222222222222222-2-2-22-2-222-2-2-222-2-2-20000-2-20020000002000000000000000000000000002-22-20000
χ222222222222222222222-2-2-22-2-222-2-2-222-2-2-20000-2-2002000000200000000000000000000000000-22-220000
χ232222222222222-2-222-2-2222-222-2-2-2-22-2-2-2-2-20000-220020000002000000000000000000220000-2-200000000
χ242222222222222-2-222-2-2222-222-2-2-2-22-2-2-2-2-20000-220020000002000000000000000000-2-200002200000000
χ252222222222222-2-222-2-222-2-2-2-22222-22222-20022-2200-20000-2-2-2222-20000-2-2000000000000000000000000
χ262222222222222-2-222-2-222-2-2-2-22222-22222-200-2-2-2200-2000022-2-2-2-22000022000000000000000000000000
χ272222222222222-2-222-2-2-2-22-22222-2-2222-2-2200002-200-2000000-200002222000000-2-2-2-20000000000000000
χ282222222222222-2-222-2-2-2-22-22222-2-2222-2-2200002-200-2000000-20000-2-2-2-200000022220000000000000000
χ292222222222222-2-222-2-2-2-2-2-2-2-2-2-222-2-2-222200002-20020000002000000000000000000002-22-20000000000
χ302222222222222-2-222-2-2-2-2-2-2-2-2-2-222-2-2-222200002-2002000000200000000000000000000-22-220000000000
χ3122222-2-22-2-222-2222-2-2-22222-22-2-222-222-2-220000-2-2002000000-20000000000000000002i−2i0000−2i2i00000000
χ3222222-2-22-2-222-2222-2-2-22222-22-2-222-222-2-220000-2-2002000000-2000000000000000000−2i2i00002i−2i00000000
χ3322222-2-22-2-222-2222-2-2-222-222-222-2-22-2-22220022-2-200-200002222-2-2-20000-22000000000000000000000000
χ3422222-2-22-2-222-2222-2-2-222-222-222-2-22-2-222200-2-2-2-200-20000-2-22-222200002-2000000000000000000000000
χ3522222-2-22-2-222-2222-2-2-2-2-222-222222-2-2-2-2-2-200002200-2000000200002i2i−2i−2i000000−2i−2i2i2i0000000000000000
χ3622222-2-22-2-222-2222-2-2-2-2-222-222222-2-2-2-2-2-200002200-200000020000−2i−2i2i2i0000002i2i−2i−2i0000000000000000
χ3722222-2-22-2-222-2222-2-2-2-2-2-222-2-2-2-2-222222-2000022002000000-2000000000000000000002-2-220000000000
χ3822222-2-22-2-222-2222-2-2-2-2-2-222-2-2-2-2-222222-2000022002000000-200000000000000000000-222-20000000000
χ3922222-2-22-2-222-2-2-22-22222-2-22-2-2-222222-2-2-200002-200-200000020000000000000000000000000000002-2-22
χ4022222-2-22-2-222-2-2-22-22222-2-22-2-2-222222-2-2-200002-200-20000002000000000000000000000000000000-222-2
χ4122222-2-22-2-222-2-2-22-222-2-22-2-22-2-2-2-2-2222222-200-222-2-222-2-20020000000000-2-22200000000000000000000
χ4222222-2-22-2-222-2-2-22-222-2-22-2-22-2-2-2-2-222222-2200-22-22-2-2-222002000000000022-2-200000000000000000000
χ4322222-2-22-2-222-2-2-22-222-2-2-2-22-222222-2-2-2-220000-22002000000-2000000000000000000000000002i−2i−2i2i0000
χ4422222-2-22-2-222-2-2-22-222-2-2-2-22-222222-2-2-2-220000-22002000000-200000000000000000000000000−2i2i2i−2i0000
χ4544444444-4-44-4-400-44000040-4-400004000000022000000000-2-20-22-2-2000022000000000000000000000000
χ4644444444-4-44-4-400-44000040-4-4000040000000-2-20000000002202-2220000-2-2000000000000000000000000
χ4744444444-4-44-4-400-440000-40440000-4000000022000000000220-22-220000-2-2000000000000000000000000
χ4844444444-4-44-4-400-440000-40440000-40000000-2-2000000000-2-202-22-2000022000000000000000000000000
χ494444444-444-4-4-4004-4000000004-40004-4000220000220-2-2-2-200000000000002-22-200000000000000000000
χ504444444-444-4-4-4004-4000000004-40004-4000-2-20000-2-2022220000000000000-22-2200000000000000000000
χ514444444-444-4-4-4004-400000000-44000-44000220000220-2-2-2-20000000000000-22-2200000000000000000000
