Finite Group Databasebeta

← Group #318749

Character table — Group #318749

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
χ91111111111111111-1-111-1-111111111-111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-111-1-111111111-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ111111111111111111-1-111-1-111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ121111111111111111-1-111-1-111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222-2-2-222-222-2-22200000000-22222-2-2-2-2-20000000000000000000000000000
χ182222222222-2-2-222-222-2-22200000000-2-2-2-2-2-222220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-200000000222-2-22-2-2220000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2000000002-2-222222-2-20000000000000000000000000000
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
χ2922-2-222-2-22222-2-2-2-2002-20022-2-222-2-200000000000000000000002-22-2000000000000
χ3022-2-222-2-22222-2-2-2-2002-20022-2-222-2-20000000000000000000000-22-22000000000000
χ3122-2-222-2-22222-2-2-2-2002-200-2-222-2-22200000000000000000000002-2-22000000000000
χ3222-2-222-2-22222-2-2-2-2002-200-2-222-2-2220000000000000000000000-222-2000000000000
χ3322-2-222-2-2-2-222-222-200-220022-2-2-2-222000000000000000000000000002i−2i2i−2i00000000
χ3422-2-222-2-2-2-222-222-200-220022-2-2-2-22200000000000000000000000000−2i2i−2i2i00000000
χ3522-2-222-2-2-2-222-222-200-2200-2-22222-2-2000000000000000000000000002i−2i−2i2i00000000
χ3622-2-222-2-2-2-222-222-200-2200-2-22222-2-200000000000000000000000000−2i2i2i−2i00000000
χ372-22-22-22-22-20002-202i−2i002i−2ii2−i2i2−i2i2−i2i2−i20000002i−2i2-22−22−22−22−2i2−i2i2−i20000000000000000
χ382-22-22-22-22-20002-202i−2i002i−2ii2−i2i2−i2i2−i2i2−i2000000−2i2i-222−22−2−22−22−i2i2−i2i20000000000000000
χ392-22-22-22-22-20002-202i−2i002i−2i−i2i2−i2i2−i2i2−i2i20000002i−2i2-2−22−22−22−22−i2i2−i2i20000000000000000
χ402-22-22-22-22-20002-202i−2i002i−2i−i2i2−i2i2−i2i2−i2i2000000−2i2i-22−22−222−22−2i2−i2i2−i20000000000000000
χ412-22-22-22-22-20002-20−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i20000002i−2i-22−22−222−22−2−i2i2−i2i20000000000000000
χ422-22-22-22-22-20002-20−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2000000−2i2i2-2−22−22−22−22i2−i2i2−i20000000000000000
χ432-22-22-22-22-20002-20−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i20000002i−2i-222−22−2−22−22i2−i2i2−i20000000000000000
χ442-22-22-22-22-20002-20−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i2000000−2i2i2-22−22−22−22−2−i2i2−i2i20000000000000000
χ452-22-22-22-2-22000-2202i−2i00−2i2ii2−i2i2−i2−i2i2−i2i202-22i−2i000002−2−22i2−i2−i2i2−222−20000000000000000
χ462-22-22-22-2-22000-2202i−2i00−2i2ii2−i2i2−i2−i2i2−i2i20-22−2i2i000002−2−22−i2i2i2−i22−2−220000000000000000
χ472-22-22-22-2-22000-2202i−2i00−2i2i−i2i2−i2i2i2−i2i2−i202-22i−2i00000−222−2−i2i2i2−i22−2−220000000000000000
χ482-22-22-22-2-22000-2202i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20-22−2i2i00000−222−2i2−i2−i2i2−222−20000000000000000
χ492-22-22-22-2-22000-220−2i2i002i−2ii2−i2i2−i2−i2i2−i2i202-2−2i2i00000−222−2i2−i2−i2i22−2−220000000000000000
χ502-22-22-22-2-22000-220−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20-222i−2i00000−222−2−i2i2i2−i2−222−20000000000000000
χ512-22-22-22-2-22000-220−2i2i002i−2i−i2i2−i2i2i2−i2i2−i202-2−2i2i000002−2−22−i2i2i2−i2−222−20000000000000000
χ522-22-22-22-2-22000-220−2i2i002i−2i−i2i2−i2i2i2−i2i2−i20-222i−2i000002−2−22i2−i2−i2i22−2−220000000000000000
χ53444-4-4-4-44004-4400-4000000000000000000000000000000000000000000000022−220000
χ54444-4-4-4-44004-4400-40000000000000000000000000000000000000000000000−22220000
χ55444-4-4-4-4400-44-4004000000000000000000000000000000000000000000002i2−2i2000000
χ56444-4-4-4-4400-44-400400000000000000000000000000000000000000000000−2i22i2000000
χ5744-44-4-44-4004-4-4004000000000000000000000000000000000000000000000000002i2−2i2
χ5844-44-4-44-4004-4-400400000000000000000000000000000000000000000000000000−2i22i2
χ5944-44-4-44-400-44400-400000000000000000000000000000000000000000000000022−2200
χ6044-44-4-44-400-44400-4000000000000000000000000000000000000000000000000−222200
χ6144-4-444-4-444-4-44-4-4400-44000000000000000000000000000000000000000000000000
χ6244-4-444-4-4-4-4-4-44444004-4000000000000000000000000000000000000000000000000
χ634-4-444-4-444-4000-4400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ644-4-444-4-444-4000-440000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ654-4-444-4-44-440004-400000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ664-4-444-4-44-440004-40000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ678-888-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8-8888000000000000000000000000000000000000000000000000000000000000

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