Finite Group Databasebeta

← Group #72323244

Character table — Group #72323244

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91
size1122244444444888888888161616161616161616161616163232323232323232323232323232323232326464646464646464646464646464646464646464646464646464128128128128128128128128128128128128
order1222222222222222222222222224444444422222444444444444444444444444444444444444444444444888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-1111-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ91111111-1-11-1-1111-111111-111-1-1-11-1-111-1-1-111-111-11-11-11-111-1-111-1-11-1ii−i−i1-111-1-1ii−i−iiiii−i−i−i−i11-1-1i−ii−iii−i−i
χ101111111-1-11-1-1111-111111-111-1-1-11-1-111-1-1-111-111-11-11-11-111-1-111-1-11-1−i−iii1-111-1-1−i−iii−i−i−i−iiiii11-1-1−ii−ii−i−iii
χ111111111-1-11-1-1111-111111-111-1-1-11-1-111-1-1-111-1-1-1-11-11-11-111-1-1-1-111-11ii−i−i-1111-1-1ii−i−i−i−i−i−iiiii-1-111i−ii−i−i−iii
χ121111111-1-11-1-1111-111111-111-1-1-11-1-111-1-1-111-1-1-1-11-11-11-111-1-1-1-111-11−i−iii-1111-1-1−i−iiiiiii−i−i−i−i-1-111−ii−iiii−i−i
χ131111111-1-11-1-1111-111111-111-1-1-11-1-111-1-1-11-1111-1-111-11-1-1-11111-1-11-1ii−i−i1-1-1-111ii−i−i−i−i−i−iiiii-1-111−ii−iiii−i−i
χ141111111-1-11-1-1111-111111-111-1-1-11-1-111-1-1-11-1111-1-111-11-1-1-11111-1-11-1−i−iii1-1-1-111−i−iiiiiii−i−i−i−i-1-111i−ii−i−i−iii
χ151111111-1-11-1-1111-111111-111-1-1-11-1-111-1-1-11-11-1-1-1-111-11-1-1-111-1-111-11ii−i−i-11-1-111ii−i−iiiii−i−i−i−i11-1-1−ii−ii−i−iii
χ161111111-1-11-1-1111-111111-111-1-1-11-1-111-1-1-11-11-1-1-1-111-11-1-1-111-1-111-11−i−iii-11-1-111−i−iii−i−i−i−iiiii11-1-1i−ii−iii−i−i
χ1722222222222222222222222-22-22-222-2-2-2-2-220000200-2-2-2-2000000000000000000000000000000002-22-200000000
χ1822222222222222222222222-22-22-222-2-2-2-2-220000200-2-2-2-200000000000000000000000000000000-22-2200000000
χ192222222222222222-2-2-2-222222222-2-2-2-22-2-2-20000-20022-2-200000000000000000000000000000000000022-2-20000
χ202222222222222222-2-2-2-222222222-2-2-2-22-2-2-20000-20022-2-2000000000000000000000000000000000000-2-2220000
χ212222222222222222-2-2-2-2222-22-22-2-2-222-222-20000-200-2-22200000000000000000000000000000000000000002-22-2
χ222222222222222222-2-2-2-2222-22-22-2-2-222-222-20000-200-2-2220000000000000000000000000000000000000000-22-22
χ232222222222222-2-22222222-22-22-2222-2-22-2-2-22200-222-2-2222222000000000000-2-2-2-2000000000000000000000000
χ242222222222222-2-22222222-22-22-2222-2-22-2-2-2-2-200-2-2-2-2-222-2-2-2-20000000000002222000000000000000000000000
χ252222222222222-2-22222222-2-2-2-2-2-22222-222-20022-20022-2-20000-2-2222-20000-2-20000000000000000000000000000
χ262222222222222-2-22222222-2-2-2-2-2-22222-222-200-2-2-20022-2-2000022-2-2-220000220000000000000000000000000000
χ272222222222222-2-22-2-2-2-222-22-22-22-2-22222220000200-2-2-2-200000000002222000000-2-2-2-200000000000000000000
χ282222222222222-2-22-2-2-2-222-22-22-22-2-22222220000200-2-2-2-20000000000-2-2-2-2000000222200000000000000000000
χ292222222222222-2-22-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-22000020022220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ302222222222222-2-22-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2200002002222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ312222222-2-22-2-2222-222222-22-2-22-2-2-2-2-2-222220000-200-22-22000000000000000000000000000000002-2-2200000000
