Finite Group Databasebeta

← Group #247409

Character table — Group #247409

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444442244444422444444488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111-1-1111-1-111111111-1-1-1-1-1-1-1-111-11-1-11-1-1-111-1-1-1-1
χ411111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-11-1-11-1-1-1-1-11111
χ5111111111111111111111111-1-1111-1-1111111111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1111111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1111111-111-1-11111-1-1-1-11111-1-1-1-1111-111-1-1-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-1111111-111-1-1-1-1-1-11111-1-1-1-11111-1-11-111-1-1-1-111-1-111
χ111111111111111111-1-1-1-1-1-11111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-1-1-111
χ121111111111111111-1-1-1-1-1-11111-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1
χ131111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11-11111-1-111
χ141111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11-111-1-111-1-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-111111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-111111-1-1-1-1-1-111
χ1722222222222-2-2-2-222222-2-2-2-22200-2-2-2000000000000000000000-2002000000000
χ1822222222222-2-2-2-222222-2-2-2-2-2-200-222000000000000000000000200-2000000000
χ1922222222222-2-2-2-22-2-2-2-222-2-222002-2-2000000000000000000000200-2000000000
χ2022222222222-2-2-2-22-2-2-2-222-2-2-2-200222000000000000000000000-2002000000000
χ2122222222-2-2-22222-222-2-2-2-2-2-20022200-2-2000000000000000000-20000200000000
χ2222222222-2-2-22222-222-2-2-2-2-2-200-2-22002200000000000000000020000-200000000
χ2322222222-2-2-22222-2-2-22222-2-20022-20022000000000000000000-20000-200000000
χ2422222222-2-2-22222-2-2-22222-2-200-2-2-200-2-200000000000000000020000200000000
χ2522222222-2-2-2-2-2-2-2-222-2-222220000-20000000000000000000000002-2002-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-222220000-2000000000000000000000000-2200-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-222000020000000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-22200002000000000000000000000000-22002-2000000
χ29222-2-2-22-20002-22-20002i−2i2i−2i00002i−2i0002-222−2−2i2i2−i2−i2i2i2−i2−i222−2−20000000000000000
χ30222-2-2-22-20002-22-20002i−2i2i−2i00002i−2i0002-2−2−222−i2−i2i2i2−i2−i2i2i2−2−2220000000000000000
χ31222-2-2-22-20002-22-20002i−2i2i−2i0000−2i2i000-2222−2−2i2i2−i2−i2−i2−i2i2i2−2−2220000000000000000
χ32222-2-2-22-20002-22-20002i−2i2i−2i0000−2i2i000-22−2−222−i2−i2i2i2i2i2−i2−i222−2−20000000000000000
χ33222-2-2-22-20002-22-2000−2i2i−2i2i00002i−2i000-2222−2−2−i2−i2i2i2i2i2−i2−i2−2−2220000000000000000
χ34222-2-2-22-20002-22-2000−2i2i−2i2i00002i−2i000-22−2−222i2i2−i2−i2−i2−i2i2i222−2−20000000000000000
χ35222-2-2-22-20002-22-2000−2i2i−2i2i0000−2i2i0002-222−2−2−i2−i2i2i2−i2−i2i2i222−2−20000000000000000
χ36222-2-2-22-20002-22-2000−2i2i−2i2i0000−2i2i0002-2−2−222i2i2−i2−i2i2i2−i2−i2−2−2220000000000000000
χ372-2-2-22-2222-2-22-2-2220000002-22-20002-20000002-22-20000000000000000002-20000
χ382-2-2-22-2222-2-22-2-2220000002-22-20002-2000000-22-22000000000000000000-220000
χ392-2-2-22-2222-2-22-2-2220000002-2-22000-220000002-22-2000000000000000000-220000
χ402-2-2-22-2222-2-22-2-2220000002-2-22000-22000000-22-220000000000000000002-20000
χ412-2-2-22-2222-2-2-222-22000000-222-2000-22002-22-20000000000002-200000000000000
χ422-2-2-22-2222-2-2-222-22000000-222-2000-2200-22-22000000000000-2200000000000000
χ432-2-2-22-2222-2-2-222-22000000-22-220002-2002-22-2000000000000-2200000000000000
χ442-2-2-22-2222-2-2-222-22000000-22-220002-200-22-220000000000002-200000000000000
χ45444-4-4-44-4000-44-440004i−4i−4i4i0000000000000000000000000000000000000000000
χ46444-4-4-44-4000-44-44000−4i4i4i−4i0000000000000000000000000000000000000000000
χ4744-44-4-4-44000000004-4000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ4844-44-4-4-44000000004-400000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ4944-44-4-4-4400000000-44000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ5044-44-4-4-4400000000-4400000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ5144-4-444-4-444-40000-4000000000000000000000000022−22−222200000000000000000000
χ5244-4-444-4-444-40000-40000000000000000000000000−222222−2200000000000000000000
χ5344-4-444-4-4-4-4400004000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ5444-4-444-4-4-4-440000400000000000000000000000000000−2i22i22i2−2i20000000000000000
χ554-4444-4-4-44-440000-400000000000000000000000000000000000000000000022−2200
χ564-4444-4-4-44-440000-4000000000000000000000000000000000000000000000−222200
χ574-4444-4-4-4-44-400004000000000000000000000000000000000000000000000002i2−2i2
χ584-4444-4-4-4-44-40000400000000000000000000000000000000000000000000000−2i22i2
χ594-4-44-444-400044-4-400000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ604-4-44-444-400044-4-40000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ614-4-44-444-4000-4-44400000000000000000022−22−22220000000000000000000000000000
χ624-4-44-444-4000-4-444000000000000000000−222222−220000000000000000000000000000
χ634-4-4-44-444-4444-4-44-4000000-4400000000000000000000000000000000000000000
χ644-4-4-44-444-444-444-4-40000004-400000000000000000000000000000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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