Finite Group Databasebeta

← Group #6586021

Character table — Group #6586021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444444444444488888888222222444444444444444488888888888844444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111111111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-11111111111-1-111-1-1
χ91111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11-1-1-11-1-1-1-1-111-1-111-1-11-11-11-11-1
χ101111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-11-1-1-11-1-1-1-1-1-111-1-111-11-11-11-11
χ111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1111-1111111-1-111-1-1-11-11-11-11
χ121111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1111-111111-1-111-1-1111-11-11-11-1
χ131111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-111111-1-1-11-111-1-1-1-111-1-1111-1-111-1-11
χ141111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-11111-11-1-1-1111-1-111-1-111-1-1-111-1-111-1
χ151111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-11-1111-1-1-111-1-111-1-111-111-1-111-1
χ161111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1111-11-1-11111-1-111-1-11-1-111-1-11
χ17111111111-1-1-1-11111-1-1-1-111111111111-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ18111111111-1-1-1-11111-1-1-1-111111111111-1-111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ19111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ20111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111
χ21111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1
χ22111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111
χ23111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ24111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1
χ25111111111-1-1-1-1-1-1-1-1111111111111111-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1111-1-11-111-1
χ26111111111-1-1-1-1-1-1-1-1111111111111111-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-11-11111-1-11111-1-1-111-11-1-11
χ27111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-111-11-1-1-1-111-1-1-1-111-111-11-1-11
χ28111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-11111-1-1-1-1-1-1-11111-1-11-1-11-111-1
χ29111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-1111-1-1-1-11-1-111-1-11111-1-11-11-1-11-11
χ30111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111111111-1-1-1-111-1-111-11-1-11-1-1-11111-1-1-1-111-11-111-11-1
χ31111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-11-111-1111-1-1-1-11111-1-1-11-111-11-1
χ32111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111111111-1-1-1-1-1-111-1-1-11111-111-1-111-1-1-1-1111-11-1-11-11
χ3322222222-2222222222222-2-2-200000000-2-200000000-2-22222-2-22222000000000000000000-2-200-2-200000000000000000000
χ3422222222-2222222222222-2-2-200000000-2-200000000-2-2-2-2-2-2-2-2-2-2-2-200000000000000000022002200000000000000000000
χ3522222222-22222-2-2-2-2-2-2-2-2-2-2-200000000-2-2000000002222-2-22222-2-2000000000000000000-2200-2200000000000000000000
χ3622222222-22222-2-2-2-2-2-2-2-2-2-2-200000000-2-20000000022-2-22222-2-2220000000000000000002-2002-200000000000000000000
χ3722222222-2-2-2-2-22222-2-2-2-2-2-2-2000000002200000000222222-2-2-2-2-2-2000000000000000000-2-2002200000000000000000000
χ3822222222-2-2-2-2-22222-2-2-2-2-2-2-200000000220000000022-2-2-2-2-2-222220000000000000000002200-2-200000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-22222-2-2-2000000002200000000-2-222-2-222-2-222000000000000000000-22002-200000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-22222-2-2-2000000002200000000-2-2-2-2222222-2-20000000000000000002-200-2200000000000000000000
χ412222-2-2-2-2222-2-2000000002-2-22222-2-2-2-22-222-2-222-2-200000000000022-2-2000000002-22-20000000000000000000000000000
χ422222-2-2-2-2222-2-2000000002-2-22222-2-2-2-22-2-2-222-2-22200000000000022-2-200000000-22-220000000000000000000000000000
