Finite Group Databasebeta

← Group #320795

Character table — Group #320795

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444444488888888888888161616161616161632323232
order12222222444444444444444488888888888888888888888844888888888888224444444444
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
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1111-11-1
χ911111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ1211111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-111-1-1-1-111-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222-2-2-2-2-2-222-2-2222200000000000000002222-2-2-2-2-2-20000000022-2-2000000000000
χ182222222222-2-2-2-2-2-222-2-222220000000000000000-2-2-2-22222-2-200000000-2-222000000000000
χ192222222222-2-2-2-2-2-222-2-2-2-2-2-200000000000000002222-2-2-2-22200000000-2-222000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2-2-20000000000000000-2-2-2-22222220000000022-2-2000000000000
χ2122222222-2-222-2-2-2-2-2-22222-2-2000000002222-2-2-2-2000000002-2000022-2-20000000000000000
χ2222222222-2-222-2-2-2-2-2-22222-2-200000000-2-2-2-22222000000002-20000-2-2220000000000000000
χ2322222222-2-222-2-2-2-2-2-222-2-222000000002222-2-2-2-200000000-220000-2-2220000000000000000
χ2422222222-2-222-2-2-2-2-2-222-2-22200000000-2-2-2-2222200000000-22000022-2-20000000000000000
χ2522222222-2-2-2-22222-2-2-2-222-2-22222-2-2-2-20000000000000000-2222-2-200000000000000000000
χ2622222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-222220000000000000000-22-2-22200000000000000000000
χ2722222222-2-2-2-22222-2-2-2-2-2-2222222-2-2-2-200000000000000002-2-2-22200000000000000000000
χ2822222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-2222200000000000000002-222-2-200000000000000000000
χ2922-22-2-22-222-2-222-2-2-2-22200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000002-22i−2i00000000
χ3022-22-2-22-222-2-222-2-2-2-22200002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000-22−2i2i00000000
χ3122-22-2-22-222-2-222-2-2-2-2220000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000002-2−2i2i00000000
χ3222-22-2-22-222-2-222-2-2-2-2220000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000-222i−2i00000000
χ3322-22-2-22-2-2-22222-2-222-2-200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000002i−2i2-20000
χ3422-22-2-22-2-2-22222-2-222-2-200002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000−2i2i-220000
χ3522-22-2-22-2-2-22222-2-222-2-20000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000002i−2i-220000
χ3622-22-2-22-2-2-22222-2-222-2-20000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000−2i2i2-20000
χ372-2-2222-2-22-20000002-2002i−2i2i−2i2−22−22−22−222−2−222−2−2000022-2-200i2−i2i2−i2i2−i2i2−i2002i−2i000000000000
χ382-2-2222-2-22-20000002-2002i−2i2i−2i2−22−22−22−2−2−222−2−2220000-2-22200i2−i2i2−i2−i2i2−i2i200−2i2i000000000000
χ392-2-2222-2-22-20000002-2002i−2i2i−2i−22−22−22−2222−2−222−2−20000-2-22200−i2i2−i2i2i2−i2i2−i200−2i2i000000000000
χ402-2-2222-2-22-20000002-2002i−2i2i−2i−22−22−22−22−2−222−2−222000022-2-200−i2i2−i2i2−i2i2−i2i2002i−2i000000000000
χ412-2-2222-2-22-20000002-200−2i2i−2i2i2−22−22−22−222−2−222−2−2000022-2-200−i2i2−i2i2−i2i2−i2i200−2i2i000000000000
χ422-2-2222-2-22-20000002-200−2i2i−2i2i2−22−22−22−2−2−222−2−2220000-2-22200−i2i2−i2i2i2−i2i2−i2002i−2i000000000000
χ432-2-2222-2-22-20000002-200−2i2i−2i2i−22−22−22−2222−2−222−2−20000-2-22200i2−i2i2−i2−i2i2−i2i2002i−2i000000000000
χ442-2-2222-2-22-20000002-200−2i2i−2i2i−22−22−22−22−2−222−2−222000022-2-200i2−i2i2−i2i2−i2i2−i200−2i2i000000000000
χ452-2-2222-2-2-22000000-22002i−2i−2i2i2−22−2−22−2222−2−2−2−22222-2-2000000i2−i2−i2i2i2−i2−i2i22i−2i00000000000000
χ462-2-2222-2-2-22000000-22002i−2i−2i2i2−22−2−22−22−2−22222−2−2-2-222000000i2−i2−i2i2−i2i2i2−i2−2i2i00000000000000
χ472-2-2222-2-2-22000000-22002i−2i−2i2i−22−222−22−222−2−2−2−222-2-222000000−i2i2i2−i2i2−i2−i2i2−2i2i00000000000000
χ482-2-2222-2-2-22000000-22002i−2i−2i2i−22−222−22−2−2−22222−2−222-2-2000000−i2i2i2−i2−i2i2i2−i22i−2i00000000000000
χ492-2-2222-2-2-22000000-2200−2i2i2i−2i2−22−2−22−2222−2−2−2−22222-2-2000000−i2i2i2−i2−i2i2i2−i2−2i2i00000000000000
χ502-2-2222-2-2-22000000-2200−2i2i2i−2i2−22−2−22−22−2−22222−2−2-2-222000000−i2i2i2−i2i2−i2−i2i22i−2i00000000000000
χ512-2-2222-2-2-22000000-2200−2i2i2i−2i−22−222−22−222−2−2−2−222-2-222000000i2−i2−i2i2−i2i2i2−i22i−2i00000000000000
χ522-2-2222-2-2-22000000-2200−2i2i2i−2i−22−222−22−2−2−22222−2−222-2-2000000i2−i2−i2i2i2−i2−i2i2−2i2i00000000000000
χ53444-44-4-4-400004-44-400000000000000000000000022−2222−2222−2222−2200000000000000000000000000
χ54444-44-4-4-400004-44-4000000000000000000000000−2222−2222−2222−222200000000000000000000000000
χ55444-44-4-4-40000-44-4400000000000000000000000022−2222−22−2222−222200000000000000000000000000
χ56444-44-4-4-40000-44-44000000000000000000000000−2222−222222−2222−2200000000000000000000000000
χ5744-44-4-44-44444-4-444-4-4-4-4000000000000000000000000000000000000000000000000000000
χ5844-44-4-44-4-4-4-4-4-4-4444444000000000000000000000000000000000000000000000000000000
χ5944-4-4-44-4400004-4-4400000000000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000000000
χ6044-4-4-44-4400004-4-440000000000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000000000
χ6144-4-4-44-440000-444-400000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000
χ6244-4-4-44-440000-444-40000000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000
χ634-444-4-4-444-4000000-440000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ644-444-4-4-444-4000000-44000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ654-444-4-4-44-440000004-40000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ664-444-4-4-44-440000004-4000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ674-44-4-444-4004-40000004-400000000000000004i−4i−4i4i0000000000000000000000000000000000
χ684-44-4-444-4004-40000004-40000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ694-44-4-444-400-44000000-440000000000004i−4i−4i4i00000000000000000000000000000000000000
χ704-44-4-444-400-44000000-44000000000000−4i4i4i−4i00000000000000000000000000000000000000
χ714-4-4-44-444004-4000000-440000000000000000000022−22−2222−222222−2200000000000000000000000000
χ724-4-4-44-444004-4000000-4400000000000000000000−222222−2222−22−222200000000000000000000000000
χ734-4-4-44-44400-440000004-40000000000000000000022−22−222222−22−222200000000000000000000000000
χ744-4-4-44-44400-440000004-400000000000000000000−222222−22−222222−2200000000000000000000000000

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