Finite Group Databasebeta

← Group #320752

Character table — Group #320752

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444444488888888888888161616161616161632323232
order12222222444444444444444488888888888888888888888844888888888888224444442444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ911111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-11
χ1011111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1
χ1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-111-1
χ1211111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-11111-1-1-1-1-11-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-111111-11-1
χ172222222222-2-2-2-2-2-222-2-22222000000002222-2-2-2-200000000-2-2000022-2-20000000000000000
χ182222222222-2-2-2-2-2-222-2-2222200000000-2-2-2-2222200000000-2-20000-2-2220000000000000000
χ192222222222-2-2-2-2-2-222-2-2-2-2-2-2000000002222-2-2-2-200000000220000-2-2220000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2-2-200000000-2-2-2-222220000000022000022-2-20000000000000000
χ2122222222-2-222-2-2-2-2-2-22222-2-200000000000000002222-2-2-2-2-220000000022-2-2000000000000
χ2222222222-2-222-2-2-2-2-2-22222-2-20000000000000000-2-2-2-22222-2200000000-2-222000000000000
χ2322222222-2-222-2-2-2-2-2-222-2-22200000000000000002222-2-2-2-22-200000000-2-222000000000000
χ2422222222-2-222-2-2-2-2-2-222-2-2220000000000000000-2-2-2-222222-20000000022-2-2000000000000
χ2522222222-2-2-2-22222-2-2-2-222-2-22222-2-2-2-200000000000000002-222-2-200000000000000000000
χ2622222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-2222200000000000000002-2-2-22200000000000000000000
χ2722222222-2-2-2-22222-2-2-2-2-2-2222222-2-2-2-20000000000000000-22-2-22200000000000000000000
χ2822222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-222220000000000000000-2222-2-200000000000000000000
χ2922-2-222-2-222-2-222-2-2-2-22200002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000002-22i−2i000000
χ3022-2-222-2-222-2-222-2-2-2-22200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000-22−2i2i000000
χ3122-2-222-2-222-2-222-2-2-2-2220000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000002-2−2i2i000000
χ3222-2-222-2-222-2-222-2-2-2-2220000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000-222i−2i000000
χ3322-2-222-2-2-2-22222-2-222-2-200002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000002-200002i−2i0000
χ3422-2-222-2-2-2-22222-2-222-2-200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000-220000−2i2i0000
χ3522-2-222-2-2-2-22222-2-222-2-20000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000002-20000−2i2i0000
χ3622-2-222-2-2-2-22222-2-222-2-20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000-2200002i−2i0000
χ372-22-22-22-22-20000002-2002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000022-2-2i2i2−i2−i2i2i2−i2−i2002−22−2002i−2i2−22−2000000000000
χ382-22-22-22-22-20000002-2002i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000-2-222−i2−i2i2i2−i2−i2i2i2002−22−200−2i2i−22−22000000000000
χ392-22-22-22-22-20000002-2002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000022-2-2−i2−i2i2i2−i2−i2i2i200−22−22002i−2i−22−22000000000000
χ402-22-22-22-22-20000002-2002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000-2-222i2i2−i2−i2i2i2−i2−i200−22−2200−2i2i2−22−2000000000000
χ412-22-22-22-22-20000002-200−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000022-2-2i2i2−i2−i2i2i2−i2−i200−22−2200−2i2i−22−22000000000000
χ422-22-22-22-22-20000002-200−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000-2-222−i2−i2i2i2−i2−i2i2i200−22−22002i−2i2−22−2000000000000