χ524444444-444-4-4-4004-400000000-44000-44000-2-20000-2-20222200000000000002-22-200000000000000000000
χ534444444-4-4-4-44400-4-400000000004-40004-40000000000000000000002i−2i2i−2i0000002i−2i2i−2i0000000000000000
χ544444444-4-4-4-44400-4-400000000004-40004-4000000000000000000000−2i2i−2i2i000000−2i2i−2i2i0000000000000000
χ554444444-4-4-4-44400-4-40000000000-44000-440000000000000000000002i−2i2i−2i000000−2i2i−2i2i0000000000000000
χ564444444-4-4-4-44400-4-40000000000-44000-44000000000000000000000−2i2i−2i2i0000002i−2i2i−2i0000000000000000
χ5744444-4-44444-4400-4-40000404-40000-4000000022000000000220-2-22-200002-2000000000000000000000000
χ5844444-4-44444-4400-4-40000404-40000-40000000-2-2000000000-2-2022-220000-22000000000000000000000000
χ5944444-4-44444-4400-4-40000-40-4400004000000022000000000-2-20-2-2220000-22000000000000000000000000
χ6044444-4-44444-4400-4-40000-40-44000040000000-2-200000000022022-2-200002-2000000000000000000000000
χ6144444-4-4-444-44-400-4400000000004-4000-440000000000000000000002-2-22000000-222-20000000000000000
χ6244444-4-4-444-44-400-4400000000004-4000-44000000000000000000000-222-20000002-2-220000000000000000
χ6344444-4-4-444-44-400-440000000000-440004-40000000000000000000002-2-220000002-2-220000000000000000
χ6444444-4-4-444-44-400-440000000000-440004-4000000000000000000000-222-2000000-222-20000000000000000
χ6544444-4-4-4-4-4-4-440044000000004-4000-440002-200002-20-2-22200000000000002-2-2200000000000000000000
χ6644444-4-4-4-4-4-4-440044000000004-4000-44000-220000-22022-2-20000000000000-222-200000000000000000000
χ6744444-4-4-4-4-4-4-44004400000000-440004-40002-200002-20-2-2220000000000000-222-200000000000000000000
χ6844444-4-4-4-4-4-4-44004400000000-440004-4000-220000-22022-2-200000000000002-2-2200000000000000000000
χ6988-8-880008-800044004-4000-40000000000000000000004-44-40000000000000000000000000000000000000
χ7088-8-880008-800044004-4000-4000000000000000000000-44-440000000000000000000000000000000000000
χ7188-8-880008-8000-4-400-4400040000000000004-40000-44000000000000000000000000000000000000000000
χ7288-8-880008-8000-4-400-440004000000000000-4400004-4000000000000000000000000000000000000000000
χ7388-8-88000-880004400-44000-4000000000000440000-4-4000000000000000000000000000000000000000000
χ7488-8-88000-880004400-44000-4000000000000-4-4000044000000000000000000000000000000000000000000
χ7588-8-88000-88000-4-4004-400040000000000000000000004-4-440000000000000000000000000000000000000
χ7688-8-88000-88000-4-4004-40004000000000000000000000-444-40000000000000000000000000000000000000
χ77161616-16-16000000000000008-80000000000000000000000000000000000000000000000000000000000000000
χ78161616-16-1600000000000000-880000000000000000000000000000000000000000000000000000000000000000
χ791616-1616-1616-16000000000000000000000000000000000000000000000000000000000000000000000000000000
χ801616-1616-16-1616000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8116-1600000-8008008-800000000000000000000004-40000000004-400000000000000000000000000000000000
χ8216-1600000-8008008-80000000000000000000000-44000000000-4400000000000000000000000000000000000
χ8316-1600000-800800-8800000000000000000000004-4000000000-4400000000000000000000000000000000000
χ8416-1600000-800800-880000000000000000000000-440000000004-400000000000000000000000000000000000
χ8532-32000001600-1600000000000000000000000000000000000000000000000000000000000000000000000000

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