Finite Group Databasebeta

← Group #293321

Character table — Group #293321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444422444444444444444888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-11-1-111111111111111111111-11-1-1-1-11-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-111111111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-111-11-1-1-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-111-111111-1-1-1-1
χ9111111111111-1-1-1-1-1-11-1-111111-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1111-1-111-1-1
χ10111111111111-1-1-1-1-1-11-1-111111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-111-1-11-1-111-1-111
χ11111111111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-111-111-1-1-1-111
χ12111111111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-111-1-1-11111-1-1
χ13111111111111-1-1-1-1-1-11-1-1111-1-1-11111111111-1-1-1-11111-1-1-1-11-11-1-11-1-1-1-111-1-111
χ14111111111111-1-1-1-1-1-11-1-1111-1-1-1111111-1-1-1-11111-1-1-1-111111-11-1-11-1-111-1-111-1-1
χ15111111111111-1-1-1-1-1-11-1-1111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-11-1-1111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-11111-1-1-1-111
χ172222222222222222-2-2-222-2-2-222-22200000000000000000000-200-2000000000000
χ182222222222222222-2-2-222-2-2-2-2-2-2-2-2000000000000000000002002000000000000
χ19222222222222-2-2-2-222-2-2-2-2-2-2222-2-200000000000000000000200-2000000000000
χ20222222222222-2-2-2-222-2-2-2-2-2-2-2-222200000000000000000000-2002000000000000
χ2122222222-2-2-2-2222222-2-2-222-200-200000000000000000000000020-2-20200000000
χ2222222222-2-2-2-2222222-2-2-222-200-2000000000000000000000000-20220-200000000
χ2322222222-2-2-2-22222-2-22-2-2-2-220020022-2-200000000000000000-200002000000000
χ2422222222-2-2-2-22222-2-22-2-2-2-2200200-2-2220000000000000000020000-2000000000
χ2522222222-2-2-2-2-2-2-2-222222-2-2200-20022-2-20000000000000000020000-2000000000
χ2622222222-2-2-2-2-2-2-2-222222-2-2200-200-2-22200000000000000000-200002000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-22222-2002000000000000000000000000202-20-200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-22222-2002000000000000000000000000-20-220200000000
χ29222-2-22-2-22-22-22i2i−2i−2i0002i−2i0002-202i−2i000000000000i2i2−i2−i222−2−2000000000000i2−i22−2
χ30222-2-22-2-22-22-22i2i−2i−2i0002i−2i0002-202i−2i000000000000−i2−i2i2i2−2−222000000000000−i2i2−22
χ31222-2-22-2-22-22-22i2i−2i−2i0002i−2i000-220−2i2i000000000000i2i2−i2−i222−2−2000000000000−i2i2−22
χ32222-2-22-2-22-22-22i2i−2i−2i0002i−2i000-220−2i2i000000000000−i2−i2i2i2−2−222000000000000i2−i22−2
χ33222-2-22-2-22-22-2−2i−2i2i2i000−2i2i0002-20−2i2i000000000000i2i2−i2−i2−2−222000000000000i2−i2−22
χ34222-2-22-2-22-22-2−2i−2i2i2i000−2i2i0002-20−2i2i000000000000−i2−i2i2i222−2−2000000000000−i2i22−2
χ35222-2-22-2-22-22-2−2i−2i2i2i000−2i2i000-2202i−2i000000000000i2i2−i2−i2−2−222000000000000−i2i22−2
χ36222-2-22-2-22-22-2−2i−2i2i2i000−2i2i000-2202i−2i000000000000−i2−i2i2i222−2−2000000000000i2−i2−22
χ372-2-22-222-22-2-220000002002-2-2000002i−2i2i−2i000022-2-200002i−2i2i−2i0000000000000000
χ382-2-22-222-22-2-220000002002-2-2000002i−2i2i−2i0000-2-2220000−2i2i−2i2i0000000000000000
χ392-2-22-222-22-2-220000002002-2-200000−2i2i−2i2i000022-2-20000−2i2i−2i2i0000000000000000
χ402-2-22-222-22-2-220000002002-2-200000−2i2i−2i2i0000-2-22200002i−2i2i−2i0000000000000000
χ412-2-22-222-2-222-2000000200-22-2000002i−2i−2i2i22-2-200002i−2i2i−2i00000000000000000000
χ422-2-22-222-2-222-2000000200-22-2000002i−2i−2i2i-2-2220000−2i2i−2i2i00000000000000000000
χ432-2-22-222-2-222-2000000200-22-200000−2i2i2i−2i22-2-20000−2i2i−2i2i00000000000000000000
χ442-2-22-222-2-222-2000000200-22-200000−2i2i2i−2i-2-22200002i−2i2i−2i00000000000000000000
χ45444-4-44-4-4-44-444i4i−4i−4i000−4i4i00000000000000000000000000000000000000000000
χ46444-4-44-4-4-44-44−4i−4i4i4i0004i−4i00000000000000000000000000000000000000000000
χ4744-44-4-4-4400004-44-4000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ4844-44-4-4-4400004-44-400000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ4944-44-4-4-440000-44-44000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5044-44-4-4-440000-44-4400000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5144-4-44-44-400004i−4i−4i4i000000000000000000000000000000000000000002i−2i2-20000
χ5244-4-44-44-400004i−4i−4i4i00000000000000000000000000000000000000000−2i2i-220000
χ5344-4-44-44-40000−4i4i4i−4i000000000000000000000000000000000000000002i−2i-220000
χ5444-4-44-44-40000−4i4i4i−4i00000000000000000000000000000000000000000−2i2i2-20000
χ554-4444-4-4-4000000004-40000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ564-4444-4-4-4000000004-4000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ574-4444-4-4-400000000-440000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ584-4444-4-4-400000000-44000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ594-4-44-444-44-4-44000000-400-44400000000000000000000000000000000000000000
χ604-4-44-444-4-444-4000000-4004-4400000000000000000000000000000000000000000
χ614-4-4-444-4444-4-40000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ624-4-4-444-4444-4-4000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ634-4-4-444-44-4-4440000000000000000000000000000022−22−222200000000000000000000
χ644-4-4-444-44-4-44400000000000000000000000000000−222222−2200000000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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