Finite Group Databasebeta

← Group #349655

Character table — Group #349655

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444444444444444444444222244444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-11-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111
χ61111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ81111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-111111-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-111111-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-111-1-11111111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-111-1-1111111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1111-1
χ141111111111111111-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111-1-1-11
χ151111111111111111-1-11-1-1-1-11111-1-1-1-11-1-1-1-1-1-111-111-1-1111111-1-11111-1-1-1-1-1-11111-1-1-11
χ161111111111111111-1-11-1-1-1-11111-1-1-1-11-1-1-1-1-1-111-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1111-1
χ1722222222222-2-2-2-2222-22222222222-2-2-20000-2-200-20000-2-2000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-2-2-2-222-2-2-200002200-2000022000000000000000000000000
χ1922222222222-2-2-2-22-2-2-22222-2-2-2-2-2-222-20000-2-2002000022000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2-22222-2-222-20000220020000-2-2000000000000000000000000
χ2122222222-2-2-22222-222-200000000-2-222-200000022-2-2-222000000-2-2000000000000000000
χ2222222222-2-2-22222-222-200000000-2-222-2000000-2-2-222-2-200000022000000000000000000
χ2322222222-2-2-22222-2-2-2-20000000022-2-2-2000000222-2-2-2-200000022000000000000000000
χ2422222222-2-2-22222-2-2-2-20000000022-2-2-2000000-2-222222000000-2-2000000000000000000
χ2522222222-2-2-2-2-2-2-2-222200000000-2-2-2-2222-2-20000200000022-2-200000000000000000000
χ2622222222-2-2-2-2-2-2-2-222200000000-2-2-2-22-2-22200002000000-2-22200000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22000000002222222-2-20000-2000000-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-220000000022222-2-2220000-200000022-2-200000000000000000000
χ29222-2-2-22-22-2-2000022-202i2i−2i−2i2i2i−2i−2i2-2000000000000000000000000i2i2−i2−i2i2i2−i2−i22−22−2000000
χ30222-2-2-22-22-2-2000022-202i2i−2i−2i2i2i−2i−2i2-2000000000000000000000000−i2−i2i2i2−i2−i2i2i2−22−22000000
χ31222-2-2-22-22-2-2000022-20−2i−2i2i2i−2i−2i2i2i2-2000000000000000000000000i2i2−i2−i2i2i2−i2−i2−22−22000000
χ32222-2-2-22-22-2-2000022-20−2i−2i2i2i−2i−2i2i2i2-2000000000000000000000000−i2−i2i2i2−i2−i2i2i22−22−2000000
χ33222-2-2-22-22-2-200002-2202i2i−2i−2i−2i−2i2i2i-22000000000000000000000000i2i2−i2−i2−i2−i2i2i22−2−22000000
χ34222-2-2-22-22-2-200002-2202i2i−2i−2i−2i−2i2i2i-22000000000000000000000000−i2−i2i2i2i2i2−i2−i2−222−2000000
χ35222-2-2-22-22-2-200002-220−2i−2i2i2i2i2i−2i−2i-22000000000000000000000000i2i2−i2−i2−i2−i2i2i2−222−2000000
χ36222-2-2-22-22-2-200002-220−2i−2i2i2i2i2i−2i−2i-22000000000000000000000000−i2−i2i2i2i2i2−i2−i22−2−22000000
χ372-2222-2-2-222-222-2-2-20022-22-200000000-22-22-22-22-202-20000000000000000000000000000
χ382-2222-2-2-222-222-2-2-20022-22-200000000-2-22-222-2-220-220000000000000000000000000000
χ392-2222-2-2-222-222-2-2-2002-22-2200000000-22-22-2-22-220-220000000000000000000000000000
χ402-2222-2-2-222-222-2-2-2002-22-2200000000-2-22-22-222-202-20000000000000000000000000000
χ412-2222-2-2-222-2-2-222-200-22-22-20000000020000-22000002i−2i002i−2i2i−2i2i−2i000000000000000000
χ422-2222-2-2-222-2-2-222-200-22-22-20000000020000-2200000−2i2i00−2i2i−2i2i−2i2i000000000000000000
χ432-2222-2-2-222-2-2-222-200-2-22-2200000000200002-2000002i−2i00−2i2i−2i2i2i−2i000000000000000000
χ442-2222-2-2-222-2-2-222-200-2-22-2200000000200002-200000−2i2i002i−2i2i−2i−2i2i000000000000000000
χ452-2222-2-2-2-2-2222-2-2200-200002i−2i2i−2i000020000002-20-22002i−2i2i−2i−2i2i00000000000000000000
χ462-2222-2-2-2-2-2222-2-2200-200002i−2i2i−2i00002000000-2202-2002i−2i−2i2i2i−2i00000000000000000000
χ472-2222-2-2-2-2-2222-2-2200-20000−2i2i−2i2i000020000002-20-2200−2i2i−2i2i2i−2i00000000000000000000
χ482-2222-2-2-2-2-2222-2-2200-20000−2i2i−2i2i00002000000-2202-200−2i2i2i−2i−2i2i00000000000000000000
χ492-2222-2-2-2-2-22-2-222200200002i−2i2i−2i0000-22-2-2200000002i−2i−2i2i0000−2i2i000000000000000000
χ502-2222-2-2-2-2-22-2-222200200002i−2i2i−2i0000-2-222-20000000−2i2i−2i2i00002i−2i000000000000000000
χ512-2222-2-2-2-2-22-2-22220020000−2i2i−2i2i0000-22-2-220000000−2i2i2i−2i00002i−2i000000000000000000
χ522-2222-2-2-2-2-22-2-22220020000−2i2i−2i2i0000-2-222-200000002i−2i2i−2i0000−2i2i000000000000000000
χ53444-4-4-44-4-4440000-44-4000000000-44000000000000000000000000000000000000000000
χ54444-4-4-44-4-4440000-4-440000000004-4000000000000000000000000000000000000000000
χ5544-44-4-4-440004-44-400000000000000000000000000000000000000000000000000002i2−2i200
χ5644-44-4-4-440004-44-40000000000000000000000000000000000000000000000000000−2i22i200
χ5744-44-4-4-44000-44-44000000000000000000000000000000000000000000000000002i2−2i20000
χ5844-44-4-4-44000-44-4400000000000000000000000000000000000000000000000000−2i22i20000
χ594-44-4-44-444-440000-40004i−4i−4i4i000000000000000000000000000000000000000000000000
χ604-44-4-44-444-440000-4000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ614-44-4-44-44-44-40000400000004-4-4400000000000000000000000000000000000000000000
χ624-44-4-44-44-44-4000040000000-444-400000000000000000000000000000000000000000000
χ634-4-44-444-40004-4-440000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ644-4-44-444-40004-4-44000000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ654-4-44-444-4000-444-4000000000000000000000000000000000000002i2−2i22i2−2i200000000000000
χ664-4-44-444-4000-444-400000000000000000000000000000000000000−2i22i2−2i22i200000000000000
χ674-4-4-44-4440000000000000000000004-400000000000000000000002-2-222-2-220000000000
χ684-4-4-44-4440000000000000000000004-40000000000000000000000-222-2-222-20000000000
χ694-4-4-44-444000000000000000000000-4400000000000000000000002-2-22-222-20000000000
χ704-4-4-44-444000000000000000000000-440000000000000000000000-222-22-2-220000000000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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