Finite Group Databasebeta

← Group #321921

Character table — Group #321921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order12222244444444888888888888444444444488888888888888888888888888444488882244
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ911111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-11-1-11
χ1011111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-111-111-1
χ1111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-111-1-1-111-1
χ1211111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-111-1-1111-1-11
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1
χ17222222222-2-2-2-222222-2-2-2-22222-2-22222-2-2-2-222-2-222-2-2-2-20000000000000000000000000000
χ18222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222220000000000000000000000000000
χ19222222222-2-2-2-22-2-2-2-222222222-2-2-2-2-2-22222-2-22222-2-2-2-20000000000000000000000000000
χ20222222222-2-2-2-22-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2-2-222-2-222220000000000000000000000000000
χ212222-2-222-22222-2222222220000-2-200000000-2-2-2-200000000000000000000002-22-200000000
χ222222-2-222-22222-2222222220000-2-200000000-2-2-2-20000000000000000000000-22-2200000000
χ232222-2-222-22222-2-2-2-2-2-2-2-2-20000-2-200000000222200000000000000000000002-2-2200000000
χ242222-2-222-22222-2-2-2-2-2-2-2-2-20000-2-20000000022220000000000000000000000-222-200000000
χ252222-2-222-2-2-2-2-2-22222-2-2-2-200002200000000-2-222000000000000000000000000002i−2i2i−2i0000
χ262222-2-222-2-2-2-2-2-22222-2-2-2-200002200000000-2-22200000000000000000000000000−2i2i−2i2i0000
χ272222-2-222-2-2-2-2-2-2-2-2-2-222220000220000000022-2-2000000000000000000000000002i−2i−2i2i0000
χ282222-2-222-2-2-2-2-2-2-2-2-2-222220000220000000022-2-200000000000000000000000000−2i2i2i−2i0000
χ292222-2-2-2-2222-2-220000000022222-2000000000000-2-222-2-2000022-2-2000022-2-2000000000000
χ302222-2-2-2-2222-2-220000000022222-2000000000000-2-222-2-20000-2-2220000-2-222000000000000
χ312222-2-2-2-2222-2-2200000000-2-2-2-22-200000000000022-2-222000022-2-20000-2-222000000000000
χ322222-2-2-2-2222-2-2200000000-2-2-2-22-200000000000022-2-2220000-2-222000022-2-2000000000000
χ332222-2-2-2-22-2-2222000000002222-22000000000000-2-2-2-22222-2-2000022-2-20000000000000000
χ342222-2-2-2-22-2-2222000000002222-22000000000000-2-2-2-222-2-2220000-2-2220000000000000000
χ352222-2-2-2-22-2-222200000000-2-2-2-2-220000000000002222-2-222-2-20000-2-2220000000000000000
χ362222-2-2-2-22-2-222200000000-2-2-2-2-220000000000002222-2-2-2-222000022-2-20000000000000000
χ372-2-222-22-220000-2000022-2-222-2-200000022-2-2002-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-2-222-22-220000-2000022-2-222-2-200000022-2-2002-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ392-2-222-22-220000-2000022-2-2-2-222000000-2-222002-2-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ402-2-222-22-220000-2000022-2-2-2-222000000-2-222002-2-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ412-2-222-22-220000-20000-2-22222-2-2000000-2-22200-222-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ422-2-222-22-220000-20000-2-22222-2-2000000-2-22200-222-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ432-2-222-22-220000-20000-2-222-2-22200000022-2-200-22-220000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ442-2-222-22-220000-20000-2-222-2-22200000022-2-200-22-220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ452-2-22-22-2220000-222-2-2000022-2-20022-2-200002-200-220000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ462-2-22-22-2220000-222-2-2000022-2-20022-2-200002-200-220000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ472-2-22-22-2220000-222-2-20000-2-22200-2-22200002-2002-20000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ482-2-22-22-2220000-222-2-20000-2-22200-2-22200002-2002-20000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ492-2-22-22-2220000-2-2-222000022-2-200-2-2220000-2200-220000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ502-2-22-22-2220000-2-2-222000022-2-200-2-2220000-2200-220000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ512-2-22-22-2220000-2-2-2220000-2-2220022-2-20000-22002-20000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ522-2-22-22-2220000-2-2-2220000-2-2220022-2-20000-22002-20000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ53444444-4-4-444-4-4-4000000000000-440000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-444-40000000000004-40000000000000000000000000000000000000000000000
χ5544-4-400000004-402i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i2002-22-22-22-2000000002i2−2i20000000000000000000000000000
χ5644-4-400000004-402i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i200-22-22-22-2200000000−2i22i20000000000000000000000000000
χ5744-4-400000004-40−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i200-22-22-22-22000000002i2−2i20000000000000000000000000000
χ5844-4-400000004-40−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2002-22-22-22-200000000−2i22i20000000000000000000000000000
χ5944-4-40000000-4402i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2002-22-2-22-2200000000−2i22i20000000000000000000000000000
χ6044-4-40000000-4402i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i200-22-222-22-2000000002i2−2i20000000000000000000000000000
χ6144-4-40000000-440−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i200-22-222-22-200000000−2i22i20000000000000000000000000000
χ6244-4-40000000-440−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i2002-22-2-22-22000000002i2−2i20000000000000000000000000000
χ634-44-4000004-40002i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i2002-2-222-2-220000002i2−2i2000000000000000000000000000000
χ644-44-4000004-40002i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i200-222-2-222-2000000−2i22i2000000000000000000000000000000
χ654-44-4000004-4000−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i200-222-2-222-20000002i2−2i2000000000000000000000000000000
χ664-44-4000004-4000−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2002-2-222-2-22000000−2i22i2000000000000000000000000000000
χ674-44-400000-440002i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2002-2-22-222-2000000−2i22i2000000000000000000000000000000
χ684-44-400000-440002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i200-222-22-2-220000002i2−2i2000000000000000000000000000000
χ694-44-400000-44000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i200-222-22-2-22000000−2i22i2000000000000000000000000000000
χ704-44-400000-44000−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i2002-2-22-222-20000002i2−2i2000000000000000000000000000000
χ714-4-444-4-44-40000444-4-4000000000000000000-44000000000000000000000000000000000000
χ724-4-444-4-44-400004-4-4440000000000000000004-4000000000000000000000000000000000000
χ734-4-44-444-4-400004000044-4-40000000000000000-440000000000000000000000000000000000
χ744-4-44-444-4-4000040000-4-44400000000000000004-40000000000000000000000000000000000

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