χ432222-2-2-2-2222-2-2000000002-2-2-2-2-2-222222-222-2-2-2-222000000000000-2-22200000000-222-20000000000000000000000000000
χ442222-2-2-2-2222-2-2000000002-2-2-2-2-2-222222-2-2-22222-2-2000000000000-2-222000000002-2-220000000000000000000000000000
χ452222-2-2-2-22-2-222000000002-2-22222-2-2-2-2-2222-2-222-2-2000000000000-2-22200000000-22-220000000000000000000000000000
χ462222-2-2-2-22-2-222000000002-2-22222-2-2-2-2-22-2-222-2-222000000000000-2-222000000002-22-20000000000000000000000000000
χ472222-2-2-2-22-2-222000000002-2-2-2-2-2-22222-2222-2-2-2-22200000000000022-2-2000000002-2-220000000000000000000000000000
χ482222-2-2-2-22-2-222000000002-2-2-2-2-2-22222-22-2-22222-2-200000000000022-2-200000000-222-20000000000000000000000000000
χ4922-2-2-222-202i−2i2i−2i22-2-22i2i−2i−2i000i2i2−i2−i2i2i2−i2−i20000000000002-22-2002i−2i2i−2i2−22−2i2i2−i2−i222−2−20000000000000000i2−i2i2−i22−22−200000000
χ5022-2-2-222-202i−2i2i−2i22-2-22i2i−2i−2i000i2i2−i2−i2i2i2−i2−i2000000000000-22-2200−2i2i−2i2i2−22−2i2i2−i2−i222−2−20000000000000000−i2i2−i2i2−22−2200000000
χ5122-2-2-222-202i−2i2i−2i22-2-22i2i−2i−2i000−i2−i2i2i2−i2−i2i2i20000000000002-22-2002i−2i2i−2i−22−22−i2−i2i2i2−2−2220000000000000000−i2i2−i2i2−22−2200000000
χ5222-2-2-222-202i−2i2i−2i22-2-22i2i−2i−2i000−i2−i2i2i2−i2−i2i2i2000000000000-22-2200−2i2i−2i2i−22−22−i2−i2i2i2−2−2220000000000000000i2−i2i2−i22−22−200000000
χ5322-2-2-222-202i−2i2i−2i-2-222−2i−2i2i2i000i2i2−i2−i2i2i2−i2−i20000000000002-2-22002i−2i−2i2i2−22−2−i2−i2i2i2−2−2220000000000000000i2−i2−i2i22−2−2200000000
χ5422-2-2-222-202i−2i2i−2i-2-222−2i−2i2i2i000i2i2−i2−i2i2i2−i2−i2000000000000-222-200−2i2i2i−2i2−22−2−i2−i2i2i2−2−2220000000000000000−i2i2i2−i2−222−200000000
χ5522-2-2-222-202i−2i2i−2i-2-222−2i−2i2i2i000−i2−i2i2i2−i2−i2i2i20000000000002-2-22002i−2i−2i2i−22−22i2i2−i2−i222−2−20000000000000000−i2i2i2−i2−222−200000000
χ5622-2-2-222-202i−2i2i−2i-2-222−2i−2i2i2i000−i2−i2i2i2−i2−i2i2i2000000000000-222-200−2i2i2i−2i−22−22i2i2−i2−i222−2−20000000000000000i2−i2−i2i22−2−2200000000
χ5722-2-2-222-20−2i2i−2i2i22-2-2−2i−2i2i2i000i2i2−i2−i2i2i2−i2−i20000000000002-22-200−2i2i−2i2i−22−22i2i2−i2−i2−2−2220000000000000000i2−i2i2−i2−22−2200000000
χ5822-2-2-222-20−2i2i−2i2i22-2-2−2i−2i2i2i000i2i2−i2−i2i2i2−i2−i2000000000000-22-22002i−2i2i−2i−22−22i2i2−i2−i2−2−2220000000000000000−i2i2−i2i22−22−200000000
χ5922-2-2-222-20−2i2i−2i2i22-2-2−2i−2i2i2i000−i2−i2i2i2−i2−i2i2i20000000000002-22-200−2i2i−2i2i2−22−2−i2−i2i2i222−2−20000000000000000−i2i2−i2i22−22−200000000
χ6022-2-2-222-20−2i2i−2i2i22-2-2−2i−2i2i2i000−i2−i2i2i2−i2−i2i2i2000000000000-22-22002i−2i2i−2i2−22−2−i2−i2i2i222−2−20000000000000000i2−i2i2−i2−22−2200000000
χ6122-2-2-222-20−2i2i−2i2i-2-2222i2i−2i−2i000i2i2−i2−i2i2i2−i2−i20000000000002-2-2200−2i2i2i−2i−22−22−i2−i2i2i222−2−20000000000000000i2−i2−i2i2−222−200000000
χ6222-2-2-222-20−2i2i−2i2i-2-2222i2i−2i−2i000i2i2−i2−i2i2i2−i2−i2000000000000-222-2002i−2i−2i2i−22−22−i2−i2i2i222−2−20000000000000000−i2i2i2−i22−2−2200000000
χ6322-2-2-222-20−2i2i−2i2i-2-2222i2i−2i−2i000−i2−i2i2i2−i2−i2i2i20000000000002-2-2200−2i2i2i−2i2−22−2i2i2−i2−i2−2−2220000000000000000−i2i2i2−i22−2−2200000000
χ6422-2-2-222-20−2i2i−2i2i-2-2222i2i−2i−2i000−i2−i2i2i2−i2−i2i2i2000000000000-222-2002i−2i−2i2i2−22−2i2i2−i2−i2−2−2220000000000000000i2−i2−i2i2−222−200000000
χ652-2-222-22-22000000002i−2i2i−2i-2-222i−2i2i−2i2i−2i2i−2i002-22-22i−2i2i−2i2i−2i0000000000000000002-22-20000000000002-22i−2i0000000000000000
χ662-2-222-22-22000000002i−2i2i−2i-2-222i−2i2i−2i2i−2i2i−2i00-22-22−2i2i−2i2i2i−2i0000000000000000002-22-2000000000000-22−2i2i0000000000000000
χ672-2-222-22-22000000002i−2i2i−2i-2-22−2i2i−2i2i−2i2i−2i2i002-22-2−2i2i−2i2i2i−2i000000000000000000-22-22000000000000-222i−2i0000000000000000
χ682-2-222-22-22000000002i−2i2i−2i-2-22−2i2i−2i2i−2i2i−2i2i00-22-222i−2i2i−2i2i−2i000000000000000000-22-220000000000002-2−2i2i0000000000000000
χ692-2-222-22-2200000000−2i2i−2i2i-2-222i−2i2i−2i2i−2i2i−2i002-22-22i−2i2i−2i−2i2i000000000000000000-22-22000000000000-22−2i2i0000000000000000
