Finite Group Databasebeta

← Group #324134

Character table — Group #324134

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444422444488888888888888888888888888888888244488882444
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ911111111-1-1-1-11-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-11-1-11
χ1011111111-1-1-1-11-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-111-1
χ1111111111-1-1-1-11-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1-111-1
χ1211111111-1-1-1-11-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1111-1-11
χ1311111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1-1-11111-1-1
χ1411111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1111-1-1-1-111
χ1511111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-1-111-1-111
χ1611111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1111-1-111-1-1
χ172222222222222-2-2-2-222-2-2-2-22-2-2-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ182222222222222-2-2-2-222-2-2-2-22-2-2-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ19222222222222-22222-2-22222-2-2-2-2-2-2-2000000000000000000000000000000002-2-2200000000
χ20222222222222-22222-2-22222-2-2-2-2-2-2-200000000000000000000000000000000-222-200000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000002i−2i2i−2i0000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000−2i2i−2i2i0000
χ2322222222-2-2-2-22222222-2-2-2-2222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ2422222222-2-2-2-22222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000002i−2i−2i2i0000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000−2i2i2i−2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-2-22222-222-2-2220000000000000000000000000000000022-2-200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-22222-222-2-22200000000000000000000000000000000-2-22200000000
χ2922-2-222-2-22i2i−2i−2i20000-2-20000200002i−2i2i2i−2i−2i0000000022-2-222−2−2i2i2−i2−i2i2i2−i2−i222−2−2000000000000
χ3022-2-222-2-22i2i−2i−2i20000-2-20000200002i−2i2i2i−2i−2i0000000022-2-2−2−222−i2−i2i2i2−i2−i2i2i2−2−222000000000000
χ3122-2-222-2-22i2i−2i−2i20000-2-20000200002i−2i−2i−2i2i2i00000000-2-22222−2−2i2i2−i2−i2−i2−i2i2i2−2−222000000000000
χ3222-2-222-2-22i2i−2i−2i20000-2-20000200002i−2i−2i−2i2i2i00000000-2-222−2−222−i2−i2i2i2i2i2−i2−i222−2−2000000000000
χ3322-2-222-2-2−2i−2i2i2i20000-2-2000020000−2i2i2i2i−2i−2i00000000-2-22222−2−2−i2−i2i2i2i2i2−i2−i2−2−222000000000000
χ3422-2-222-2-2−2i−2i2i2i20000-2-2000020000−2i2i2i2i−2i−2i00000000-2-222−2−222i2i2−i2−i2−i2−i2i2i222−2−2000000000000
χ3522-2-222-2-2−2i−2i2i2i20000-2-2000020000−2i2i−2i−2i2i2i0000000022-2-222−2−2−i2−i2i2i2−i2−i2i2i222−2−2000000000000
χ3622-2-222-2-2−2i−2i2i2i20000-2-2000020000−2i2i−2i−2i2i2i0000000022-2-2−2−222i2i2−i2−i2i2i2−i2−i2−2−222000000000000
χ372-22-22-22-20000200002-222-2-2-2002-20000002i2i−2i−2i00002i−2i2i−2i00002i−2i2i−2i2-22-20000000000000000
χ382-22-22-22-20000200002-222-2-2-2002-20000002i2i−2i−2i00002i−2i2i−2i0000−2i2i−2i2i-22-220000000000000000
χ392-22-22-22-20000200002-222-2-2-2002-2000000−2i−2i2i2i0000−2i2i−2i2i00002i−2i2i−2i-22-220000000000000000
χ402-22-22-22-20000200002-222-2-2-2002-2000000−2i−2i2i2i0000−2i2i−2i2i0000−2i2i−2i2i2-22-20000000000000000
χ412-22-22-22-20000200002-2-2-222-200-220000002i2i−2i−2i0000−2i2i−2i2i2-22-2000000002i−2i2i−2i000000000000
