Finite Group Databasebeta

← Group #72317176

Character table — Group #72317176

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85
size112224444448888888888161616161616161616161632323232323232323232323232323232323232646464646464646464646464646464646464128128128128128128128128128128128128128128128128
order1222222222222222222222222222444422224444444444444444444444444444444444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-11111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1111-1-1111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111111111-1-1111-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ711111111111111111111111111111111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ9111111111111111-1-11111-1-1-1-1-1-1-111-1-11-111-11-11111-1-111-1-1-1-1111-111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−ii−ii−ii−ii−i
χ10111111111111111-1-11111-1-1-1-1-1-1-111-1-11-111-11-11111-1-111-1-1-1-1111-111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−ii−ii−ii−ii
χ11111111111111111-1-11111-1-1-1-1-1-1-111-1-11-1-1-1-11-11111-1-111-1-111-1-1-1111-1-111iiii−i−i−i−i-1-111ii−i−i−ii−ii−ii−ii
χ12111111111111111-1-11111-1-1-1-1-1-1-111-1-11-1-1-1-11-11111-1-111-1-111-1-1-1111-1-111−i−i−i−iiiii-1-111−i−iiii−ii−ii−ii−i
χ13111111111111111-1-11111-1-1-1-1-1-1-111-1-1-1111-1-111111-1-1-1-111-1-1111-1-1-111-1-1iiii−i−i−i−i-1-111−i−iiii−i−iii−i−ii
χ14111111111111111-1-11111-1-1-1-1-1-1-111-1-1-1111-1-111111-1-1-1-111-1-1111-1-1-111-1-1−i−i−i−iiiii-1-111ii−i−i−iii−i−iii−i
χ15111111111111111-1-11111-1-1-1-1-1-1-111-1-1-11-1-1-1-111111-1-1-1-11111-1-1-11-1-11111iiii−i−i−i−i11-1-1−i−iii−iii−i−iii−i
χ16111111111111111-1-11111-1-1-1-1-1-1-111-1-1-11-1-1-1-111111-1-1-1-11111-1-1-11-1-11111−i−i−i−iiiii11-1-1ii−i−ii−i−iii−i−ii
χ172222222222222222222222222-2-2222-2-22-20022-2-2-2-2-2-2-222-2-2000000-2-22200000000000000000000000000
χ182222222222222222222222222-2-2222-2-2-22002-22-2-2-2-2-2-2-2-22200000022-2-200000000000000000000000000
χ1922222222222222222-2-2-2-222-2-2222-2-2220000-20022-2-2-2-2000000000000000000000000000000002200-2-200
χ2022222222222222222-2-2-2-222-2-2222-2-2220000-20022-2-2-2-200000000000000000000000000000000-2-2002200
χ2122222222222222222-2-2-2-222-2-2-2-22-2-2-2-20000-200-2-2222200000000000000000000000000000000002i−2i00−2i2i
χ2222222222222222222-2-2-2-222-2-2-2-22-2-2-2-20000-200-2-222220000000000000000000000000000000000−2i2i002i−2i
χ23222222222222222-2-22222-2-2-2-222-222222200-222-2-2-2-2222222000000-2-2-2-200000000000000000000000000
χ24222222222222222-2-22222-2-2-2-222-22222-2-200-2-2-2-2-2-2-222-2-2-2-2000000222200000000000000000000000000
χ25222222222222222-2-2-2-2-2-2-2-22222-2-2-2220000200-2-222-2-200000000000000000000000000000000002200-2-2
χ26222222222222222-2-2-2-2-2-2-2-22222-2-2-2220000200-2-222-2-20000000000000000000000000000000000-2-20022
χ27222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2000020022-2-222000000000000000000000000000000002i−2i00−2i2i00
χ28222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2000020022-2-22200000000000000000000000000000000−2i2i002i−2i00
χ2922222-2-222222-2-2-22222222-2222-2-2-2-22-20000-2002-22-22-20000000000000000000000002-22-2000000000000
χ3022222-2-222222-2-2-22222222-2222-2-2-2-22-20000-2002-22-22-2000000000000000000000000-22-22000000000000
χ3122222-2-222222-2-2-22222222-222-22-2-2-2-220022-200-22-22-22000022-2-22-200002-2000000000000000000000000
χ3222222-2-222222-2-2-22222222-222-22-2-2-2-2200-2-2-200-22-22-220000-2-222-220000-22000000000000000000000000
χ3322222-2-222222-2-2-222-2-2-2-22-2-2-22-2-2222-200002002-2-22-2200000000000000000000000000002i−2i2i−2i00000000
χ3422222-2-222222-2-2-222-2-2-2-22-2-2-22-2-2222-200002002-2-22-220000000000000000000000000000−2i2i−2i2i00000000
χ3522222-2-222222-2-2-222-2-2-2-22-2-2-2-22-222-220000200-222-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ3622222-2-222222-2-2-222-2-2-2-22-2-2-2-22-222-220000200-222-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3722222-2-222222-2-2-2-2-22222-22-2-22-22-2-22-20022200-22-222-20000-2-2-2-2220000-22000000000000000000000000
χ3822222-2-222222-2-2-2-2-22222-22-2-22-22-2-22-200-2-2200-22-222-200002222-2-200002-2000000000000000000000000
χ3922222-2-222222-2-2-2-2-22222-22-2-2-222-2-2-2200002002-22-2-220000000000000000000000002-2-22000000000000
χ4022222-2-222222-2-2-2-2-22222-22-2-2-222-2-2-2200002002-22-2-22000000000000000000000000-222-2000000000000
