Finite Group Databasebeta

← Group #348347

Character table — Group #348347

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444442222444444444488888888244444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ51111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-111-1
χ81111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11-1-11
χ91111111111111111-1-1-1-11111-1-1-1-111111111111-1-11-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ101111111111111111-1-1-1-11111-1-1-1-111111111111-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1111111-1-111-1-1-11-11
χ121111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-11111-1-111-1-1111-11-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-11111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1111111-1-1-1-111-1-1-1-1111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1111111-1-1-1-1-1-11111-1-1-111-1
χ172222222222-2-2-222-20000-2-22200002222222222-200-200-2-20000-2-20000000000000000
χ182222222222-2-2-222-20000-2-222000022-2-2-2-2-2-2-2-2-200-200220000220000000000000000
χ192222222222-2-2-222-20000-2-2-2-20000-2-22222-2-2-2-2200200-2-20000220000000000000000
χ202222222222-2-2-222-20000-2-2-2-20000-2-2-2-2-2-22222200200220000-2-20000000000000000
χ2122222222-2-2222-2-222222-2-222-2-2-2-2-2-200000000-2222-2-2000000000000000000000000
χ2222222222-2-2222-2-222222-2-2-2-2-2-2-2-222000000002-2-2-222000000000000000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-2222222-2-200000000-2-2-2222000000000000000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2-2-222222200000000222-2-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000022220000-2-200000000200-200002i2i−2i−2i002i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2000022220000-2-200000000200-20000−2i−2i2i2i00−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2000022-2-200002200000000-200200002i2i−2i−2i00−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2000022-2-200002200000000-20020000−2i−2i2i2i002i2i−2i−2i000000000000
χ2922-22-2-22-22-20002-200000002i−2i00002i−2i2i2i−2i−2i22-2-2000000000000000000i2−i22−22−2i2−i20000
χ3022-22-2-22-22-20002-200000002i−2i00002i−2i2i2i−2i−2i22-2-2000000000000000000−i2i2−22−22−i2i20000
χ3122-22-2-22-22-20002-200000002i−2i00002i−2i−2i−2i2i2i-2-222000000000000000000i2−i2−222−2−i2i20000
χ3222-22-2-22-22-20002-200000002i−2i00002i−2i−2i−2i2i2i-2-222000000000000000000−i2i22−2−22i2−i20000
χ3322-22-2-22-22-20002-20000000−2i2i0000−2i2i2i2i−2i−2i-2-222000000000000000000i2−i22−2−22−i2i20000
χ3422-22-2-22-22-20002-20000000−2i2i0000−2i2i2i2i−2i−2i-2-222000000000000000000−i2i2−222−2i2−i20000
χ3522-22-2-22-22-20002-20000000−2i2i0000−2i2i−2i−2i2i2i22-2-2000000000000000000i2−i2−22−22i2−i20000
χ3622-22-2-22-22-20002-20000000−2i2i0000−2i2i−2i−2i2i2i22-2-2000000000000000000−i2i22−22−2−i2i20000
χ372-2-2-22-222222-2-2-2-2200002-20000000000002i−2i2i−2i02-202-2002i−2i2i−2i2i−2i0000000000000000
χ382-2-2-22-222222-2-2-2-2200002-20000000000002i−2i2i−2i0-220-2200−2i2i−2i2i2i−2i0000000000000000
χ392-2-2-22-222222-2-2-2-2200002-2000000000000−2i2i−2i2i02-202-200−2i2i−2i2i−2i2i0000000000000000
χ402-2-2-22-222222-2-2-2-2200002-2000000000000−2i2i−2i2i0-220-22002i−2i2i−2i−2i2i0000000000000000
χ412-2-2-22-22222-222-2-2-222-2-2-220022-2-20000002i−2i2i−2i000000000000−2i2i2i−2i2i−2i000000000000
χ422-2-2-22-22222-222-2-2-222-2-2-220022-2-2000000−2i2i−2i2i0000000000002i−2i−2i2i−2i2i000000000000
χ432-2-2-22-22222-222-2-2-2-2-222-2200-2-2220000002i−2i2i−2i000000000000−2i2i−2i2i−2i2i000000000000
χ442-2-2-22-22222-222-2-2-2-2-222-2200-2-222000000−2i2i−2i2i0000000000002i−2i2i−2i2i−2i000000000000
χ452-2-2-22-222-2-22-2-22220000-22000000002-22-2000002-20-222-20000002-2-22000000000000
χ462-2-2-22-222-2-22-2-22220000-22000000002-22-200000-2202-22-2000000-222-2000000000000
χ472-2-2-22-222-2-22-2-22220000-2200000000-22-22000002-20-22-22000000-222-2000000000000
χ482-2-2-22-222-2-22-2-22220000-2200000000-22-2200000-2202-2-220000002-2-22000000000000
χ492-2-2-22-222-2-2-22222-222-2-22-200-2-222002-22-20000000000-222-2-22000000000000000000
χ502-2-2-22-222-2-2-22222-222-2-22-200-2-22200-22-2200000000002-2-222-2000000000000000000
χ512-2-2-22-222-2-2-22222-2-2-2222-20022-2-2002-22-20000000000-22-222-2000000000000000000
χ522-2-2-22-222-2-2-22222-2-2-2222-20022-2-200-22-2200000000002-22-2-22000000000000000000
χ53444-4-4-4-440044-400-44-44-4000000000000000000000000000000000000000000000000
χ54444-4-4-4-440044-400-4-44-44000000000000000000000000000000000000000000000000
χ55444-4-4-4-4400-4-44004000000004i−4i4i−4i0000000000000000000000000000000000000000
χ56444-4-4-4-4400-4-4400400000000−4i4i−4i4i0000000000000000000000000000000000000000
χ5744-44-4-44-4-44000-4400000004i−4i0000−4i4i00000000000000000000000000000000000000
χ5844-44-4-44-4-44000-440000000−4i4i00004i−4i00000000000000000000000000000000000000
χ594-44-4-444-44-4000-4400000000000000000004i−4i−4i4i000000000000000000000000000000
χ604-44-4-444-44-4000-440000000000000000000−4i4i4i−4i000000000000000000000000000000
χ614-44-4-444-4-440004-40000000000000004i−4i−4i4i0000000000000000000000000000000000
χ624-44-4-444-4-440004-4000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ634-4-44-44-44004-4400-4000000004i−4i−4i4i0000000000000000000000000000000000000000
χ644-4-44-44-44004-4400-400000000−4i4i4i−4i0000000000000000000000000000000000000000
χ654-4-44-44-4400-44-40044-4-44000000000000000000000000000000000000000000000000
χ664-4-44-44-4400-44-4004-444-4000000000000000000000000000000000000000000000000
χ6788-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8888-8-8-8000000000000000000000000000000000000000000000000000000000000

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