Finite Group Databasebeta

← Group #72316601

Character table — Group #72316601

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size112224444444488888888888161616161616161616161616161616161616161632323232323232323232323232323232323264646464646464646464646464646464128128128128128128128128128128128128128128128128
order1222222222222222222222222222222222222244444422444444444444444444444444444444444444448888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111111-1-11111-1-11111-1111-1-111111111-11-1-1-1-1-11-11-11-111-1-1-1-1-111-1-1-111-1-111-1-1ii−i−iii−i−i11-1-1i−iii−i−ii−iii−i−i
χ1011111111111-1-11111-1-11111-1111-1-111111111-11-1-1-1-1-11-11-11-111-1-1-1-1-111-1-1-111-1-111-1-1−i−iii−i−iii11-1-1−ii−i−iii−ii−i−iii
χ1111111111111-1-11111-1-11111-1111-1-111111111-11-1-1-1-1-1-11-111-111-1-1-1-1-1-1-111-111-1-1-1-111ii−i−iii−i−i-1-111−iiii−i−i−ii−i−iii
χ1211111111111-1-11111-1-11111-1111-1-111111111-11-1-1-1-1-1-11-111-111-1-1-1-1-1-1-111-111-1-1-1-111−i−iii−i−iii-1-111i−i−i−iiii−iii−i−i
χ1311111111111-1-11111-1-11111-1111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11-11-11-111-1111111-1-1-1-1-11111-1-1ii−i−iii−i−i-1-111i−i−i−iiii−i−i−iii
χ1411111111111-1-11111-1-11111-1111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11-11-11-111-1111111-1-1-1-1-11111-1-1−i−iii−i−iii-1-111−iiii−i−i−iiii−i−i
χ1511111111111-1-11111-1-11111-1111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-111-111-11111-1-111-1-1-111-1-111ii−i−iii−i−i11-1-1−ii−i−iii−iiii−i−i
χ1611111111111-1-11111-1-11111-1111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-111-111-11111-1-111-1-1-111-1-111−i−iii−i−iii11-1-1i−iii−i−ii−i−i−iii
χ1722222222222222222222222222-22222222222-2-22222-20000-2-2-2-2-222220000-2-2-2-2-20000000000000000000000000000
χ1822222222222222222222222222-222-2-2-2-2-2-2-2-2-2-22222-20000-2-2-2-2-2-2-2-2-20000-222220000000000000000000000000000
χ192222222222222222222-2-2-2-22-2-22220000000022-2-2-2-220000-2-22-2-200000000200000000000000000000220000-2-20000
χ202222222222222222222-2-2-2-22-2-22220000000022-2-2-2-220000-2-22-2-200000000200000000000000000000-2-20000220000
χ212222222222222222222-2-2-2-22-2-2-22200000000-2-2-2-2-2-2-2000022-22200000000-200000000000000000000000000002i−2i2i−2i
χ222222222222222222222-2-2-2-22-2-2-22200000000-2-2-2-2-2-2-2000022-22200000000-20000000000000000000000000000−2i2i−2i2i
χ232222222222222-2-2-2-22222222-2-22-2-2000000002222-2-222222-2-2-22200002222-20000-2-2-2-2000000000000000000000000
χ242222222222222-2-2-2-22222222-2-22-2-2000000002222-2-22-2-2-2-2-2-2-2220000-2-2-2-2-200002222000000000000000000000000
χ252222222222222-2-2-2-22222222-2-2-2-2-200000000-2-222-2-2-20000222-2-200000000200000000000000002-22-2000000000000
χ262222222222222-2-2-2-22222222-2-2-2-2-200000000-2-222-2-2-20000222-2-20000000020000000000000000-22-22000000000000
χ272222222222222-2-2-2-222-2-2-2-22222-2-20000000022-2-2222000022-2-2-200000000-2000000002222-2-2-2-20000000000000000
χ282222222222222-2-2-2-222-2-2-2-22222-2-20000000022-2-2222000022-2-2-200000000-200000000-2-2-2-222220000000000000000
χ292222222222222-2-2-2-222-2-2-2-2222-2-2-200000000-2-2-2-222-20000-2-222200000000200000000000000000000002-22-2000000
χ302222222222222-2-2-2-222-2-2-2-2222-2-2-200000000-2-2-2-222-20000-2-22220000000020000000000000000000000-22-22000000
χ3122222222222-2-22222-2-22222-222-2-2-2222222222-2-2-2-2-220000-22-2-22-2-2-2-200002-2-2220000000000000000000000000000
χ3222222222222-2-22222-2-22222-222-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-220000-22-2-2222220000222-2-20000000000000000000000000000
