Finite Group Databasebeta

← Group #72262924

Character table — Group #72262924

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79
size112224444888888816161616161616161616161616161632323232323232323232323232323232323264646464646464646464128128128128128128128128128128128128128128128128128128128128
order1222222222222222222222244444444222224444444444444444444444444448888888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-11111111111-1-11-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-11111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1111-1-1111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1111-1-1111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-11-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-11-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1
χ91111111111111-1-1111-1-1-1-1-111-1-1-1-111-11-11111-111-111-1-1-1-1-1111-1-1-111-1-1i−ii−i11-1-1i−ii−iii−i−iii−i−i
χ101111111111111-1-1111-1-1-1-1-111-1-1-1-111-11-11111-111-111-1-1-1-1-1111-1-1-111-1-1−ii−ii11-1-1−ii−ii−i−iii−i−iii
χ111111111111111-1-1111-1-1-1-1-111-1-1-1-111-11-1-1-111-111-111-1-111-1-1-1-111111-1-1i−ii−i-1-111i−ii−i−i−iii−i−iii
χ121111111111111-1-1111-1-1-1-1-111-1-1-1-111-11-1-1-111-111-111-1-111-1-1-1-111111-1-1−ii−ii-1-111−ii−iiii−i−iii−i−i
χ131111111111111-1-1111-1-1-1-1-111-1-1-1-111-1-11111-1111-1-1-111-1-1-1111-1-1-1-1-111i−i−ii-1-111i−i−iiii−i−i−i−iii
χ141111111111111-1-1111-1-1-1-1-111-1-1-1-111-1-11111-1111-1-1-111-1-1-1111-1-1-1-1-111−iii−i-1-111−iii−i−i−iiiii−i−i
χ151111111111111-1-1111-1-1-1-1-111-1-1-1-111-1-11-1-11-1111-1-1-11111-1-1-1-1111-1-111i−i−ii11-1-1i−i−ii−i−iiiii−i−i
χ161111111111111-1-1111-1-1-1-1-111-1-1-1-111-1-11-1-11-1111-1-1-11111-1-1-1-1111-1-111−iii−i11-1-1−iii−iii−i−i−i−iii
χ17222222222222222222222-2-2-2-222-2-2-2-220000200-2-2-2000000-20000000000002i−2i000000−2i2i00000000
χ18222222222222222222222-2-2-2-222-2-2-2-220000200-2-2-2000000-2000000000000−2i2i0000002i−2i00000000
χ192222222222222222-2-22222222-2-22222-22200-222-2-2-2222200-2000000-2-2-2-200000000000000000000
χ202222222222222222-2-22222222-2-22222-2-2-200-2-2-2-2-2-2-2-2-2-200-2000000222200000000000000000000
χ212222222222222222-2-2222-2-2-2-2-2-2-2-2-2-2-20000-200222000000200000000002i−2i000000−2i2i0000000000
χ222222222222222222-2-2222-2-2-2-2-2-2-2-2-2-2-20000-20022200000020000000000−2i2i0000002i−2i0000000000
χ232222222222222-2-2222-2-2-222-2-2-2-222-2-2-20000200-2-22000000200000000000022000000-2-200000000
χ242222222222222-2-2222-2-2-222-2-2-2-222-2-2-20000200-2-220000002000000000000-2-20000002200000000
χ252222222222222-2-22-2-2-2-2-222-2-22222-2-220000-20022-2000000-2000000000022000000-2-20000000000
χ262222222222222-2-22-2-2-2-2-222-2-22222-2-220000-20022-2000000-20000000000-2-2000000220000000000
χ272222222222222-2-22-2-2-2-2-2-2-22222-2-22222-200-22-2-2-2222-2-2002000000-2-22200000000000000000000
χ282222222222222-2-22-2-2-2-2-2-2-22222-2-2222-2200-2-22-2-22-2-22200200000022-2-200000000000000000000
χ2922222-2-2222-2-2-2222222-2-22-222-2-22-2-2-220000-2002-22000000-2000000000000000000000000002i−2i2i−2i
χ3022222-2-2222-2-2-2222222-2-22-222-2-22-2-2-220000-2002-22000000-200000000000000000000000000−2i2i−2i2i
χ3122222-2-2222-2-2-2222222-2-2-22-2-2-2-2-222220022-200-22-200002222-2-2-22-2000000000000000000000000
χ3222222-2-2222-2-2-2222222-2-2-22-2-2-2-2-2222200-2-2-200-22-20000-2-22-2222-22000000000000000000000000
χ3322222-2-2222-2-2-2222-2-22-2-22-222222-2-2-2-20000200-22-2000000200000000000000000000002-22-20000
χ3422222-2-2222-2-2-2222-2-22-2-22-222222-2-2-2-20000200-22-200000020000000000000000000000-22-220000
χ3522222-2-2222-2-2-2222-2-22-2-2-22-2-222-2222-200002002-22000000-2000000000000002-22-2000000000000
χ3622222-2-2222-2-2-2222-2-22-2-2-22-2-222-2222-200002002-22000000-200000000000000-22-22000000000000
χ3722222-2-2222-2-2-2-2-2222-2222-2-2-2222-222-20022-200-2220000-2-2-22-2-22-22000000000000000000000000
