Finite Group Databasebeta

← Group #307478

Character table — Group #307478

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1111-11-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-1-11-1-1-11-1-1-1-1-111-1-1
χ411111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-11
χ71111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-1-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1111-1-111-1-1111-1
χ91111111111111111-1-1-1-111111111-1-111111111-1-1-1-11111-1-1-11-1-1-111111-1-1-1-1
χ101111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1111-1111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1111-1-111-11
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11-11111-1-111-1-11-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-11-1-1-1-1-1-111111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-11-111-1-1-1-1-11
χ17222222222-2-222-2-220000-2-22222220022-2-2000000000000000-2000-200000000
χ18222222222-2-222-2-220000-2-22222-2-200-2-2-2-20000000000000002000200000000
χ19222222222-2-222-2-220000-2-2-2-2-2-22200-2-2220000000000000002000-200000000
χ20222222222-2-222-2-220000-2-2-2-2-2-2-2-2002222000000000000000-2000200000000
χ2122222222-222-2-222-22222-2-2000000-2-2000022-2-200000000002000-2000000000
χ2222222222-222-2-222-22222-2-2000000-2-20000-2-2220000000000-20002000000000
χ2322222222-222-2-222-2-2-2-2-2-2-200000022000022-2-20000000000-20002000000000
χ2422222222-222-2-222-2-2-2-2-2-2-2000000220000-2-22200000000002000-2000000000
χ252-22-2-2-2222002-200-20000002i2i−2i−2i2i−2i002-2002−22−20000i2i2−i2−i200000000i2−i22−20000
χ262-22-2-2-2222002-200-20000002i2i−2i−2i2i−2i002-200−22−220000−i2−i2i2i200000000−i2i2−220000
χ272-22-2-2-2222002-200-20000002i2i−2i−2i−2i2i00-22002−22−20000i2i2−i2−i200000000−i2i2−220000
χ282-22-2-2-2222002-200-20000002i2i−2i−2i−2i2i00-2200−22−220000−i2−i2i2i200000000i2−i22−20000
χ292-22-2-2-2222002-200-2000000−2i−2i2i2i2i−2i00-22002−22−20000−i2−i2i2i200000000i2−i2−220000
χ302-22-2-2-2222002-200-2000000−2i−2i2i2i2i−2i00-2200−22−220000i2i2−i2−i200000000−i2i22−20000
χ312-22-2-2-2222002-200-2000000−2i−2i2i2i−2i2i002-2002−22−20000−i2−i2i2i200000000−i2i22−20000
χ322-22-2-2-2222002-200-2000000−2i−2i2i2i−2i2i002-200−22−220000i2i2−i2−i200000000i2−i2−220000
χ332-2-2-222-22222-2-2-2-222i2i−2i−2i2-20000002i−2i0000000000002i−2i2i−2i0000000000002-200
χ342-2-2-222-22222-2-2-2-222i2i−2i−2i2-20000002i−2i000000000000−2i2i−2i2i000000000000-2200
χ352-2-2-222-22222-2-2-2-22−2i−2i2i2i2-2000000−2i2i0000000000002i−2i2i−2i000000000000-2200
χ362-2-2-222-22222-2-2-2-22−2i−2i2i2i2-2000000−2i2i000000000000−2i2i−2i2i0000000000002-200
χ372-2-2-222-22-22222-2-2-22i2i−2i−2i-222-22-200−2i2i002-200002i2i−2i−2i00000000000000000000
χ382-2-2-222-22-22222-2-2-22i2i−2i−2i-22-22-2200−2i2i00-220000−2i−2i2i2i00000000000000000000
χ392-2-2-222-22-22222-2-2-2−2i−2i2i2i-222-22-2002i−2i002-20000−2i−2i2i2i00000000000000000000
χ402-2-2-222-22-22222-2-2-2−2i−2i2i2i-22-22-22002i−2i00-2200002i2i−2i−2i00000000000000000000
χ412-2-2-222-22-2-2-22222-200002-22-22-2000000-220000000000002i−2i002i−2i0000000000
χ422-2-2-222-22-2-2-22222-200002-22-22-2000000-22000000000000−2i2i00−2i2i0000000000
χ432-2-2-222-22-2-2-22222-200002-2-22-220000002-20000000000002i−2i00−2i2i0000000000
χ442-2-2-222-22-2-2-22222-200002-2-22-220000002-2000000000000−2i2i002i−2i0000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ46444-44-4-4-404-4004-40000000000000000000000022−2222−2200000000000000000000
χ47444-44-4-4-404-4004-400000000000000000000000−2222−222200000000000000000000
χ48444-44-4-4-40-4400-4404-44-4000000000000000000000000000000000000000000
χ49444-44-4-4-40-4400-440-44-44000000000000000000000000000000000000000000
χ5044-44-4-4-44400-4400-40000000000000000000000000022−22−22220000000000000000
χ5144-44-4-4-44400-4400-400000000000000000000000000−222222−220000000000000000
χ5244-44-4-4-44-4004-40040000004i−4i−4i4i000000000000000000000000000000000000
χ5344-44-4-4-44-4004-4004000000−4i4i4i−4i000000000000000000000000000000000000
χ544-44-4-4-444-400-4400400000000000000000022−22−2222000000000000000000000000
χ554-44-4-4-444-400-44004000000000000000000−222222−22000000000000000000000000
χ564-4-444-44-404-400-44000000000000000000000002i2−2i2−2i22i200000000000000000000
χ574-4-444-44-404-400-4400000000000000000000000−2i22i22i2−2i200000000000000000000
χ584-4-444-44-40-44004-404i−4i−4i4i000000000000000000000000000000000000000000
χ594-4-444-44-40-44004-40−4i4i4i−4i000000000000000000000000000000000000000000
χ604-4-4-444-444-4-4-4-44440000-440000000000000000000000000000000000000000
χ6188-8-8-888-8000000000000000000000000000000000000000000000000000000
χ628-888-88-8-8000000000000000000000000000000000000000000000000000000

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