χ432-22-22-22-22-20000002-200−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000022-2-2−i2−i2i2i2−i2−i2i2i2002−22−200−2i2i2−22−2000000000000
χ442-22-22-22-22-20000002-200−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000-2-222i2i2−i2−i2i2i2−i2−i2002−22−2002i−2i−22−22000000000000
χ452-22-22-22-2-22000000-22002i−2i−2i2ii2−i2i2−i2−i2i2−i2i222-2-20000i2i2−i2−i2−i2−i2i2i2002−2−222i−2i002−2−22000000000000
χ462-22-22-22-2-22000000-22002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2-2-2220000−i2−i2i2i2i2i2−i2−i2002−2−22−2i2i00−222−2000000000000
χ472-22-22-22-2-22000000-22002i−2i−2i2i−i2i2−i2i2i2−i2i2−i222-2-20000−i2−i2i2i2i2i2−i2−i200−222−22i−2i00−222−2000000000000
χ482-22-22-22-2-22000000-22002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2-2-2220000i2i2−i2−i2−i2−i2i2i200−222−2−2i2i002−2−22000000000000
χ492-22-22-22-2-22000000-2200−2i2i2i−2ii2−i2i2−i2−i2i2−i2i222-2-20000i2i2−i2−i2−i2−i2i2i200−222−2−2i2i00−222−2000000000000
χ502-22-22-22-2-22000000-2200−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2-2-2220000−i2−i2i2i2i2i2−i2−i200−222−22i−2i002−2−22000000000000
χ512-22-22-22-2-22000000-2200−2i2i2i−2i−i2i2−i2i2i2−i2i2−i222-2-20000−i2−i2i2i2i2i2−i2−i2002−2−22−2i2i002−2−22000000000000
χ522-22-22-22-2-22000000-2200−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2-2-2220000i2i2−i2−i2−i2−i2i2i2002−2−222i−2i00−222−2000000000000
χ534444-4-4-4-400004-44-4000000000000000022−2222−2222−2222−220000000000000000000000000000000000
χ544444-4-4-4-400004-44-40000000000000000−2222−2222−2222−22220000000000000000000000000000000000
χ554444-4-4-4-40000-44-44000000000000000022−2222−22−2222−22220000000000000000000000000000000000
χ564444-4-4-4-40000-44-440000000000000000−2222−222222−2222−220000000000000000000000000000000000
χ5744-4-444-4-44444-4-444-4-4-4-4000000000000000000000000000000000000000000000000000000
χ5844-4-444-4-4-4-4-4-4-4-4444444000000000000000000000000000000000000000000000000000000
χ5944-4-4-4-44400004-4-4400000000000000000000000022−2222−2222−2222−2200000000000000000000000000
χ6044-4-4-4-44400004-4-44000000000000000000000000−2222−2222−2222−222200000000000000000000000000
χ6144-4-4-4-4440000-444-400000000000000000000000022−2222−22−2222−222200000000000000000000000000
χ6244-4-4-4-4440000-444-4000000000000000000000000−2222−222222−2222−2200000000000000000000000000
χ634-44-4-44-44004-40000004-400000000000022−22−222222−22−22220000000000000000000000000000000000
χ644-44-4-44-44004-40000004-4000000000000−222222−22−222222−220000000000000000000000000000000000
χ654-44-4-44-4400-44000000-4400000000000022−22−2222−222222−220000000000000000000000000000000000
χ664-44-4-44-4400-44000000-44000000000000−222222−2222−22−22220000000000000000000000000000000000
χ674-4-444-4-444-4000000-4400000022−22−222222−22−2222000000000000000000000000000000000000000000
χ684-4-444-4-444-4000000-44000000−222222−22−222222−22000000000000000000000000000000000000000000
χ694-4-444-4-44-440000004-400000022−22−2222−222222−22000000000000000000000000000000000000000000
χ704-4-444-4-44-440000004-4000000−222222−2222−22−2222000000000000000000000000000000000000000000
χ714-4-44-444-4004-4000000-440000000000000000000000004i−4i−4i4i00000000000000000000000000
χ724-4-44-444-4004-4000000-44000000000000000000000000−4i4i4i−4i00000000000000000000000000
χ734-4-44-444-400-440000004-4000000000000000000004i−4i−4i4i000000000000000000000000000000
χ744-4-44-444-400-440000004-400000000000000000000−4i4i4i−4i000000000000000000000000000000

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