χ702-2-222-22-2200000000−2i2i−2i2i-2-222i−2i2i−2i2i−2i2i−2i00-22-22−2i2i−2i2i−2i2i000000000000000000-22-220000000000002-22i−2i0000000000000000
χ712-2-222-22-2200000000−2i2i−2i2i-2-22−2i2i−2i2i−2i2i−2i2i002-22-2−2i2i−2i2i−2i2i0000000000000000002-22-20000000000002-2−2i2i0000000000000000
χ722-2-222-22-2200000000−2i2i−2i2i-2-22−2i2i−2i2i−2i2i−2i2i00-22-222i−2i2i−2i−2i2i0000000000000000002-22-2000000000000-222i−2i0000000000000000
χ732-2-22-22-22200002-22-20000-22-22i−2i2i−2i−2i2i−2i2i002-2-222i−2i−2i2i0000002-2000000002i−2i2i−2i000000002i−2i002-20000000000000000000000
χ742-2-22-22-22200002-22-20000-22-22i−2i2i−2i−2i2i−2i2i00-222-2−2i2i2i−2i0000002-2000000002i−2i2i−2i00000000−2i2i00-220000000000000000000000
χ752-2-22-22-22200002-22-20000-22-2−2i2i−2i2i2i−2i2i−2i002-2-22−2i2i2i−2i0000002-200000000−2i2i−2i2i00000000−2i2i002-20000000000000000000000
χ762-2-22-22-22200002-22-20000-22-2−2i2i−2i2i2i−2i2i−2i00-222-22i−2i−2i2i0000002-200000000−2i2i−2i2i000000002i−2i00-220000000000000000000000
χ772-2-22-22-2220000-22-220000-22-22i−2i2i−2i−2i2i−2i2i002-2-222i−2i−2i2i000000-2200000000−2i2i−2i2i00000000−2i2i00-220000000000000000000000
χ782-2-22-22-2220000-22-220000-22-22i−2i2i−2i−2i2i−2i2i00-222-2−2i2i2i−2i000000-2200000000−2i2i−2i2i000000002i−2i002-20000000000000000000000
χ792-2-22-22-2220000-22-220000-22-2−2i2i−2i2i2i−2i2i−2i002-2-22−2i2i2i−2i000000-22000000002i−2i2i−2i000000002i−2i00-220000000000000000000000
χ802-2-22-22-2220000-22-220000-22-2−2i2i−2i2i2i−2i2i−2i00-222-22i−2i−2i2i000000-22000000002i−2i2i−2i00000000−2i2i002-20000000000000000000000
χ814444-4-4-4-4-444-4-400000000-44400000000-440000000000000000000000000000000000000000000000000000000000000000
χ824444-4-4-4-4-4-4-44400000000-444000000004-40000000000000000000000000000000000000000000000000000000000000000
χ8344-4-44-4-4404i−4i−4i4i000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000022−22−22220000000000000000000000000000000000000000
χ8444-4-44-4-4404i−4i−4i4i00000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000−222222−220000000000000000000000000000000000000000
χ8544-4-44-4-440−4i4i4i−4i000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000−222222−220000000000000000000000000000000000000000
χ8644-4-44-4-440−4i4i4i−4i00000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000022−22−22220000000000000000000000000000000000000000
χ874-44-444-4-4000004-4-44000000022−22−2222−222222−220000000000000000000000000022−22−2222000000000000000000000000000000000000
χ884-44-444-4-4000004-4-440000000−222222−2222−22−222200000000000000000000000000−222222−22000000000000000000000000000000000000
χ894-44-444-4-400000-444-4000000022−22−2222−222222−2200000000000000000000000000−222222−22000000000000000000000000000000000000
χ904-44-444-4-400000-444-40000000−222222−2222−22−22220000000000000000000000000022−22−2222000000000000000000000000000000000000
χ914-44-4-4-4440000000004-4-4400022−22−222222−22−222200000000000000000000000000000022−22−222200000000000000000000000000000000
χ924-44-4-4-4440000000004-4-44000−222222−22−222222−22000000000000000000000000000000−222222−2200000000000000000000000000000000
χ934-44-4-4-444000000000-444-400022−22−222222−22−2222000000000000000000000000000000−222222−2200000000000000000000000000000000
χ944-44-4-4-444000000000-444-4000−222222−22−222222−2200000000000000000000000000000022−22−222200000000000000000000000000000000
χ954-4-444-44-4-4000000004i−4i4i−4i44-4000000000000000000−4i4i000000000000000000000000000000000000000000000000000000
χ964-4-444-44-4-400000000−4i4i−4i4i44-40000000000000000004i−4i000000000000000000000000000000000000000000000000000000
χ974-4-44-44-44-400004-44-400004-44000000000000000000000000-44000000000000000000000000000000000000000000000000
χ984-4-44-44-44-40000-44-4400004-440000000000000000000000004-4000000000000000000000000000000000000000000000000

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