Finite Group Databasebeta

← Group #248893

Character table — Group #248893

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222222222222444444444444444444444444444444442444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111-1-1-11-1-1-1-1-11111
χ811111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1111-111111-1-1-1-1
χ911111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1-11111-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-111-1-1-1-111-1-111
χ1111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-111-1-111-1-111
χ1211111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-111-1-111-1-111-1-1
χ1311111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1111-111-1-1-1-111
χ1411111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-11-1-11111-1-1
χ1511111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1-1111-1-1-11111-1-1
χ1611111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1-1111-1-1-1111-1-1-1-111
χ17222222222222222222222222-2-2-2-2-2-2-2-2-2-22200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-222-2-2222200000000000000000000000000000000
χ2122222222-2-2-22222-2-2-2-2-2000022-2-200002-200000000000000000000022-20-200000000
χ2222222222-2-2-22222-2-2-2-2-2000022-2-200002-2000000000000000000000-2-220200000000
χ2322222222-2-2-22222-2-2-2-2-20000-2-2220000-2200000000000000000022-2000-2000000000
χ2422222222-2-2-22222-2-2-2-2-20000-2-2220000-22000000000000000000-2-220002000000000
χ2522222222-2-2-2-2-2-2-22222-2000022-2-20000-220000000000000000000002-220-200000000
χ2622222222-2-2-2-2-2-2-22222-2000022-2-20000-22000000000000000000000-22-20200000000
χ2722222222-2-2-2-2-2-2-22222-20000-2-22200002-20000000000000000002-22000-2000000000
χ2822222222-2-2-2-2-2-2-22222-20000-2-22200002-2000000000000000000-22-20002000000000
χ29222-2-2-22-22-2-222-2-222-2-222i2i−2i−2i00000000002i−2i000000000000000000000000i2−i2i2−i22−22−2
χ30222-2-2-22-22-2-222-2-222-2-222i2i−2i−2i00000000002i−2i000000000000000000000000−i2i2−i2i2−22−22
χ31222-2-2-22-22-2-222-2-222-2-22−2i−2i2i2i0000000000−2i2i000000000000000000000000i2−i2i2−i2−22−22
χ32222-2-2-22-22-2-222-2-222-2-22−2i−2i2i2i0000000000−2i2i000000000000000000000000−i2i2−i2i22−22−2
χ33222-2-2-22-22-2-2-2-222-2-22222i2i−2i−2i0000000000−2i2i000000000000000000000000i2−i2−i2i22−2−22
χ34222-2-2-22-22-2-2-2-222-2-22222i2i−2i−2i0000000000−2i2i000000000000000000000000−i2i2i2−i2−222−2
χ35222-2-2-22-22-2-2-2-222-2-2222−2i−2i2i2i00000000002i−2i000000000000000000000000i2−i2−i2i2−222−2
χ36222-2-2-22-22-2-2-2-222-2-2222−2i−2i2i2i00000000002i−2i000000000000000000000000−i2i2i2−i22−2−22
χ372-2-22-2-222-22-20000000022-22-22-22-22-2000000000022-2-2000022-2-20000000000000000
χ382-2-22-2-222-22-20000000022-22-22-22-22-20000000000-2-2220000-2-2220000000000000000
χ392-2-22-2-222-22-20000000022-22-2-22-22-2200000022-2-2000022-2-200000000000000000000
χ402-2-22-2-222-22-20000000022-22-2-22-22-22000000-2-2220000-2-22200000000000000000000
χ412-2-22-2-222-22-2000000002-22-222-22-2-22000000000022-2-20000-2-2220000000000000000
χ422-2-22-2-222-22-2000000002-22-222-22-2-220000000000-2-222000022-2-20000000000000000
χ432-2-22-2-222-22-2000000002-22-22-22-222-200000022-2-20000-2-22200000000000000000000
χ442-2-22-2-222-22-2000000002-22-22-22-222-2000000-2-222000022-2-200000000000000000000
χ45444-4-4-44-4-44444-4-4-4-444-4000000000000000000000000000000000000000000000000
χ46444-4-4-44-4-444-4-44444-4-4-4000000000000000000000000000000000000000000000000
χ4744-444-4-4-400000004-44-400000000000000000000000002-22-22-22-20000000000000000
χ4844-444-4-4-400000004-44-40000000000000000000000000-22-22-22-220000000000000000
χ4944-444-4-4-40000000-44-4400000000000000000000000002-22-2-22-220000000000000000
χ5044-444-4-4-40000000-44-440000000000000000000000000-22-222-22-20000000000000000
χ5144-4-4-44-4400000004-4-44000000000000000002-22-22-22-2000000000000000000000000
χ5244-4-4-44-4400000004-4-4400000000000000000-22-22-22-22000000000000000000000000
χ5344-4-4-44-440000000-444-4000000000000000002-22-2-22-22000000000000000000000000
χ5444-4-4-44-440000000-444-400000000000000000-22-222-22-2000000000000000000000000
χ554-444-44-4-40004-44-4000000000000000000000000000002-2-222-2-220000000000000000
χ564-444-44-4-40004-44-400000000000000000000000000000-222-2-222-20000000000000000
χ574-444-44-4-4000-44-44000000000000000000000000000002-2-22-222-20000000000000000
χ584-444-44-4-4000-44-4400000000000000000000000000000-222-22-2-220000000000000000
χ594-44-44-4-440004-4-440000000000000000000002-2-222-2-22000000000000000000000000
χ604-44-44-4-440004-4-44000000000000000000000-222-2-222-2000000000000000000000000
χ614-44-44-4-44000-444-40000000000000000000002-2-22-222-2000000000000000000000000
χ624-44-44-4-44000-444-4000000000000000000000-222-22-2-22000000000000000000000000
χ634-4-44-4-4444-4400000000-400004-4-440000000000000000000000000000000000000000
χ644-4-44-4-4444-4400000000-40000-444-40000000000000000000000000000000000000000
χ654-4-4-4444-444-400000000-400000000004-4000000000000000000000000000000000000
χ664-4-4-4444-444-400000000-40000000000-44000000000000000000000000000000000000
χ674-4-4-4444-4-4-440000000044i−4i−4i4i00000000000000000000000000000000000000000000
χ684-4-4-4444-4-4-44000000004−4i4i4i−4i00000000000000000000000000000000000000000000

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