Finite Group Databasebeta

← Group #318525

Character table — Group #318525

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order12222244444444888888888888448888888888888888884444444488888888244488888888
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
χ51111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ911111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11-11-1
χ1011111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-11-11
χ1111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-11-11
χ1211111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1111-11-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-11-1-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-11-1111-1-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-11-1-1-111-111-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-11-1111-1-11-1-11
χ17222222222-2-2-2-22222222220000-2-2000000-2-2-2-200000000000000000000000000002i−2i2i−2i0000
χ18222222222-2-2-2-22222222220000-2-2000000-2-2-2-20000000000000000000000000000−2i2i−2i2i0000
χ19222222222-2-2-2-22-2-2-2-2-2-2-2-20000-2-2000000222200000000000000000000000000002i−2i−2i2i0000
χ20222222222-2-2-2-22-2-2-2-2-2-2-2-20000-2-200000022220000000000000000000000000000−2i2i2i−2i0000
χ21222222-2-2-22222-2000000002222-2-222-2-2-2-200000000000022-2-222-2-200000000000000000000
χ22222222-2-2-22222-2000000002222-2-222-2-2-2-2000000000000-2-222-2-22200000000000000000000
χ23222222-2-2-22222-200000000-2-2-2-2-2-2-2-2222200000000000022-2-2-2-22200000000000000000000
χ24222222-2-2-22222-200000000-2-2-2-2-2-2-2-22222000000000000-2-22222-2-200000000000000000000
χ252222-2-222-222-2-2-20000000022222-2-2-222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ262222-2-222-222-2-2-20000000022222-2-2-222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ272222-2-222-222-2-2-200000000-2-2-2-22-222-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ282222-2-222-222-2-2-200000000-2-2-2-22-222-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ292222-2-2-2-2222-2-222222-2-2-2-22222-22-2-2-2-22222-2-22222-2-2-2-20000000000000000000000000000
χ302222-2-2-2-2222-2-222222-2-2-2-2-2-2-2-2-222222-2-222-2-2-2-2-2-222220000000000000000000000000000
χ312222-2-2-2-2222-2-22-2-2-2-222222222-22-2-2-2-222-2-222-2-2-2-222220000000000000000000000000000
χ322222-2-2-2-2222-2-22-2-2-2-22222-2-2-2-2-222222-2-2-2-2222222-2-2-2-20000000000000000000000000000
χ332222-2-2-2-22-2-22222222-2-2-2-200002-2000000-2-22200000000000000000000000022-2-200000000
χ342222-2-2-2-22-2-22222222-2-2-2-200002-2000000-2-222000000000000000000000000-2-22200000000
χ352222-2-2-2-22-2-2222-2-2-2-2222200002-200000022-2-20000000000000000000000002-2-2200000000
χ362222-2-2-2-22-2-2222-2-2-2-2222200002-200000022-2-2000000000000000000000000-222-200000000
χ372-22-22-20002-22-20i2i2−i2−i2i2i2−i2−i222-2-2002-20000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i002i−2i2−22−22−22−2000000000000
χ382-22-22-20002-22-20i2i2−i2−i2i2i2−i2−i222-2-2002-20000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i00−2i2i−22−22−22−22000000000000
χ392-22-22-20002-22-20i2i2−i2−i2i2i2−i2−i2-2-22200-220000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2002i−2i00−2i2i2−22−2−22−22000000000000
χ402-22-22-20002-22-20i2i2−i2−i2i2i2−i2−i2-2-22200-220000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i200−2i2i002i−2i−22−222−22−2000000000000
χ412-22-22-20002-22-20−i2−i2i2i2−i2−i2i2i222-2-2002-20000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2002i−2i002i−2i−22−22−22−22000000000000
χ422-22-22-20002-22-20−i2−i2i2i2−i2−i2i2i222-2-2002-20000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00−2i2i2−22−22−22−2000000000000
χ432-22-22-20002-22-20−i2−i2i2i2−i2−i2i2i2-2-22200-220000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2002i−2i00−2i2i−22−222−22−2000000000000