χ322222222-2-22-2-2222-222222-22-2-22-2-2-2-2-2-222220000-200-22-2200000000000000000000000000000000-222-200000000
χ332222222-2-22-2-2222-2-2-2-2-22-222-2-2-2222-2-2-222-200002002-2-220000000000000000000000000000000000002i−2i−2i2i0000
χ342222222-2-22-2-2222-2-2-2-2-22-222-2-2-2222-2-2-222-200002002-2-22000000000000000000000000000000000000−2i2i2i−2i0000
χ352222222-2-22-2-2222-2-2-2-2-22-22-2-22-2-222222-2-2-20000200-222-200000000000000000000000000000000000000002i−2i−2i2i
χ362222222-2-22-2-2222-2-2-2-2-22-22-2-22-2-222222-2-2-20000200-222-20000000000000000000000000000000000000000−2i2i2i−2i
χ372222222-2-22-2-22-2-2-222222-2-222-222-2-2-2-2-222-22-20022-2-222-222-2-2000000000000-2-222000000000000000000000000
χ382222222-2-22-2-22-2-2-222222-2-222-222-2-2-2-2-222-2-22002-22-222-2-2-22200000000000022-2-2000000000000000000000000
χ392222222-2-22-2-22-2-2-222222-2-2-2222-2-2-2222-2-2-200222002-2-220000-2-2-2-2220000-220000000000000000000000000000
χ402222222-2-22-2-22-2-2-222222-2-2-2222-2-2-2222-2-2-200-2-22002-2-2200002222-2-200002-20000000000000000000000000000
χ412222222-2-22-2-22-2-2-2-2-2-2-22-2-222-2222222-2-2-220000-200-22-2200000000002i2i−2i−2i000000−2i−2i2i2i00000000000000000000
χ422222222-2-22-2-22-2-2-2-2-2-2-22-2-222-2222222-2-2-220000-200-22-220000000000−2i−2i2i2i0000002i2i−2i−2i00000000000000000000
χ432222222-2-22-2-22-2-2-2-2-2-2-22-2-2-2222-222-2-222220000-2002-22-200000000000000000000000022-2-2-2-222000000000000
χ442222222-2-22-2-22-2-2-2-2-2-2-22-2-2-2222-222-2-222220000-2002-22-2000000000000000000000000-2-22222-2-2000000000000
χ45444444444-4-4-4-400444-4-4-4-40000004-40000000000000000000000000002i−2i2i−2i0000002i−2i2i−2i00000000000000000000
χ46444444444-4-4-4-400444-4-4-4-40000004-4000000000000000000000000000−2i2i−2i2i000000−2i2i−2i2i00000000000000000000
χ47444444444-4-4-4-4004-4-444-4-4000000-440000000000000000000000000002i−2i2i−2i000000−2i2i−2i2i00000000000000000000
χ48444444444-4-4-4-4004-4-444-4-4000000-44000000000000000000000000000−2i2i−2i2i0000002i−2i2i−2i00000000000000000000
χ494444444-4-4-444-400-444-4-4-44000000-440000000000000000000000000002-2-220000002-2-2200000000000000000000
χ504444444-4-4-444-400-444-4-4-44000000-44000000000000000000000000000-222-2000000-222-200000000000000000000
χ514444444-4-4-444-400-4-4-444-440000004-40000000000000000000000000002-2-22000000-222-200000000000000000000
χ524444444-4-4-444-400-4-4-444-440000004-4000000000000000000000000000-222-20000002-2-2200000000000000000000
χ5344444-4-4444-4-4400-40000-44040-40-400004000002200000000000222-2-220000-2-20000000000000000000000000000
χ5444444-4-4444-4-4400-40000-44040-40-40000400000-2-200000000000-2-2-222-20000220000000000000000000000000000
χ5544444-4-4444-4-4400-40000-440-404040000-4000002200000000000-2-22-2-2-20000220000000000000000000000000000
χ5644444-4-4444-4-4400-40000-440-404040000-400000-2-20000000000022-22220000-2-20000000000000000000000000000
χ5744444-4-444-444-400-400004-4000000004-404-4022000220000-2-2-2-20000000000002-22-2000000000000000000000000
χ5844444-4-444-444-400-400004-4000000004-404-40-2-2000-2-200002222000000000000-22-22000000000000000000000000
χ5944444-4-444-444-400-400004-400000000-440-44022000220000-2-2-2-2000000000000-22-22000000000000000000000000
