Finite Group Databasebeta

← Group #308609

Character table — Group #308609

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444442222448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1111111-1-1-1-11111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ411111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-111111
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-11-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-111-1
χ91111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1111
χ101111111111111111-1-1-1-111111111-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-11111-1-1-1
χ111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1111111-1-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-111111111-11111-1-11-1-111-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-111-1-1-111-1-1111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-111111-1-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-111-1-1-11111-1
χ17222222222-2-22-222-22222-2-2000000-2-22200000022-2-2000000000000000-20000000
χ18222222222-2-22-222-22222-2-2000000-2-2-2-2000000-2-22200000000000000020000000
χ19222222222-2-22-222-2-2-2-2-2-2-20000002222000000-2-222000000000000000-20000000
χ20222222222-2-22-222-2-2-2-2-2-2-200000022-2-200000022-2-200000000000000020000000
χ2122222222-222-22-2-220000-2-22222220000-2-2-2-2-2-2000000000000200000000000000
χ2222222222-222-22-2-220000-2-22222-2-200002222-2-2000000000000-200000000000000
χ2322222222-222-22-2-220000-2-2-2-2-2-222000022-2-222000000000000-200000000000000
χ2422222222-222-22-2-220000-2-2-2-2-2-2-2-20000-2-22222000000000000200000000000000
χ25222-2-2-2-22200-20-22022-2-200i2i2−i2−i200002i−2i0000i2−i22i−2i00i2i2−i2−i222−2−20000000000002−20
χ26222-2-2-2-22200-20-22022-2-200i2i2−i2−i20000−2i2i0000i2−i2−2i2i00i2i2−i2−i2−2−222000000000000−220
χ27222-2-2-2-22200-20-22022-2-200−i2−i2i2i200002i−2i0000−i2i22i−2i00−i2−i2i2i2−2−222000000000000−220
χ28222-2-2-2-22200-20-22022-2-200−i2−i2i2i20000−2i2i0000−i2i2−2i2i00−i2−i2i2i222−2−20000000000002−20
χ29222-2-2-2-22200-20-220-2-22200i2i2−i2−i200002i−2i0000i2−i2−2i2i00−i2−i2i2i2−2−2220000000000002−20
χ30222-2-2-2-22200-20-220-2-22200i2i2−i2−i20000−2i2i0000i2−i22i−2i00−i2−i2i2i222−2−2000000000000−220
χ31222-2-2-2-22200-20-220-2-22200−i2−i2i2i200002i−2i0000−i2i2−2i2i00i2i2−i2−i222−2−2000000000000−220
χ32222-2-2-2-22200-20-220-2-22200−i2−i2i2i20000−2i2i0000−i2i22i−2i00i2i2−i2−i2−2−2220000000000002−20
χ3322-22-22-2-2222-2-22-2-22-22-22-20000002-20000000000000000000002-2000002-200000
χ3422-22-22-2-2222-2-22-2-22-22-22-20000002-2000000000000000000000-2200000-2200000
χ3522-22-22-2-2222-2-22-2-2-22-222-2000000-220000000000000000000002-200000-2200000
χ3622-22-22-2-2222-2-22-2-2-22-222-2000000-22000000000000000000000-22000002-200000
χ3722-22-22-2-22-2-2-222-222-22-2-2200002i−2i-2200002i−2i00000000000000000002i−2i00000000
χ3822-22-22-2-22-2-2-222-222-22-2-220000−2i2i-220000−2i2i0000000000000000000−2i2i00000000
χ3922-22-22-2-22-2-2-222-22-22-22-2200002i−2i2-200002i−2i0000000000000000000−2i2i00000000
χ4022-22-22-2-22-2-2-222-22-22-22-220000−2i2i2-20000−2i2i00000000000000000002i−2i00000000
χ4122-22-22-2-2-2-2-222-22200002-200002i−2i000000−2i2i0000002-22-200000002i−2i0000000000
χ4222-22-22-2-2-2-2-222-22200002-200002i−2i000000−2i2i000000-22-220000000−2i2i0000000000
χ4322-22-22-2-2-2-2-222-22200002-20000−2i2i0000002i−2i0000002-22-20000000−2i2i0000000000
χ4422-22-22-2-2-2-2-222-22200002-20000−2i2i0000002i−2i000000-22-2200000002i−2i0000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-4-44-400404-400000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ47444-4-4-4-44-400404-40000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ4844-44-44-4-4-4444-4-44-40000-440000000000000000000000000000000000000000000
χ4944-4-44-44-440040-4-404-4-44000000000000000000000000000000000000000000000
χ5044-4-44-44-440040-4-40-444-4000000000000000000000000000000000000000000000
χ5144-4-44-44-4-400-40440000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ5244-4-44-44-4-400-4044000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ534-444-4-44-404-40400-400000000000000004-40000000000000000000000000000000
χ544-444-4-44-404-40400-40000000000000000-440000000000000000000000000000000
χ554-444-4-44-40-440-4004000000000000000000000000000000000000000000002i2−2i2000
χ564-444-4-44-40-440-400400000000000000000000000000000000000000000000−2i22i2000
χ574-4-444-4-4404-40-400400000000000000000000000000000022−2222−22000000000000000
χ584-4-444-4-4404-40-4004000000000000000000000000000000−2222−2222000000000000000
χ594-4-444-4-440-440400-40000004i−4i4i−4i000000000000000000000000000000000000000
χ604-4-444-4-440-440400-4000000−4i4i−4i4i000000000000000000000000000000000000000
χ614-4-4-4-44440000000000000022−22−22220000000000000022−2200002-2-22000000000000000
χ624-4-4-4-44440000000000000022−22−222200000000000000−22220000-222-2000000000000000
χ634-4-4-4-444400000000000000−222222−220000000000000022−220000-222-2000000000000000
χ644-4-4-4-444400000000000000−222222−2200000000000000−222200002-2-22000000000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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