χ422-22-22-22-20000200002-2-2-222-200-220000002i2i−2i−2i0000−2i2i−2i2i-22-2200000000−2i2i−2i2i000000000000
χ432-22-22-22-20000200002-2-2-222-200-22000000−2i−2i2i2i00002i−2i2i−2i2-22-200000000−2i2i−2i2i000000000000
χ442-22-22-22-20000200002-2-2-222-200-22000000−2i−2i2i2i00002i−2i2i−2i-22-22000000002i−2i2i−2i000000000000
χ452-2-222-2-220000222-2-2-220000-22-20000000000002i2i−2i−2i2i−2i−2i2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ462-2-222-2-220000222-2-2-220000-22-20000000000002i2i−2i−2i2i−2i−2i2i−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ472-2-222-2-220000222-2-2-220000-22-2000000000000−2i−2i2i2i−2i2i2i−2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ482-2-222-2-220000222-2-2-220000-22-2000000000000−2i−2i2i2i−2i2i2i−2i−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ492-2-222-2-2200002-2-222-220000-2-220000000000002i2i−2i−2i−2i2i2i−2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ502-2-222-2-2200002-2-222-220000-2-220000000000002i2i−2i−2i−2i2i2i−2i−222−22−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ512-2-222-2-2200002-2-222-220000-2-22000000000000−2i−2i2i2i2i−2i−2i2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ522-2-222-2-2200002-2-222-220000-2-22000000000000−2i−2i2i2i2i−2i−2i2i−222−22−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ53444-4-4-4-444-44-400000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000
χ54444-4-4-4-444-44-40000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000
χ55444-4-4-4-44-44-4400000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ56444-4-4-4-44-44-440000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ5744-44-4-44-44i−4i−4i4i04i−4i4i−4i004-44-4000000000000000000000000000000000000000000000000000
χ5844-44-4-44-44i−4i−4i4i0−4i4i−4i4i00-44-44000000000000000000000000000000000000000000000000000
χ5944-44-4-44-4−4i4i4i−4i04i−4i4i−4i00-44-44000000000000000000000000000000000000000000000000000
χ6044-44-4-44-4−4i4i4i−4i0−4i4i−4i4i004-44-4000000000000000000000000000000000000000000000000000
χ6144-4-444-4-44i4i−4i−4i-40000440000-40000−4i4i00000000000000000000000000000000000000000000
χ6244-4-444-4-4−4i−4i4i4i-40000440000-400004i−4i00000000000000000000000000000000000000000000
χ634-444-44-4-4000004i−4i−4i4i00000000000002i2−2i22i2−2i222−22−2222000000000000000000000000000000000000
χ644-444-44-4-4000004i−4i−4i4i0000000000000−2i22i2−2i22i2−222222−22000000000000000000000000000000000000
χ654-444-44-4-400000−4i4i4i−4i00000000000002i2−2i22i2−2i2−222222−22000000000000000000000000000000000000
χ664-444-44-4-400000−4i4i4i−4i0000000000000−2i22i2−2i22i222−22−2222000000000000000000000000000000000000
χ674-44-44-44-40000-40000-4444-4-4400-440000000000000000000000000000000000000000000000
χ684-44-44-44-40000-40000-44-4-4444004-40000000000000000000000000000000000000000000000
χ694-4-444-4-440000-444-4-44-400004-44000000000000000000000000000000000000000000000000
χ704-4-444-4-440000-4-4-4444-4000044-4000000000000000000000000000000000000000000000000
χ714-4-4-4-4444000000000004-4-44000000022−22−22220000−222222−2200000000000000000000000000000000
χ724-4-4-4-4444000000000004-4-440000000−222222−22000022−22−222200000000000000000000000000000000
χ734-4-4-4-444400000000000-444-4000000022−22−2222000022−22−222200000000000000000000000000000000
χ744-4-4-4-444400000000000-444-40000000−222222−220000−222222−2200000000000000000000000000000000

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