χ3322222222222-2-22222-2-2-2-2-2-2-2-2-22-2-200000000-222222-20000-222-2200000000-2000000000000000000002i−2i0000−2i2i0000
χ3422222222222-2-22222-2-2-2-2-2-2-2-2-22-2-200000000-222222-20000-222-2200000000-200000000000000000000−2i2i00002i−2i0000
χ3522222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000002-22222200002-2-22-200000000200000000000000000000000000002-2-22
χ3622222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000002-22222200002-2-22-20000000020000000000000000000000000000-222-2
χ3722222222222-2-2-2-2-2-2-2-22222-2-2-222200000000-22-2-222-22-22-2-22-22-2000022-2-220000-2-222000000000000000000000000
χ3822222222222-2-2-2-2-2-2-2-22222-2-2-222200000000-22-2-222-2-22-22-22-22-20000-2-2222000022-2-2000000000000000000000000
χ3922222222222-2-2-2-2-2-2-2-22222-2-2-2-222000000002-2-2-222200002-22-2200000000-200000000000000002-2-22000000000000
χ4022222222222-2-2-2-2-2-2-2-22222-2-2-2-222000000002-2-2-222200002-22-2200000000-20000000000000000-222-2000000000000
χ4122222222222-2-2-2-2-2-2-2-2-2-2-2-2-22222200000000-2222-2-2-200002-2-2-22000000002000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ4222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22222200000000-2222-2-2-200002-2-2-2200000000200000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ4322222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-222000000002-222-2-220000-2222-200000000-200000000000000000000002i−2i−2i2i000000
χ4422222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-222000000002-222-2-220000-2222-200000000-20000000000000000000000−2i2i2i−2i000000
χ454444444-4-4-4-4440000-4-444-4-440000000000000004-4000000000000000000000000000002-22-22-22-20000000000000000
χ464444444-4-4-4-4440000-4-444-4-440000000000000004-400000000000000000000000000000-22-22-22-220000000000000000
χ474444444-4-4-4-4440000-4-4-4-4444000000000000000-44000000000000000000000000000002-22-2-22-220000000000000000
χ484444444-4-4-4-4440000-4-4-4-4444000000000000000-4400000000000000000000000000000-22-222-22-20000000000000000
χ494444444-4-4-4-4-4-400004444-4-4-4000000000000000-44000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ504444444-4-4-4-4-4-400004444-4-4-4000000000000000-4400000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ514444444-4-4-4-4-4-4000044-4-444-40000000000000004-4000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ524444444-4-4-4-4-4-4000044-4-444-40000000000000004-400000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ5344444-4-444-4-44400004-40000-4004002222-2-2-2-24-40000-400000000022-2-2000002-22-20000000000000000000000000000
χ5444444-4-444-4-44400004-40000-400400-2-2-2-222224-40000-4000000000-2-22200000-22-220000000000000000000000000000
χ5544444-4-444-4-44400004-40000-400-4002222-2-2-2-2-440000400000000022-2-200000-22-220000000000000000000000000000
χ5644444-4-444-4-44400004-40000-400-400-2-2-2-22222-4400004000000000-2-222000002-22-20000000000000000000000000000
χ5744444-4-444-4-4-4-40000-4400004004002222-2-2-2-2-4-400004000000000-2-222000002-2-220000000000000000000000000000
χ5844444-4-444-4-4-4-40000-440000400400-2-2-2-22222-4-40000400000000022-2-200000-222-20000000000000000000000000000
χ5944444-4-444-4-4-4-40000-440000400-4002222-2-2-2-2440000-4000000000-2-22200000-222-20000000000000000000000000000
χ6044444-4-444-4-4-4-40000-440000400-400-2-2-2-22222440000-400000000022-2-2000002-2-220000000000000000000000000000
χ6144444-4-4-4-444440000-440000-44-40000000000000004-402222000000000-2-2-2-2000002-22-2000000000000000000000000
