Finite Group Databasebeta

← Group #320237

Character table — Group #320237

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444444444488888888888888888888888888888888224444442444
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1-11
χ10111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-111-1
χ11111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-111-1
χ12111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-1-11
χ13111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-11-1
χ14111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-11-11
χ15111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-11-11
χ16111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-11-11-1
χ172222222222-2-22222-2-2-2-222-2-2-2-222-2-200000000000000000000000022-2-222-2-2000000000000
χ182222222222-2-22222-2-2-2-222-2-2-2-222-2-2000000000000000000000000-2-222-2-222000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-22200000000000000000000000022-2-2-2-222000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-222000000000000000000000000-2-22222-2-2000000000000
χ2122222222-2-2222222-2-2-2-2-2-22222-2-2-2-2000000000000000022-2-222-2-200000000000000000000
χ2222222222-2-2222222-2-2-2-2-2-22222-2-2-2-20000000000000000-2-222-2-22200000000000000000000
χ2322222222-2-222-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000022-2-2-2-22200000000000000000000
χ2422222222-2-222-2-2-2-2-2-2-2-2-2-222-2-222220000000000000000-2-22222-2-200000000000000000000
χ2522222222-2-2-2-222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2622222222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2922-222-2-2-2002-222-2-20000002-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002-2002-2i2−i2i2−i2i2−i2i2−i2000000000000
χ3022-222-2-2-2002-222-2-20000002-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200-2200-22−i2i2−i2i2−i2i2−i2i2000000000000
χ3122-222-2-2-2002-222-2-20000002-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002-2002-2−i2i2−i2i2−i2i2−i2i2000000000000
χ3222-222-2-2-2002-222-2-20000002-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200-2200-22i2−i2i2−i2i2−i2i2−i2000000000000
χ3322-222-2-2-2002-2-2-2220000002-2-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002-200-22i2−i2i2−i2−i2i2−i2i2000000000000
χ3422-222-2-2-2002-2-2-2220000002-2-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200-22002-2−i2i2−i2i2i2−i2i2−i2000000000000
χ3522-222-2-2-2002-2-2-2220000002-2-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002-200-22−i2i2−i2i2i2−i2i2−i2000000000000
χ3622-222-2-2-2002-2-2-2220000002-2-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200-22002-2i2−i2i2−i2−i2i2−i2i2000000000000
χ3722-222-2-2-200-2222-2-2000000-22-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-2002-200i2−i2−i2i2i2−i2−i2i2000000000000
χ3822-222-2-2-200-2222-2-2000000-22-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-2200-2200−i2i2i2−i2−i2i2i2−i2000000000000
χ3922-222-2-2-200-2222-2-2000000-22-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-2002-200−i2i2i2−i2−i2i2i2−i2000000000000
χ4022-222-2-2-200-2222-2-2000000-22-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-2200-2200i2−i2−i2i2i2−i2−i2i2000000000000
χ4122-222-2-2-200-22-2-222000000-222-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22-200-2200i2−i2−i2i2−i2i2i2−i2000000000000
χ4222-222-2-2-200-22-2-222000000-222-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2-22002-200−i2i2i2−i2i2−i2−i2i2000000000000
χ4322-222-2-2-200-22-2-222000000-222-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22-200-2200−i2i2i2−i2i2−i2−i2i2000000000000
χ4422-222-2-2-200-22-2-222000000-222-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2-22002-200i2−i2−i2i2−i2i2i2−i2000000000000
χ452-222-22-2-222-2-2000022-2-2-2-222000000000000002i−2i2i−2i2i−2i2i−2i00000000000000002-200002i−2i0000
χ462-222-22-2-222-2-2000022-2-2-2-222000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000-220000−2i2i0000
χ472-222-22-2-222-2-2000022-2-2-2-22200000000000000−2i2i−2i2i−2i2i−2i2i00000000000000002-20000−2i2i0000
χ482-222-22-2-222-2-2000022-2-2-2-22200000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000-2200002i−2i0000
χ492-222-22-2-2-2-222000022-2-222-2-2000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000002i−2i2-2000000
χ502-222-22-2-2-2-222000022-2-222-2-2000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000−2i2i-22000000
χ512-222-22-2-2-2-222000022-2-222-2-200000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000002i−2i-22000000
χ522-222-22-2-2-2-222000022-2-222-2-200000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000−2i2i2-2000000
χ53444-4-4-4-444-4004i−4i4i−4i00004-400004i−4i0000000000000000000000000000000000000000000000
χ54444-4-4-4-444-400−4i4i−4i4i00004-40000−4i4i0000000000000000000000000000000000000000000000
χ55444-4-4-4-44-44004i−4i4i−4i0000-440000−4i4i0000000000000000000000000000000000000000000000
χ56444-4-4-4-44-4400−4i4i−4i4i0000-4400004i−4i0000000000000000000000000000000000000000000000
χ5744-4-4-444-400004i−4i−4i4i4-44-4000000004i−4i00000000000000000000000000000000000000000000
χ5844-4-4-444-400004i−4i−4i4i-44-4400000000−4i4i00000000000000000000000000000000000000000000
χ5944-4-4-444-40000−4i4i4i−4i4-44-400000000−4i4i00000000000000000000000000000000000000000000
χ6044-4-4-444-40000−4i4i4i−4i-44-44000000004i−4i00000000000000000000000000000000000000000000
χ614-444-44-4-444440000-4-444-4-4-4-400000000000000000000000000000000000000000000000000
χ624-444-44-4-4-4-4-4-40000-4-444444400000000000000000000000000000000000000000000000000
χ634-44-44-44-44-40000000000-44000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000
χ644-44-44-44-44-40000000000-4400000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000
χ654-44-44-44-4-4400000000004-4000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ664-44-44-44-4-4400000000004-400000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ674-4-44-4-444004-40000000000-440000000000000022−22−2222−222222−220000000000000000000000000000
χ684-4-44-4-444004-40000000000-4400000000000000−222222−2222−22−22220000000000000000000000000000
χ694-4-44-4-44400-4400000000004-40000000000000022−22−222222−22−22220000000000000000000000000000
χ704-4-44-4-44400-4400000000004-400000000000000−222222−22−222222−220000000000000000000000000000
χ714-4-4-444-44000000004-4-4400000000004-4-440000000000000000000000000000000000000000
χ724-4-4-444-44000000004-4-440000000000-444-40000000000000000000000000000000000000000
χ734-4-4-444-4400000000-444-4000000000000004-4-44000000000000000000000000000000000000
χ744-4-4-444-4400000000-444-400000000000000-444-4000000000000000000000000000000000000

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