χ4122222-2-222222-2-2-2-2-2-2-2-2-2-22222-22222-20000-200-222-2-22000000000000000022-2-2-2-2220000000000000000
χ4222222-2-222222-2-2-2-2-2-2-2-2-2-22222-22222-20000-200-222-2-220000000000000000-2-22222-2-20000000000000000
χ4322222-2-222222-2-2-2-2-2-2-2-2-2-2222-22222-220000-2002-2-222-200000000000000000000000000002-2-2200000000
χ4422222-2-222222-2-2-2-2-2-2-2-2-2-2222-22222-220000-2002-2-222-20000000000000000000000000000-222-200000000
χ4544444444-4-44-44-4-4000000000044000-4-400220000000000000222-2-2-20000-22000000000000000000000000
χ4644444444-4-44-44-4-4000000000044000-4-400-2-20000000000000-2-2-222200002-2000000000000000000000000
χ4744444444-4-44-44-4-40000000000-4-40004400220000000000000-2-22-2-2200002-2000000000000000000000000
χ4844444444-4-44-44-4-40000000000-4-40004400-2-2000000000000022-222-20000-22000000000000000000000000
χ494444444-444-4-4-44-40044-4-400000004-400040000400000000-4-4000000000000000000000000000000000000
χ504444444-444-4-4-44-40044-4-400000004-4000-40000-40000000044000000000000000000000000000000000000
χ514444444-444-4-4-44-400-4-4440000000-44004000040000000-4-400000000000000000000000000000000000000
χ524444444-444-4-4-44-400-4-4440000000-4400-40000-400000004400000000000000000000000000000000000000
χ5344444-4-44-4-44-4-44400000000004-4000-4400220000000000000-2-2-22-2-2000022000000000000000000000000
χ5444444-4-44-4-44-4-44400000000004-4000-4400-2-20000000000000222-2220000-2-2000000000000000000000000
χ5544444-4-44-4-44-4-4440000000000-440004-40022000000000000022-22-220000-2-2000000000000000000000000
χ5644444-4-44-4-44-4-4440000000000-440004-400-2-20000000000000-2-22-22-2000022000000000000000000000000
χ5744444-4-4-444-4-44-440044-4-40000000-440000000000000000000000000004-400000000000000000000000000
χ5844444-4-4-444-4-44-440044-4-40000000-44000000000000000000000000000-4400000000000000000000000000
χ5944444-4-4-444-4-44-4400-4-44400000004-400000000000000000000000004-40000000000000000000000000000
χ6044444-4-4-444-4-44-4400-4-44400000004-40000000000000000000000000-440000000000000000000000000000
χ618888888-8-8-8-88-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ6288888-8-8-8-8-8-8888-80000000000000000000000000000000000000000000000000000000000000000000000
χ63888-8-88-800000000440000-440000-40000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ64888-8-88-800000000440000-440000-4000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ65888-8-88-800000000-4-400004-4000040000000000000000000000000000000002-22-2-22-220000000000000000
χ66888-8-88-800000000-4-400004-400004000000000000000000000000000000000-22-222-22-20000000000000000
χ67888-8-8-8800000000440000-4-4000040000000000000000000000000000000002-2-222-2-220000000000000000
χ68888-8-8-8800000000440000-4-400004000000000000000000000000000000000-222-2-222-20000000000000000
χ69888-8-8-8800000000-4-40000440000-40000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ70888-8-8-8800000000-4-40000440000-4000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ7188-8-880008-80000000008-800000000000040000-4000000004-4000000000000000000000000000000000000
χ7288-8-880008-80000000008-8000000000000-40000400000000-44000000000000000000000000000000000000
χ7388-8-880008-8000000000-8800000000000040000-400000000-44000000000000000000000000000000000000
χ7488-8-880008-8000000000-88000000000000-400004000000004-4000000000000000000000000000000000000
χ7588-8-88000-8800000008-8000000000000040000-400000004-400000000000000000000000000000000000000
χ7688-8-88000-8800000008-80000000000000-4000040000000-4400000000000000000000000000000000000000
χ7788-8-88000-880000000-88000000000000040000-40000000-4400000000000000000000000000000000000000
χ7888-8-88000-880000000-880000000000000-40000400000004-400000000000000000000000000000000000000
χ791616-1616-160000000000000000008-8000000000000000000000000000000000000000000000000000000000000
χ801616-1616-16000000000000000000-88000000000000000000000000000000000000000000000000000000000000
χ8116-1600000-800800008-8000000000000000004-400000000000004-40000000000000000000000000000000000
χ8216-1600000-800800008-800000000000000000-440000000000000-440000000000000000000000000000000000
χ8316-1600000-80080000-88000000000000000004-40000000000000-440000000000000000000000000000000000
χ8416-1600000-80080000-8800000000000000000-4400000000000004-40000000000000000000000000000000000
χ8532-32000001600-1600000000000000000000000000000000000000000000000000000000000000000000000000

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