Finite Group Databasebeta

← Group #308178

Character table — Group #308178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-1-1111-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-111-1-111-1
χ71111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11
χ91111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-11
χ101111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-11111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111111-1-1-1-1111-1-1-1-1111
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111111-1-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1111111111-1-1-1-1-111-1-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1-111-1-1111
χ172222222222-2-2-222-22222-2-20000000000-2-22200000022-2-20000-200000000000000
χ182222222222-2-2-222-22222-2-20000000000-2-2-2-2000000-2-2220000200000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-200000000002222000000-2-2220000-200000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2000000000022-2-200000022-2-20000200000000000000
χ2122222222-2-2222-2-220000-2-222222222-2-20000-2-200000000000000000-2000000000
χ2222222222-2-2222-2-220000-2-22222-2-2-2-2220000-2-2000000000000000002000000000
χ2322222222-2-2222-2-220000-2-2-2-2-2-222-2-22200002200000000000000000-2000000000
χ2422222222-2-2222-2-220000-2-2-2-2-2-2-2-222-2-2000022000000000000000002000000000
χ25222-2-2-2-222-20002-202i2i−2i−2i00i2i2−i2−i2000000002-2i2−i222−2−22i−2i0022−2−200000000i2−i200000
χ26222-2-2-2-222-20002-202i2i−2i−2i00i2i2−i2−i200000000-22i2−i222−2−2−2i2i00−2−22200000000−i2i200000
χ27222-2-2-2-222-20002-202i2i−2i−2i00−i2−i2i2i2000000002-2−i2i2−2−2222i−2i00−2−22200000000−i2i200000
χ28222-2-2-2-222-20002-202i2i−2i−2i00−i2−i2i2i200000000-22−i2i2−2−222−2i2i0022−2−200000000i2−i200000
χ29222-2-2-2-222-20002-20−2i−2i2i2i00i2i2−i2−i2000000002-2i2−i2−2−222−2i2i00−2−22200000000i2−i200000
χ30222-2-2-2-222-20002-20−2i−2i2i2i00i2i2−i2−i200000000-22i2−i2−2−2222i−2i0022−2−200000000−i2i200000
χ31222-2-2-2-222-20002-20−2i−2i2i2i00−i2−i2i2i2000000002-2−i2i222−2−2−2i2i0022−2−200000000−i2i200000
χ32222-2-2-2-222-20002-20−2i−2i2i2i00−i2−i2i2i200000000-22−i2i222−2−22i−2i00−2−22200000000i2−i200000
χ3322-22-2-22-2222-22-2-2-200002-20000002-22-20000002-22-2000000000002-20000000000
χ3422-22-2-22-2222-22-2-2-200002-20000002-22-2000000-22-2200000000000-220000000000
χ3522-22-2-22-2222-22-2-2-200002-2000000-22-220000002-22-200000000000-220000000000
χ3622-22-2-22-2222-22-2-2-200002-2000000-22-22000000-22-22000000000002-20000000000
χ3722-22-2-22-2-2-22-2222-22i−2i2i−2i-220000002-2-222i−2i00000000000000000000002i−2i0000000
χ3822-22-2-22-2-2-22-2222-22i−2i2i−2i-22000000-222-22i−2i0000000000000000000000−2i2i0000000
χ3922-22-2-22-2-2-22-2222-2−2i2i−2i2i-220000002-2-22−2i2i0000000000000000000000−2i2i0000000
χ4022-22-2-22-2-2-22-2222-2−2i2i−2i2i-22000000-222-2−2i2i00000000000000000000002i−2i0000000
χ4122-22-2-22-2-2-2-22-22222i−2i2i−2i2-20000000000−2i2i000000000000000002i−2i0000000002-20
χ4222-22-2-22-2-2-2-22-22222i−2i2i−2i2-20000000000−2i2i00000000000000000−2i2i000000000-220
χ4322-22-2-22-2-2-2-22-2222−2i2i−2i2i2-200000000002i−2i000000000000000002i−2i000000000-220
χ4422-22-2-22-2-2-2-22-2222−2i2i−2i2i2-200000000002i−2i00000000000000000−2i2i0000000002-20
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-4-44-44000-4400000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ47444-4-4-4-44-44000-440000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ4844-44-4-44-444-44-4-4-440000-440000000000000000000000000000000000000000000
χ4944-4-444-4-44-4000-440000000000000000000000022−22−222200000000000000000000000
χ5044-4-444-4-44-4000-4400000000000000000000000−222222−2200000000000000000000000
χ5144-4-444-4-4-440004-404-4-44000000000000000000000000000000000000000000000
χ5244-4-444-4-4-440004-40-444-4000000000000000000000000000000000000000000000
χ534-4444-4-4-4004-4-400400000000004-40000000000000000000000000000000000000
χ544-4444-4-4-4004-4-40040000000000-440000000000000000000000000000000000000
χ554-4444-4-4-400-44400-40000000000000000000000000000000000000000000022−22000
χ564-4444-4-4-400-44400-400000000000000000000000000000000000000000000−2222000
χ574-4-44-44-440044-400-40000004i−4i4i−4i000000000000000000000000000000000000000
χ584-4-44-44-440044-400-4000000−4i4i−4i4i000000000000000000000000000000000000000
χ594-4-44-44-4400-4-4400400000000000000000000000000000022−2222−22000000000000000
χ604-4-44-44-4400-4-44004000000000000000000000000000000−2222−2222000000000000000
χ614-4-4-44-4440000000000000022−22−222200000000000000000022−222-2-22000000000000000
χ624-4-4-44-4440000000000000022−22−2222000000000000000000−2222-222-2000000000000000
χ634-4-4-44-44400000000000000−222222−2200000000000000000022−22-222-2000000000000000
χ644-4-4-44-44400000000000000−222222−22000000000000000000−22222-2-22000000000000000
χ658-88-8-888-8000000000000000000000000000000000000000000000000000000000

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