Finite Group Databasebeta

← Group #317608

Character table — Group #317608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888844444444448888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ91111111111111111-1-111-1-111111111-111-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ101111111111111111-1-111-1-111111111-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ111111111111111111-1-111-1-111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ121111111111111111-1-111-1-111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ172222222222-2-2-222-222-2-22200000000-222-2-2-2-2-2220000000000000000000000000000
χ182222222222-2-2-222-222-2-22200000000-2-2-222-222-2-20000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-200000000222222-2-2-2-20000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2000000002-2-2-2-2222220000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2-2-22222-2-2-2-2-200002000022-2-2000000000000000000000000
χ2222222222-2-2222-2-2222-2-2-2-2-2-2-2-22222-2000020000-2-222000000000000000000000000
χ2322222222-2-2222-2-22-2-2-2-2222222-2-2-2-220000-20000-2-222000000000000000000000000
χ2422222222-2-2222-2-22-2-2-2-222-2-2-2-2222220000-2000022-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000000020000-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000000020000-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200000000-200002000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200000000-20000200000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2922-2-222-2-22-22-2-22-22002-2002i2i−2i−2i2i2i−2i−2i0000000000000000000000002-22i−2i0000000000
χ3022-2-222-2-22-22-2-22-22002-2002i2i−2i−2i2i2i−2i−2i000000000000000000000000-22−2i2i0000000000
χ3122-2-222-2-22-22-2-22-22002-200−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-2−2i2i0000000000
χ3222-2-222-2-22-22-2-22-22002-200−2i−2i2i2i−2i−2i2i2i000000000000000000000000-222i−2i0000000000
χ3322-2-222-2-2-222-2-2-22200-22002i2i−2i−2i−2i−2i2i2i00000000000000000000002-200002i−2i00000000
χ3422-2-222-2-2-222-2-2-22200-22002i2i−2i−2i−2i−2i2i2i0000000000000000000000-220000−2i2i00000000
χ3522-2-222-2-2-222-2-2-22200-2200−2i−2i2i2i2i2i−2i−2i00000000000000000000002-20000−2i2i00000000
χ3622-2-222-2-2-222-2-2-22200-2200−2i−2i2i2i2i2i−2i−2i0000000000000000000000-2200002i−2i00000000
χ372-22-22-22-22-2000-2202-2002-2i2−i2i2−i2i2−i2i2−i20002i−2i02i−2i00i2−i2i2−i22−22−22−22−20000000000000000
χ382-22-22-22-22-2000-2202-2002-2i2−i2i2−i2i2−i2i2−i2000−2i2i0−2i2i00i2−i2i2−i2−22−22−22−220000000000000000
χ392-22-22-22-22-2000-2202-2002-2−i2i2−i2i2−i2i2−i2i20002i−2i02i−2i00−i2i2−i2i2−22−22−22−220000000000000000
χ402-22-22-22-22-2000-2202-2002-2−i2i2−i2i2−i2i2−i2i2000−2i2i0−2i2i00−i2i2−i2i22−22−22−22−20000000000000000
χ412-22-22-22-22-2000-220-2200-22i2−i2i2−i2i2−i2i2−i20002i−2i0−2i2i00−i2i2−i2i2−22−222−22−20000000000000000
χ422-22-22-22-22-2000-220-2200-22i2−i2i2−i2i2−i2i2−i2000−2i2i02i−2i00−i2i2−i2i22−22−2−22−220000000000000000
χ432-22-22-22-22-2000-220-2200-22−i2i2−i2i2−i2i2−i2i20002i−2i0−2i2i00i2−i2i2−i22−22−2−22−220000000000000000
χ442-22-22-22-22-2000-220-2200-22−i2i2−i2i2−i2i2−i2i2000−2i2i02i−2i00i2−i2i2−i2−22−222−22−20000000000000000
χ452-22-22-22-2-220002-202-200-22i2−i2i2−i2−i2i2−i2i202-2000002-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ462-22-22-22-2-220002-202-200-22i2−i2i2−i2−i2i2−i2i20-2200000-22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ472-22-22-22-2-220002-202-200-22−i2i2−i2i2i2−i2i2−i202-2000002-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ482-22-22-22-2-220002-202-200-22−i2i2−i2i2i2−i2i2−i20-2200000-22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ492-22-22-22-2-220002-20-22002-2i2−i2i2−i2−i2i2−i2i202-200000-22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ502-22-22-22-2-220002-20-22002-2i2−i2i2−i2−i2i2−i2i20-22000002-2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ512-22-22-22-2-220002-20-22002-2−i2i2−i2i2i2−i2i2−i202-200000-22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ522-22-22-22-2-220002-20-22002-2−i2i2−i2i2i2−i2i2−i20-22000002-2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ53444-4-4-4-440044-400-400000000000000000000000000000000000000000000000022−2200
χ54444-4-4-4-440044-400-4000000000000000000000000000000000000000000000000−222200
χ55444-4-4-4-4400-4-44004000000000000000000000000000000000000000000000000002i2−2i2
χ56444-4-4-4-4400-4-4400400000000000000000000000000000000000000000000000000−2i22i2
χ5744-44-4-44-4004-4400-40000000000000000000000000000000000000000000022−22000000
χ5844-44-4-44-4004-4400-400000000000000000000000000000000000000000000−2222000000
χ5944-44-4-44-400-44-400400000000000000000000000000000000000000000000002i2−2i20000
χ6044-44-4-44-400-44-40040000000000000000000000000000000000000000000000−2i22i20000
χ6144-4-444-4-44-4-4444-4-400-44000000000000000000000000000000000000000000000000
χ6244-4-444-4-4-44-444-44-4004-4000000000000000000000000000000000000000000000000
χ634-4-444-4-4444000-4-4000000022−22−222222−22−222200000000000000000000000000000000000000
χ644-4-444-4-4444000-4-40000000−222222−22−222222−2200000000000000000000000000000000000000
χ654-4-444-4-44-4-400044000000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-444-4-44-4-4000440000000−222222−2222−22−222200000000000000000000000000000000000000
χ678-888-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8-8888000000000000000000000000000000000000000000000000000000000000

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