Finite Group Databasebeta

← Group #317383

Character table — Group #317383

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888444444888888888844444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111-1-1-1-1111111
χ91111111111111111-1-1-1-1111111-1-11111-1-1-1-1111111-111-1-111-1-1-111-1-111-1-1-1-1
χ101111111111111111-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-111-1-1-111-1-111-1-111-1-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1111-1-1-1-111-1-11111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-111-1-111111-1-111-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-111
χ141111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-111111-1-1-1-111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111-1-111111-1-1-1-11111-1-1-1-1
χ17222222222-2-2-2222-222-2-2-2-20000-2222-2-200000000002000000-2000000000000
χ18222222222-2-2-2222-222-2-2-2-20000-22-2-2220000000000-20000002000000000000
χ19222222222-2-2-2222-2-2-222-2-200002-222-2-20000000000-20000002000000000000
χ20222222222-2-2-2222-2-2-222-2-200002-2-2-22200000000002000000-2000000000000
χ2122222222-2222-2-2-222222-2-22222-2-2000022-2-2-2-2000000000000000000000000
χ2222222222-2222-2-2-222222-2-2-2-2-2-2-2-20000-2-22222000000000000000000000000
χ2322222222-2222-2-2-22-2-2-2-2-2-22222220000-2-222-2-2000000000000000000000000
χ2422222222-2222-2-2-22-2-2-2-2-2-2-2-2-2-222000022-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-22200002-200000000002i2i−2i−2i0000000000000000002i−2i
χ2622222222-2-2-2-2-2-2-2-222-2-22200002-20000000000−2i−2i2i2i000000000000000000−2i2i
χ2722222222-2-2-2-2-2-2-2-2-2-222220000-2200000000002i2i−2i−2i000000000000000000−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-222220000-220000000000−2i−2i2i2i0000000000000000002i−2i
χ2922-222-2-2-202-2-200022-22-2002i2i−2i−2i0000002i−2i0000000000000000002−22−2i2−i2i2−i200
χ3022-222-2-2-202-2-200022-22-2002i2i−2i−2i0000002i−2i000000000000000000−22−22−i2i2−i2i200
χ3122-222-2-2-202-2-200022-22-200−2i−2i2i2i000000−2i2i0000000000000000002−22−2−i2i2−i2i200
χ3222-222-2-2-202-2-200022-22-200−2i−2i2i2i000000−2i2i000000000000000000−22−22i2−i2i2−i200
χ3322-222-2-2-202-2-20002-22-22002i2i−2i−2i000000−2i2i0000000000000000002−2−22i2−i2−i2i200
χ3422-222-2-2-202-2-20002-22-22002i2i−2i−2i000000−2i2i000000000000000000−222−2−i2i2i2−i200
χ3522-222-2-2-202-2-20002-22-2200−2i−2i2i2i0000002i−2i0000000000000000002−2−22−i2i2i2−i200
χ3622-222-2-2-202-2-20002-22-2200−2i−2i2i2i0000002i−2i000000000000000000−222−2i2−i2−i2i200
χ372-2-22-22-22222-2-2-22-200002-22i−2i2i−2i00000000002i−2i000002-2002i−2i0000000000000
χ382-2-22-22-22222-2-2-22-200002-22i−2i2i−2i00000000002i−2i00000-2200−2i2i0000000000000
χ392-2-22-22-22222-2-2-22-200002-2−2i2i−2i2i0000000000−2i2i000002-200−2i2i0000000000000
χ402-2-22-22-22222-2-2-22-200002-2−2i2i−2i2i0000000000−2i2i00000-22002i−2i0000000000000
χ412-2-22-22-22-222-222-2-20000-222i−2i2i−2i0000000000−2i2i00000002i−2i0002-20000000000
χ422-2-22-22-22-222-222-2-20000-222i−2i2i−2i0000000000−2i2i0000000−2i2i000-220000000000
χ432-2-22-22-22-222-222-2-20000-22−2i2i−2i2i00000000002i−2i00000002i−2i000-220000000000
χ442-2-22-22-22-222-222-2-20000-22−2i2i−2i2i00000000002i−2i0000000−2i2i0002-20000000000
χ4544-444-4-4-40-444000-44-4-44000000000000000000000000000000000000000000
χ4644-444-4-4-40-444000-4-444-4000000000000000000000000000000000000000000
χ4744-4-4-444-440004-4-400000000000004-400000000000000000000000000000000
χ4844-4-4-444-440004-4-40000000000000-4400000000000000000000000000000000
χ4944-4-4-444-4-4000-4440000000000000004i−4i000000000000000000000000000000
χ5044-4-4-444-4-4000-444000000000000000−4i4i000000000000000000000000000000
χ514-444-4-44-404-44000-40000004-4-44000000000000000000000000000000000000
χ524-444-4-44-404-44000-4000000-444-4000000000000000000000000000000000000
χ534-444-4-44-40-44-400040000000000000000004i−4i00000000000000000000000000
χ544-444-4-44-40-44-40004000000000000000000−4i4i00000000000000000000000000
χ554-44-444-4-44000-44-40000000000000000000000022−2222−2200000000000000000000
χ564-44-444-4-44000-44-400000000000000000000000−2222−222200000000000000000000
χ574-44-444-4-4-40004-44000000000000000000000002i2−2i2−2i22i200000000000000000000
χ584-44-444-4-4-40004-4400000000000000000000000−2i22i22i2−2i200000000000000000000
χ594-4-44-44-444-4-44-4-4440000-440000000000000000000000000000000000000000
χ604-4-44-44-44-4-4-4444-4400004-40000000000000000000000000000000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ628-8-8-88-888000000000000000000000000000000000000000000000000000000

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