χ442-22-22-20002-22-20−i2−i2i2i2−i2−i2i2i2-2-22200-220000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i200−2i2i002i−2i2−22−2−22−22000000000000
χ452-22-2-220002-2-220i2i2−i2−i2−i2−i2i2i222-2-200-220000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i22-2002-200i2−i2−i2i2i2−i2−i2i2000000000000
χ462-22-2-220002-2-220i2i2−i2−i2−i2−i2i2i222-2-200-220000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2-2200-2200−i2i2i2−i2−i2i2i2−i2000000000000
χ472-22-2-220002-2-220i2i2−i2−i2−i2−i2i2i2-2-222002-20000i2−i2−i2i2−i2−i2i2i2i2i2−i2−i22-200-2200i2−i2−i2i2−i2i2i2−i2000000000000
χ482-22-2-220002-2-220i2i2−i2−i2−i2−i2i2i2-2-222002-20000i2−i2−i2i2−i2−i2i2i2i2i2−i2−i2-22002-200−i2i2i2−i2i2−i2−i2i2000000000000
χ492-22-2-220002-2-220−i2−i2i2i2i2i2−i2−i222-2-200-220000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i22-2002-200−i2i2i2−i2−i2i2i2−i2000000000000
χ502-22-2-220002-2-220−i2−i2i2i2i2i2−i2−i222-2-200-220000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2-2200-2200i2−i2−i2i2i2−i2−i2i2000000000000
χ512-22-2-220002-2-220−i2−i2i2i2i2i2−i2−i2-2-222002-20000−i2i2i2−i2i2i2−i2−i2−i2−i2i2i22-200-2200−i2i2i2−i2i2−i2−i2i2000000000000
χ522-22-2-220002-2-220−i2−i2i2i2i2i2−i2−i2-2-222002-20000−i2i2i2−i2i2i2−i2−i2−i2−i2i2i2-22002-200i2−i2−i2i2−i2i2i2−i2000000000000
χ53444444-4-4-4-4-4-4-4-4000000000000440000000000000000000000000000000000000000000000
χ544444-4-444-4-4-444-4000000000000-440000000000000000000000000000000000000000000000
χ5544-4-4000040000-44-44-4000022−2222−2200000022−22000022−2222−2200000000000000000000000000000000
χ5644-4-4000040000-44-44-40000−2222−2222000000−22220000−2222−222200000000000000000000000000000000
χ5744-4-4000040000-4-44-44000022−2222−2200000022−220000−2222−222200000000000000000000000000000000
χ5844-4-4000040000-4-44-440000−2222−2222000000−2222000022−2222−2200000000000000000000000000000000
χ5944-4-40000-40000400004i−4i4i−4i22−2222−22000000−2222000000002i2−2i22i2−2i20000000000000000000000000000
χ6044-4-40000-40000400004i−4i4i−4i−2222−222200000022−2200000000−2i22i2−2i22i20000000000000000000000000000
χ6144-4-40000-4000040000−4i4i−4i4i22−2222−22000000−222200000000−2i22i2−2i22i20000000000000000000000000000
χ6244-4-40000-4000040000−4i4i−4i4i−2222−222200000022−22000000002i2−2i22i2−2i20000000000000000000000000000
χ634-44-44-4000-44-4402i22i2−2i2−2i22i22i2−2i2−2i2000000000000−2i22i2−2i22i2000000000000000000000000000000000000
χ644-44-44-4000-44-440−2i2−2i22i22i2−2i2−2i22i22i20000000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ654-44-4-44000-444-402i22i2−2i2−2i2−2i2−2i22i22i2000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ664-44-4-44000-444-40−2i2−2i22i22i22i22i2−2i2−2i20000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ674-4-44004i−4i0000002i2−2i2−2i22i222−22−222222−22−222200002i2−2i20000002i−2i−2i2i2-2-220000000000000000000000000000
χ684-4-44004i−4i0000002i2−2i2−2i22i222−22−2222−222222−220000−2i22i2000000−2i2i2i−2i-222-20000000000000000000000000000
χ694-4-44004i−4i000000−2i22i22i2−2i2−222222−2222−22−222200002i2−2i2000000−2i2i2i−2i-222-20000000000000000000000000000
χ704-4-44004i−4i000000−2i22i22i2−2i2−222222−22−222222−220000−2i22i20000002i−2i−2i2i2-2-220000000000000000000000000000
χ714-4-4400−4i4i0000002i2−2i2−2i22i2−222222−2222−22−22220000−2i22i20000002i−2i−2i2i-222-20000000000000000000000000000
χ724-4-4400−4i4i0000002i2−2i2−2i22i2−222222−22−222222−2200002i2−2i2000000−2i2i2i−2i2-2-220000000000000000000000000000
χ734-4-4400−4i4i000000−2i22i22i2−2i222−22−222222−22−22220000−2i22i2000000−2i2i2i−2i2-2-220000000000000000000000000000
χ744-4-4400−4i4i000000−2i22i22i2−2i222−22−2222−222222−2200002i2−2i20000002i−2i−2i2i-222-20000000000000000000000000000

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