Finite Group Databasebeta

← Group #266272

Character table — Group #266272

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444448888888888888888888161616161616161616161616161616161616
order12222222444444442222444444444444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ5111111111111111111111-1-1-1-1-1-11-1-1-11111-1-1-1-11111-1-1-1-111-1-111-11-1-111-1-111-1-1
χ6111111111111111111111-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-11-1-1-1-111-1-111
χ7111111111111111111111-1-1-1-1-1-11-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11-111-1-11111-1-1
χ8111111111111111111111-1-1-1-1-1-11-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11-11111-1-1-1-111
χ91111111111111111-1-1-1-111111111-1-11-1-111-1-11111111111-1-1-1-1-1-111-1-11111-1-1-1-1
χ101111111111111111-1-1-1-111111111-1-11-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111
χ111111111111111111-1-1-1-111111111-1-11-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1
χ121111111111111111-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111
χ131111111111111111-1-1-1-11-1-1-1-1-1-1111-1-1-11111-1-11111-1-1-1-1-1-111-1-1-111111-1-1-1-111
χ141111111111111111-1-1-1-11-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1111-1-11111-1-1
χ151111111111111111-1-1-1-11-1-1-1-1-1-1111-1-1-1-1-111111111-1-1-1-111-1-1111-1-1-1-1-111-1-111
χ161111111111111111-1-1-1-11-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-11111-1-111111-1-1-111-1-111-1-1
χ172222222222-2-2-222-22222-222-2-2-2-2-2222-2-200-2-20000000000000000000000000000
χ182222222222-2-2-222-22222-2-2-22222-2-2-2-2-2-200220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-222-2-2-2-2-2-2-222200220000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2-22222-222-22200-2-20000000000000000000000000000
χ2122222222-2-2222-2-220000-222-2-222-200-20022002200000000000000-2-20000000000
χ2222222222-2-2222-2-220000-222-2-222-200-200-2-200-2-200000000000000220000000000
χ2322222222-2-2222-2-220000-2-2-222-2-2-2002002200-2-2000000000000002-20000000000
χ2422222222-2-2222-2-220000-2-2-222-2-2-200200-2-2002200000000000000-220000000000
χ2522222222-2-2-2-2-2-2-2-2000022222-2-2200-2000000000000000000002-2002-200000000
χ2622222222-2-2-2-2-2-2-2-2000022222-2-2200-200000000000000000000-2200-2200000000
χ2722222222-2-2-2-2-2-2-2-200002-2-2-2-2222002000000000000000000002-200-2200000000
χ2822222222-2-2-2-2-2-2-2-200002-2-2-2-222200200000000000000000000-22002-200000000
χ29222-2-22-2-22-222-22-2-222-2-22000000-20002-200000000000000002-2000000002-20000
χ30222-2-22-2-22-222-22-2-222-2-22000000-20002-20000000000000000-2200000000-220000
χ31222-2-22-2-22-222-22-2-2-2-2222000000-2000-2200000000000000002-200000000-220000
χ32222-2-22-2-22-222-22-2-2-2-2222000000-2000-220000000000000000-22000000002-20000
χ33222-2-22-2-22-2-2-222-2222-2-2-20000002000-22000000000000002i−2i000000002i−2i000000
χ34222-2-22-2-22-2-2-222-2222-2-2-20000002000-2200000000000000−2i2i00000000−2i2i000000
χ35222-2-22-2-22-2-2-222-22-2-222-200000020002-2000000000000002i−2i00000000−2i2i000000
χ36222-2-22-2-22-2-2-222-22-2-222-200000020002-200000000000000−2i2i000000002i−2i000000
χ3722-2-2-2-22222000-2-202-22-20002-22-2000000002-200i2i2−i2−i2i2i2−i2−i200000000000000i2−i2i2−i2
χ3822-2-2-2-22222000-2-202-22-20002-22-2000000002-200−i2−i2i2i2−i2−i2i2i200000000000000−i2i2−i2i2
χ3922-2-2-2-22222000-2-202-22-2000-22-2200000000-2200i2i2−i2−i2−i2−i2i2i200000000000000i2−i2−i2i2
χ4022-2-2-2-22222000-2-202-22-2000-22-2200000000-2200−i2−i2i2i2i2i2−i2−i200000000000000−i2i2i2−i2
χ4122-2-2-2-22222000-2-20-22-220002-22-200000000-2200i2i2−i2−i2i2i2−i2−i200000000000000−i2i2−i2i2
χ4222-2-2-2-22222000-2-20-22-220002-22-200000000-2200−i2−i2i2i2−i2−i2i2i200000000000000i2−i2i2−i2
χ4322-2-2-2-22222000-2-20-22-22000-22-22000000002-200i2i2−i2−i2−i2−i2i2i200000000000000−i2i2i2−i2
χ4422-2-2-2-22222000-2-20-22-22000-22-22000000002-200−i2−i2i2i2i2i2−i2−i200000000000000i2−i2−i2i2
χ45444-4-44-4-4-4444-4-44-40000-400000040000000000000000000000000000000000000
χ46444-4-44-4-4-44-4-44-44400004000000-40000000000000000000000000000000000000
χ4744-444-4-4-44-4000-4404-4-44000000000000000000000000000000000000000000000
χ4844-444-4-4-44-4000-440-444-4000000000000000000000000000000000000000000000
χ4944-444-4-4-4-440004-400000000000004-400000000000000000000000000000000000
χ5044-444-4-4-4-440004-40000000000000-4400000000000000000000000000000000000
χ5144-4-4-4-444-4-400044000000004-4-4400000000000000000000000000000000000000
χ5244-4-4-4-444-4-40004400000000-444-400000000000000000000000000000000000000
χ534-44-44-4-4400000000000004i−4i00000000000000002i−2i2i−2i2-22-2000000000000000000
χ544-44-44-4-4400000000000004i−4i0000000000000000−2i2i−2i2i-22-22000000000000000000
χ554-44-44-4-440000000000000−4i4i00000000000000002i−2i2i−2i-22-22000000000000000000
χ564-44-44-4-440000000000000−4i4i0000000000000000−2i2i−2i2i2-22-2000000000000000000
χ574-4-44-44-44004-4400-40000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ584-4-44-44-44004-4400-4000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ594-4-44-44-4400-44-40040000000000000000000000022−22−22220000000000000000000000
χ604-4-44-44-4400-44-400400000000000000000000000−222222−220000000000000000000000
χ614-4-4-4444-4004-4-4004000000000000000004-4000000000000000000000000000000
χ624-4-4-4444-4004-4-400400000000000000000-44000000000000000000000000000000
χ634-4-4-4444-400-44400-40000000000000000000004i−4i00000000000000000000000000
χ644-4-4-4444-400-44400-4000000000000000000000−4i4i00000000000000000000000000
χ658-888-8-88-8000000000000000000000000000000000000000000000000000000000

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