Finite Group Databasebeta

← Group #350189

Character table — Group #350189

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442244444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-11111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-222-2-2220000000022-2-2-2-222-2-2-2000000000000-2-222000000000000000000
χ182222222222-2-222-2-2220000000022-2-2-2-2-2-222-200000000000022-2-2000000000000000000
χ192222222222-2-222-2-2-2-200000000-2-222-2-222222000000000000-2-2-2-2000000000000000000
χ202222222222-2-222-2-2-2-200000000-2-222-2-2-2-2-2-220000000000002222000000000000000000
χ2122222222-2-222-2-2222222222222-2-222-2-20000-200000000-2-2-2-20000000000000000000000
χ2222222222-2-222-2-22222-2-2-2-2-2-2-2-2-2-222-2-20000-20000000022220000000000000000000000
χ2322222222-2-222-2-222-2-22222-2-2-2-222-2-2-2-20000200000000-2-2220000000000000000000000
χ2422222222-2-222-2-222-2-2-2-2-2-2222222-2-2-2-2000020000000022-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22200000000-2-2-2-2220000222-2-222-2-200000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22200000000-2-2-2-22200002-2-222-2-22200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2000000002222220000-222-2-2-2-22200000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2000000002222220000-2-2-22222-2-200000000000000000000000000
χ29222-22-2-2-200-2-200222-222-2-222-2-2002-200000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ30222-22-2-2-200-2-200222-222-2-222-2-2002-200000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ31222-22-2-2-200-2-200222-2-2-222-2-222002-200000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ32222-22-2-2-200-2-200222-2-2-222-2-222002-200000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ33222-22-2-2-200-2-20022-2222-2-2-2-22200-2200000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ34222-22-2-2-200-2-20022-2222-2-2-2-22200-2200000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ35222-22-2-2-200-2-20022-22-2-22222-2-200-2200000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ36222-22-2-2-200-2-20022-22-2-22222-2-200-2200000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ372-2-2-2222-22-22-22-22-20000002i−2i2i−2i00002-2002i−2i02-22-20000002i−2i002i−2i000000000000000000
χ382-2-2-2222-22-22-22-22-20000002i−2i2i−2i00002-200−2i2i0-22-220000002i−2i00−2i2i000000000000000000
χ392-2-2-2222-22-22-22-22-2000000−2i2i−2i2i00002-2002i−2i0-22-22000000−2i2i002i−2i000000000000000000
χ402-2-2-2222-22-22-22-22-2000000−2i2i−2i2i00002-200−2i2i02-22-2000000−2i2i00−2i2i000000000000000000
χ412-2-2-2222-22-2-222-2-22002i−2i2i−2i00000000-22002i−2i000002-22-22i−2i0000−2i2i000000000000000000
χ422-2-2-2222-22-2-222-2-22002i−2i2i−2i00000000-2200−2i2i00000-22-222i−2i00002i−2i000000000000000000
χ432-2-2-2222-22-2-222-2-2200−2i2i−2i2i00000000-22002i−2i00000-22-22−2i2i0000−2i2i000000000000000000
χ442-2-2-2222-22-2-222-2-2200−2i2i−2i2i00000000-2200−2i2i000002-22-2−2i2i00002i−2i000000000000000000
χ452-2-2-2222-2-222-2-222-20000002i−2i2i−2i0000-222i−2i00000002-2-2200−2i2i2i−2i00000000000000000000
χ462-2-2-2222-2-222-2-222-20000002i−2i2i−2i0000-22−2i2i0000000-222-200−2i2i−2i2i00000000000000000000
χ472-2-2-2222-2-222-2-222-2000000−2i2i−2i2i0000-222i−2i0000000-222-2002i−2i2i−2i00000000000000000000
χ482-2-2-2222-2-222-2-222-2000000−2i2i−2i2i0000-22−2i2i00000002-2-22002i−2i−2i2i00000000000000000000
χ492-2-2-2222-2-22-22-22-22002i−2i2i−2i000000002-22i−2i000-222-20000−2i2i00−2i2i00000000000000000000
χ502-2-2-2222-2-22-22-22-22002i−2i2i−2i000000002-2−2i2i0002-2-220000−2i2i002i−2i00000000000000000000
χ512-2-2-2222-2-22-22-22-2200−2i2i−2i2i000000002-22i−2i0002-2-2200002i−2i00−2i2i00000000000000000000
χ522-2-2-2222-2-22-22-22-2200−2i2i−2i2i000000002-2−2i2i000-222-200002i−2i002i−2i00000000000000000000
χ53444-44-4-4-4004400-4-44-40000000000-4400000000000000000000000000000000000000000
χ54444-44-4-4-4004400-4-4-4400000000004-400000000000000000000000000000000000000000
χ5544-44-44-4-44400-4-400000000000000000000000000000000000000022−2222−2200000000000000
χ5644-44-44-4-44400-4-4000000000000000000000000000000000000000−2222−222200000000000000
χ5744-44-44-4-4-4-4004400000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ5844-44-44-4-4-4-400440000000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ5944-4-4-4-4440000000000000000004i−4i00000000000000000000000002i−2i−2i2i2-2-220000000000
χ6044-4-4-4-4440000000000000000004i−4i0000000000000000000000000−2i2i2i−2i-222-20000000000
χ6144-4-4-4-444000000000000000000−4i4i00000000000000000000000002i−2i−2i2i-222-20000000000
χ6244-4-4-4-444000000000000000000−4i4i0000000000000000000000000−2i2i2i−2i2-2-220000000000
χ634-44-4-44-444-400-44000000000000000000000000000000000000000000000000000002i2−2i200
χ644-44-4-44-444-400-4400000000000000000000000000000000000000000000000000000−2i22i200
χ654-44-4-44-44-44004-40000000000000000000000000000000000000000000000000002i2−2i20000
χ664-44-4-44-44-44004-4000000000000000000000000000000000000000000000000000−2i22i20000
χ674-4-444-4-44004-400-44004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ684-4-444-4-44004-400-4400−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ694-4-444-4-4400-44004-40000004i−4i−4i4i000000000000000000000000000000000000000000000
χ704-4-444-4-4400-44004-4000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ718-888-8-88-8000000000000000000000000000000000000000000000000000000000000000

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