Finite Group Databasebeta

← Group #72324303

Character table — Group #72324303

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11222444488888888816161616161616161616161616161616161616161616161616161616161632326464646464646464646464646464128128128128
order12222222222244444422222222224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111
χ511111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ611111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1
χ91111111111-1-11111-1-11-1111111111-1111111111111111111-1-1-1-1-1-1-1-1ii−i−iii−i−ii−ii−i
χ101111111111-1-11111-1-11-1111111111-1111111111111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−ii−ii
χ111111111111-1-11111-1-11-11111-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iiii−i−ii
χ121111111111-1-11111-1-11-11111-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i−iii−i
χ131111111111-1-11111-1-11-1-1-1-1-111-1-11-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−ii−ii
χ141111111111-1-11111-1-11-1-1-1-1-111-1-11-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iiii−ii−i
χ151111111111-1-11111-1-11-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii−iii−i
χ161111111111-1-11111-1-11-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1−i−iiiii−i−ii−i−ii
χ17222222222222222222-2200002-200-222-200-2-2000022-2-20000-2-22-20000000000000000
χ18222222222222222222-220000-2200-22-2200-2-20000-2-2220000-2-2-220000000000000000
χ19222222222222-2-2-2-2-2-22222-2-200002-20000-2-222-2-2000000002-2002-200000000000000
χ20222222222222-2-2-2-2-2-222-2-22200002-20000-2-2-2-222000000002-200-2200000000000000
χ21222222222222-2-2-2-2-2-2-220000002-2-2-2002-2220000000022-2-2-2200002-2000000000000
χ22222222222222-2-2-2-2-2-2-22000000-22-2-200-222200000000-2-222-220000-22000000000000
χ232222222222-2-22222-2-2-2-200002-200-2-22-200-2-2000022-2-2000022-220000000000000000
χ242222222222-2-22222-2-2-2-20000-2200-2-2-2200-2-20000-2-2220000222-20000000000000000
χ252222222222-2-2-2-2-2-2222-222-2-20000220000-2-222-2-200000000-2200-2200000000000000
χ262222222222-2-2-2-2-2-2222-2-2-2220000220000-2-2-2-22200000000-22002-200000000000000
χ272222222222-2-2-2-2-2-222-2-20000002-2-22002-2220000000022-2-22-20000-22000000000000
χ282222222222-2-2-2-2-2-222-2-2000000-22-2200-222200000000-2-2222-200002-2000000000000
χ29444444-4-44-4000000004000440000-4000000000-4-40000000000000000000000000000
χ30444444-4-44-4000000004000-4-40000-4000000000440000000000000000000000000000
χ31444444-4-44-400000000-404400000040000000-4-4000000000000000000000000000000
χ32444444-4-44-400000000-40-4-40000004000000044000000000000000000000000000000
χ3344444-444-4-40044-4-400000000040000040000000000-4-4000000000000000000000000
χ3444444-444-4-40044-4-4000000000-400000-4000000000044000000000000000000000000
χ3544444-444-4-400-4-444000000004000004000000000-4-400000000000000000000000000
χ3644444-444-4-400-4-44400000000-400000-40000000004400000000000000000000000000
χ3744444-4-4-4-440000000000000000040000044-40000000000-4-400000000000000000000
χ3844444-4-4-4-4400000000000000000-400000-44-400000000004400000000000000000000
χ3944444-4-4-4-44000000000000000040000040-4400000000-4-40000000000000000000000
χ4044444-4-4-4-440000000000000000-400000-40-4400000000440000000000000000000000
χ4144-4-4404-40000004-400002-22-200220000-2-2002-22-24-4002-22-200000000000000000000
χ4244-4-4404-40000004-400002-22-200-2-2000022002-22-2-4400-22-2200000000000000000000
χ4344-4-4404-40000004-40000-22-2200220000-2-200-22-22-44002-22-200000000000000000000
χ4444-4-4404-40000004-40000-22-2200-2-200002200-22-224-400-22-2200000000000000000000
χ4544-4-4404-4000000-4400002-2-22402-200-40-22002-2-2200002-2-2200000000000000000000
χ4644-4-4404-4000000-4400002-2-22-40-2200402-2002-2-220000-222-200000000000000000000
χ4744-4-4404-4000000-440000-222-240-2200-402-200-222-20000-222-200000000000000000000
χ4844-4-4404-4000000-440000-222-2-402-20040-2200-222-200002-2-2200000000000000000000
χ4944-4-440-4400004-40000002-22-2042-2000-4-2200-22-220000-222-200000000000000000000
χ5044-4-440-4400004-40000002-22-20-4-2200042-200-22-2200002-2-2200000000000000000000
χ5144-4-440-4400004-4000000-22-2204-22000-42-2002-22-200002-2-2200000000000000000000
χ5244-4-440-4400004-4000000-22-220-42-20004-22002-22-20000-222-200000000000000000000
χ5344-4-440-440000-440000002-2-2200220000-2-200-222-2004-4-22-2200000000000000000000
χ5444-4-440-440000-440000002-2-2200-2-200002200-222-200-442-22-200000000000000000000
χ5544-4-440-440000-44000000-222-200220000-2-2002-2-2200-44-22-2200000000000000000000
χ5644-4-440-440000-44000000-222-200-2-2000022002-2-22004-42-22-200000000000000000000
χ57888-8-8000000000004400000000000-40000000000000000000000000000002-22-20000
χ58888-8-8000000000004400000000000-4000000000000000000000000000000-22-220000
χ59888-8-800000000000-4-40000000000040000000000000000000000000000002i−2i−2i2i0000
χ60888-8-800000000000-4-4000000000004000000000000000000000000000000−2i2i2i−2i0000
χ6188-88-800000440000000-40000000000000000000000000000000000002-22-200000000
χ6288-88-800000440000000-4000000000000000000000000000000000000-22-2200000000
χ6388-88-800000-4-4000000040000000000000000000000000000000000002i−2i−2i2i00000000
χ6488-88-800000-4-400000004000000000000000000000000000000000000−2i2i2i−2i00000000
χ6516-16000800-800000008i−8i00000000000000000000000000000000000000000000000000
χ6616-16000800-80000000−8i8i00000000000000000000000000000000000000000000000000
χ6716-16000-800808-800000000000000000000000000000000000000000000000000000000
χ6816-16000-80080-8800000000000000000000000000000000000000000000000000000000

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