χ3822222-2-2222-2-2-2-2-2222-2222-2-2-2222-222-200-2-2-200-222000022-2-222-22-2000000000000000000000000
χ3922222-2-2222-2-2-2-2-2222-222-222222-22-2-2-20000-2002-2-20000002000000000000000000000000002-2-22
χ4022222-2-2222-2-2-2-2-2222-222-222222-22-2-2-20000-2002-2-2000000200000000000000000000000000-222-2
χ4122222-2-2222-2-2-2-2-22-2-2-2222-2-2-2-2-22-222200002002-2-20000002000000000000002-2-22000000000000
χ4222222-2-2222-2-2-2-2-22-2-2-2222-2-2-2-2-22-222200002002-2-2000000200000000000000-222-2000000000000
χ4322222-2-2222-2-2-2-2-22-2-2-222-2222-2-2-22-2-220000200-222000000-200000000000000000000002i−2i−2i2i0000
χ4422222-2-2222-2-2-2-2-22-2-2-222-2222-2-2-22-2-220000200-222000000-20000000000000000000000−2i2i2i−2i0000
χ45444444444-44-4-400-400000440000-4-400000220000000000220-2-22-2-22000000000000000000000000
χ46444444444-44-4-400-400000440000-4-400000-2-20000000000-2-2022-222-2000000000000000000000000
χ47444444444-44-4-400-400000-4-400004400000220000000000-2-20-2-2222-2000000000000000000000000
χ48444444444-44-4-400-400000-4-400004400000-2-2000000000022022-2-2-22000000000000000000000000
χ494444444-4-4-4-44-400400000004-400004-40040000400000-4-4000000000000000000000000000000000
χ504444444-4-4-4-44-400400000004-400004-400-40000-40000044000000000000000000000000000000000
χ514444444-4-4-4-44-40040000000-440000-4404000040000-4-400000000000000000000000000000000000
χ524444444-4-4-4-44-40040000000-440000-440-40000-400004400000000000000000000000000000000000
χ5344444-4-444-4-44400-4000004-40000-4400000220000000000-2-20-22-2-222000000000000000000000000
χ5444444-4-444-4-44400-4000004-40000-4400000-2-200000000002202-222-2-2000000000000000000000000
χ5544444-4-444-4-44400-400000-4400004-400000220000000000220-22-22-2-2000000000000000000000000
χ5644444-4-444-4-44400-400000-4400004-400000-2-20000000000-2-202-22-222000000000000000000000000
χ5744444-4-4-4-4-44-4400400000004-40000-440000000000000000000000004-40000000000000000000000
χ5844444-4-4-4-4-44-4400400000004-40000-44000000000000000000000000-440000000000000000000000
χ5944444-4-4-4-4-44-440040000000-4400004-4000000000000000000000000004-400000000000000000000
χ6044444-4-4-4-4-44-440040000000-4400004-400000000000000000000000000-4400000000000000000000
χ618888888-8-88-8-8800-8000000000000000000000000000000000000000000000000000000000000000
χ6288888-8-8-8-8888-800-8000000000000000000000000000000000000000000000000000000000000000
χ6388-8-888-800000044000-44-40000000000000000000004-44-4000000000000000000000000000000000
χ6488-8-888-800000044000-44-4000000000000000000000-44-44000000000000000000000000000000000
χ6588-8-888-8000000-4-40004-440000000000000000000004-4-44000000000000000000000000000000000
χ6688-8-888-8000000-4-40004-44000000000000000000000-444-4000000000000000000000000000000000
χ6788-8-88-8800000044000-4-440000000000044000-4-40000000000000000000000000000000000000000
χ6888-8-88-8800000044000-4-4400000000000-4-4000440000000000000000000000000000000000000000
χ6988-8-88-88000000-4-400044-4000000000004-4000-440000000000000000000000000000000000000000
χ7088-8-88-88000000-4-400044-400000000000-440004-40000000000000000000000000000000000000000
χ71161616-16-16000000000000000000008-80000000000000000000000000000000000000000000000000000
χ72161616-16-1600000000000000000000-880000000000000000000000000000000000000000000000000000
χ731616-1616-16000000000008-80000000000000000000000000000000000000000000000000000000000000
χ741616-1616-1600000000000-880000000000000000000000000000000000000000000000000000000000000
χ7516-1600000-8800008-800000000000000000004-400000000004-40000000000000000000000000000000
χ7616-1600000-8800008-80000000000000000000-440000000000-440000000000000000000000000000000
χ7716-1600000-880000-8800000000000000000004-40000000000-440000000000000000000000000000000
χ7816-1600000-880000-880000000000000000000-4400000000004-40000000000000000000000000000000
χ7932-320000016-160000000000000000000000000000000000000000000000000000000000000000000000

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