χ6044444-4-444-444-400-400004-400000000-440-440-2-2000-2-2000022220000000000002-22-2000000000000000000000000
χ6144444-4-4-4-444440040000-4-404040-40000-400000220000000000022-22-2-20000-220000000000000000000000000000
χ6244444-4-4-4-444440040000-4-404040-40000-400000-2-200000000000-2-22-22200002-20000000000000000000000000000
χ6344444-4-4-4-444440040000-4-40-40-40400004000002200000000000-2-2-22-2200002-20000000000000000000000000000
χ6444444-4-4-4-444440040000-4-40-40-4040000400000-2-200000000000222-22-20000-220000000000000000000000000000
χ6544444-4-4-4-4-4-4-4-4004000044000000004-40-4402-20002-20000-2-2220000000000002-2-22000000000000000000000000
χ6644444-4-4-4-4-4-4-4-4004000044000000004-40-440-22000-22000022-2-2000000000000-222-2000000000000000000000000
χ6744444-4-4-4-4-4-4-4-400400004400000000-4404-402-20002-20000-2-222000000000000-222-2000000000000000000000000
χ6844444-4-4-4-4-4-4-4-400400004400000000-4404-40-22000-22000022-2-20000000000002-2-22000000000000000000000000
χ69888-8-8000008-80440000000-4040-4000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ70888-8-8000008-80440000000-4040-400000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ71888-8-8000008-80-4-4000000040-404000000000000000000000000000000000000000000002-2-222-2-22000000000000
χ72888-8-8000008-80-4-4000000040-40400000000000000000000000000000000000000000000-222-2-222-2000000000000
χ73888-8-800000-880440000000-40-404000000000000000000000000000000000000000000002-22-2-22-22000000000000
χ74888-8-800000-880440000000-40-40400000000000000000000000000000000000000000000-22-222-22-2000000000000
χ75888-8-800000-880-4-400000004040-4000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ76888-8-800000-880-4-400000004040-400000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ7788-8-888-8000000000008-80000000000000000040000-40000004-40000000000000000000000000000000000000000
χ7888-8-888-8000000000008-800000000000000000-400004000000-440000000000000000000000000000000000000000
χ7988-8-888-800000000000-88000000000000000040000-4000004-4000000000000000000000000000000000000000000
χ8088-8-888-800000000000-880000000000000000-40000400000-44000000000000000000000000000000000000000000
χ8188-8-88-880000000008-8000000000000000000040000-4000000-440000000000000000000000000000000000000000
χ8288-8-88-880000000008-80000000000000000000-4000040000004-40000000000000000000000000000000000000000
χ8388-8-88-88000000000-8800000000000000000040000-400000-44000000000000000000000000000000000000000000
χ8488-8-88-88000000000-88000000000000000000-400004000004-4000000000000000000000000000000000000000000
χ851616-1616-160016-160000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ861616-1616-1600-16160000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8716-160000000-80088-8000000000000000000000004-4000000000004-400000000000000000000000000000000000000
χ8816-160000000-80088-800000000000000000000000-4400000000000-4400000000000000000000000000000000000000
χ8916-160000000-8008-88000000000000000000000004-400000000000-4400000000000000000000000000000000000000
χ9016-160000000-8008-8800000000000000000000000-44000000000004-400000000000000000000000000000000000000
χ9132-3200000001600-16000000000000000000000000000000000000000000000000000000000000000000000000000000

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