Finite Group Databasebeta

← Group #274255

Character table — Group #274255

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222222244444444444444444444444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-11-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-111111111-1-111-1-111-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-111-1-111-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-11
χ1111111111-1-1-1-111111111-1-111-1-111-1-1-111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111-11
χ1211111111-1-1-1-111111111-1-111-1-111-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1111-1
χ1311111111-1-1-1-111111111-1-111-1-1-1-111-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-11
χ1411111111-1-1-1-111111111-1-111-1-1-1-111-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ1511111111-1-1-1-111111111-1-111-1-1-1-111-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-11-1
χ1611111111-1-1-1-111111111-1-111-1-1-1-111-1-1-111-1-111-1-111-1-1-1-1111111-1-111-1-111-1-1-11
χ172222222222222-2-222-2-2222-2-2-2-22222-2-2-2-2-2000000000000000000000000000000
χ182222222222222-2-222-2-2222-2-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ19222222222222-222-2-222-2-2-2-2-2220000-200002222-2-2-2-20000000000000000000000
χ20222222222222-222-2-222-2-2-2-2-2220000-20000-2-2-2-222220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-222-2-20000200000000000000000000000000002i−2i2i−2i00
χ22222222222222-2-2-2-2-2-2-2-2-2-222-2-2000020000000000000000000000000000−2i2i−2i2i00
χ2322222222-2-2-2-22-2-222-2-22-2-2-2-22222-2-22-2-222000000000000000000000000000000
χ2422222222-2-2-2-22-2-222-2-22-2-2-2-222-2-222222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-222-2-222-222-2-2-2-200002000022-2-2-2-2220000000000000000000000
χ2622222222-2-2-2-2-222-2-222-222-2-2-2-2000020000-2-22222-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-200000000000000000000000000002i−2i−2i2i00
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-20000000000000000000000000000−2i2i2i−2i00
χ29222-2-2-2-2222-2-20-2-20022000002-20000000002i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i200002−22−2000000
χ30222-2-2-2-2222-2-20-2-20022000002-20000000002i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i20000−22−22000000
χ31222-2-2-2-2222-2-20-2-20022000002-2000000000−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i20000−22−22000000
χ32222-2-2-2-2222-2-20-2-20022000002-2000000000−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i200002−22−2000000
χ33222-2-2-2-22-2-2220-2-2002200000-220000000002i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i200002−2−22000000
χ34222-2-2-2-22-2-2220-2-2002200000-220000000002i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i20000−222−2000000
χ35222-2-2-2-22-2-2220-2-2002200000-22000000000−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i20000−222−2000000
χ36222-2-2-2-22-2-2220-2-2002200000-22000000000−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i200002−2−22000000
χ372-2-22-22-22000022-22-22-2-2002-200002i−2i0002i−2i0000000000002i−2i2i−2i2-2000000000000
χ382-2-22-22-22000022-22-22-2-2002-200002i−2i0002i−2i000000000000−2i2i−2i2i-22000000000000
χ392-2-22-22-22000022-22-22-2-2002-20000−2i2i000−2i2i0000000000002i−2i2i−2i-22000000000000
χ402-2-22-22-22000022-22-22-2-2002-20000−2i2i000−2i2i000000000000−2i2i−2i2i2-2000000000000
χ412-2-22-22-2200002-222-2-22-200-2200002i−2i000−2i2i000000002i−2i2i−2i0000002-20000000000
χ422-2-22-22-2200002-222-2-22-200-2200002i−2i000−2i2i00000000−2i2i−2i2i000000-220000000000
χ432-2-22-22-2200002-222-2-22-200-220000−2i2i0002i−2i000000002i−2i2i−2i000000-220000000000
χ442-2-22-22-2200002-222-2-22-200-220000−2i2i0002i−2i00000000−2i2i−2i2i0000002-20000000000
χ45444-4-4-4-4444-4-404400-4-400000-44000000000000000000000000000000000000000
χ46444-4-4-4-44-4-44404400-4-4000004-4000000000000000000000000000000000000000
χ4744-444-4-4-44-44-4400-4-40044-40000000000000000000000000000000000000000000
χ4844-444-4-4-44-44-4-4004400-4-440000000000000000000000000000000000000000000
χ4944-444-4-4-4-44-44400-4-4004-440000000000000000000000000000000000000000000
χ5044-444-4-4-4-44-44-4004400-44-40000000000000000000000000000000000000000000
χ5144-4-4-444-44-4-440000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ5244-4-4-444-44-4-44000000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ5344-4-4-444-4-444-40000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5444-4-4-444-4-444-4000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ554-444-4-44-40000400-4400-4000000000004-400000000000000000000000000000000
χ564-444-4-44-40000400-4400-400000000000-4400000000000000000000000000000000
χ574-444-4-44-40000-4004-40040000004i−4i0000000000000000000000000000000000000
χ584-444-4-44-40000-4004-4004000000−4i4i0000000000000000000000000000000000000
χ594-4-44-44-440000-44-4-444-4400-4400000000000000000000000000000000000000000
χ604-4-44-44-440000-4-44-44-444004-400000000000000000000000000000000000000000
χ614-4-4-44-444000004-400-4400000000000000000000000022−22−2222000000000000000000
χ624-4-4-44-444000004-400-44000000000000000000000000−222222−22000000000000000000
χ634-4-4-44-44400000-44004-4000000000000000000000000000022−22−222200000000000000
χ644-4-4-44-44400000-44004-40000000000000000000000000000−222222−2200000000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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