χ6244444-4-4-4-444440000-440000-44-40000000000000004-40-2-2-2-2000000000222200000-22-22000000000000000000000000
χ6344444-4-4-4-444440000-440000-4-44000000000000000-4402222000000000-2-2-2-200000-22-22000000000000000000000000
χ6444444-4-4-4-444440000-440000-4-44000000000000000-440-2-2-2-20000000002222000002-22-2000000000000000000000000
χ6544444-4-4-4-444-4-400004-4000044-4000000000000000-4402-22-2000000000-2-222000002-2-22000000000000000000000000
χ6644444-4-4-4-444-4-400004-4000044-4000000000000000-440-22-2200000000022-2-200000-222-2000000000000000000000000
χ6744444-4-4-4-444-4-400004-400004-440000000000000004-402-22-2000000000-2-22200000-222-2000000000000000000000000
χ6844444-4-4-4-444-4-400004-400004-440000000000000004-40-22-2200000000022-2-2000002-2-22000000000000000000000000
χ6988-88-80000008-844-4-400000000004-4000044-4-40000000000000000004-40000000000000000000000000000000000000
χ7088-88-80000008-844-4-400000000004-40000-4-444000000000000000000-440000000000000000000000000000000000000
χ7188-88-80000008-8-4-4440000000000-4444-4-4000000000000000000004-4000000000000000000000000000000000000000
χ7288-88-80000008-8-4-4440000000000-44-4-44400000000000000000000-44000000000000000000000000000000000000000
χ7388-88-8000000-8844-4-40000000000-44000044-4-4000000000000000000-440000000000000000000000000000000000000
χ7488-88-8000000-8844-4-40000000000-440000-4-4440000000000000000004-40000000000000000000000000000000000000
χ7588-88-8000000-88-4-44400000000004-444-4-400000000000000000000-44000000000000000000000000000000000000000
χ7688-88-8000000-88-4-44400000000004-4-4-444000000000000000000004-4000000000000000000000000000000000000000
χ7788-8-888-8000000000000008-8000000000000000000000040-4000000000004-4000000000000000000000000000000000
χ7888-8-888-8000000000000008-80000000000000000000000-40400000000000-44000000000000000000000000000000000
χ7988-8-888-800000000000000-8800000000000000000000040-400000000004-400000000000000000000000000000000000
χ8088-8-888-800000000000000-88000000000000000000000-4040000000000-4400000000000000000000000000000000000
χ8188-8-88-880000000000008-800000000000000000000000040-400000000000-44000000000000000000000000000000000
χ8288-8-88-880000000000008-8000000000000000000000000-404000000000004-4000000000000000000000000000000000
χ8388-8-88-88000000000000-880000000000000000000000040-40000000000-4400000000000000000000000000000000000
χ8488-8-88-88000000000000-8800000000000000000000000-40400000000004-400000000000000000000000000000000000
χ85161616-16-16000016-1600000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ86161616-16-160000-161600000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8716-16000008-80000008-8000000000000008-80000000000000000000000000000000000000000000000000000000000000
χ8816-16000008-80000008-800000000000000-880000000000000000000000000000000000000000000000000000000000000
χ8916-16000008-8000000-880000000000008-8000000000000000000000000000000000000000000000000000000000000000
χ9016-16000008-8000000-88000000000000-88000000000000000000000000000000000000000000000000000000000000000
χ9116-1600000-8800008-8000000000000000000008-8000000000000000000000000000000000000000000000000000000000
χ9216-1600000-8800008-800000000000000000000-88000000000000000000000000000000000000000000000000000000000
χ9316-1600000-880000-880000000000000000008-800000000000000000000000000000000000000000000000000000000000
χ9416-1600000-880000-88000000000000000000-8800000000000000000000000000000000000000000000000000000000000

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