Finite Group Databasebeta

← Group #311234

Character table — Group #311234

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-11-1111-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-11-1-1-11-1-1-1-1-1-111-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-11111-1-111-11
χ71111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1111-1-111-1-1-1-1-11
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-111111-1
χ91111111111111111-1-1-1-1111111-1-11111111111-1-1-1-111111-11-1-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-11111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-111-111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-11111-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111111-1-111-1-1-1-11-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11-1-1-1-1-11111-1-1111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1111-1-111-1-1-11
χ17222222222-22-2-222-22222-2-20000-2-200000022-2-2000000000-200020000000000
χ18222222222-22-2-222-22222-2-20000-2-2000000-2-2220000000002000-20000000000
χ19222222222-22-2-222-2-2-2-2-2-2-200002200000022-2-20000000002000-20000000000
χ20222222222-22-2-222-2-2-2-2-2-2-2000022000000-2-222000000000-200020000000000
χ2122222222-22-222-2-220000-2-22222002222-2-2000000000000-20-20000000000000
χ2222222222-22-222-2-220000-2-2222200-2-2-2-2-2-20000000000002020000000000000
χ2322222222-22-222-2-220000-2-2-2-2-2-20022-2-22200000000000020-20000000000000
χ2422222222-22-222-2-220000-2-2-2-2-2-200-2-22222000000000000-2020000000000000
χ25222-2-2-2-2222-2-2-22-220000-222i2i−2i−2i0000002i−2i0000000000000002i−2i02-200000000
χ26222-2-2-2-2222-2-2-22-220000-222i2i−2i−2i0000002i−2i000000000000000−2i2i0-2200000000
χ27222-2-2-2-2222-2-2-22-220000-22−2i−2i2i2i000000−2i2i0000000000000002i−2i0-2200000000
χ28222-2-2-2-2222-2-2-22-220000-22−2i−2i2i2i000000−2i2i000000000000000−2i2i02-200000000
χ29222-2-2-2-22-222-2-2-2222i2i−2i−2i2-22i2i−2i−2i2i−2i0000−2i2i000022-2-200000000000000000000
χ30222-2-2-2-22-222-2-2-2222i2i−2i−2i2-2−2i−2i2i2i2i−2i00002i−2i0000-2-22200000000000000000000
χ31222-2-2-2-22-222-2-2-222−2i−2i2i2i2-22i2i−2i−2i−2i2i0000−2i2i0000-2-22200000000000000000000
χ32222-2-2-2-22-222-2-2-222−2i−2i2i2i2-2−2i−2i2i2i−2i2i00002i−2i000022-2-200000000000000000000
χ33222-2-2-2-22-2-2222-22-22i2i−2i−2i-220000−2i2i0000000000000022-2-20000000000002i−2i00
χ34222-2-2-2-22-2-2222-22-22i2i−2i−2i-220000−2i2i00000000000000-2-222000000000000−2i2i00
χ35222-2-2-2-22-2-2222-22-2−2i−2i2i2i-2200002i−2i0000000000000022-2-2000000000000−2i2i00
χ36222-2-2-2-22-2-2222-22-2−2i−2i2i2i-2200002i−2i00000000000000-2-2220000000000002i−2i00
χ372-222-22-2-20-202-20020000002-22-2002i−2i2i−2i002−22−200002−22−200000000i2−i2i2−i20000
χ382-222-22-2-20-202-20020000002-22-2002i−2i2i−2i00−22−220000−22−2200000000−i2i2−i2i20000
χ392-222-22-2-20-202-20020000002-22-200−2i2i−2i2i002−22−200002−22−200000000−i2i2−i2i20000
χ402-222-22-2-20-202-20020000002-22-200−2i2i−2i2i00−22−220000−22−2200000000i2−i2i2−i20000
χ412-222-22-2-20-202-2002000000-22-22002i−2i−2i2i002−22−20000−22−2200000000−i2i2i2−i20000
χ422-222-22-2-20-202-2002000000-22-22002i−2i−2i2i00−22−2200002−22−200000000i2−i2−i2i20000
χ432-222-22-2-20-202-2002000000-22-2200−2i2i2i−2i002−22−20000−22−2200000000i2−i2−i2i20000
χ442-222-22-2-20-202-2002000000-22-2200−2i2i2i−2i00−22−2200002−22−200000000−i2i2i2−i20000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ46444-4-4-4-444-4-4444-4-400004-40000000000000000000000000000000000000000
χ4744-444-4-4-440-400-4404-44-4000000000000000000000000000000000000000000
χ4844-444-4-4-440-400-440-44-44000000000000000000000000000000000000000000
χ4944-444-4-4-4-404004-40000000000000000000000022−2222−2200000000000000000000
χ5044-444-4-4-4-404004-400000000000000000000000−2222−222200000000000000000000
χ5144-4-4-444-440400-4-40000000000000000000000022−22−222200000000000000000000
χ5244-4-4-444-440400-4-400000000000000000000000−222222−2200000000000000000000
χ5344-4-4-444-4-40-4004404i−4i−4i4i000000000000000000000000000000000000000000
χ5444-4-4-444-4-40-400440−4i4i4i−4i000000000000000000000000000000000000000000
χ554-444-44-4-4040-4400-400000000000000000022−22−2222000000000000000000000000
χ564-444-44-4-4040-4400-4000000000000000000−222222−22000000000000000000000000
χ574-44-44-44-40404-400-40000000000000000000000000022−22−22220000000000000000
χ584-44-44-44-40404-400-400000000000000000000000000−222222−220000000000000000
χ594-44-44-44-40-40-440040000004i−4i−4i4i000000000000000000000000000000000000
χ604-44-44-44-40-40-44004000000−4i4i4i−4i000000000000000000000000000000000000
χ618-8-88-8-888000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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