Finite Group Databasebeta

← Group #136113

Character table — Group #136113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order122244442244444422444488888888448888161616161616161616161616161616168888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111-1-111-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111-1-111-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ91111-1-1-1-111-1-1-111-1111-1-1-1-1-1-1-111111-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111-1-1-111-1111-1-1-1-1-1-1-111111-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-111-1-1-111-1111-1-1-1-1-1-1-111111-111-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ121111-1-1-1-111-1-1-111-1111-1-1-1-1-1-1-111111-111-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ131111-1-1-1-111-1-1-111-1-1-11-111-1-1-1-11111-11-1-1111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ141111-1-1-1-111-1-1-111-1-1-11-111-1-1-1-11111-11-1-1111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ151111-1-1-1-111-1-1-111-1-1-11-111-1-1-1-11111-11-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ161111-1-1-1-111-1-1-111-1-1-11-111-1-1-1-11111-11-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ1922222222222-2-2-2-2222-2-22200000000-2-2000022−2−222−2−222−2−222−2−20000000000000000
χ2022222222222-2-2-2-2222-2-22200000000-2-20000−2−222−2−222−2−222−2−2220000000000000000
χ2122222222222-2-2-2-22-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−2220000000000000000
χ2222222222222-2-2-2-22-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-22222-200-2-20022-2-222-2-2000000000000000000000000002-22-200000000
χ2422222222-2-2-22222-200-2-20022-2-222-2-200000000000000000000000000-22-2200000000
χ2522222222-2-2-22222-200-2-200-2-222-2-2220000000000000000000000000000002-22-20000
χ2622222222-2-2-22222-200-2-200-2-222-2-222000000000000000000000000000000-22-220000
χ272222-2-2-2-222-222-2-2-222-22-2-200000000-22000022−2−2−2−22222−2−2−2−2220000000000000000
χ282222-2-2-2-222-222-2-2-222-22-2-200000000-220000−2−22222−2−2−2−22222−2−20000000000000000
χ292222-2-2-2-222-222-2-2-2-2-2-2222000000002-2000022−2−2−2−222−2−22222−2−20000000000000000
χ302222-2-2-2-222-222-2-2-2-2-2-2222000000002-20000−2−22222−2−222−2−2−2−2220000000000000000
χ312222-2-2-2-222-2-2-222-2222-2-2-22222-2-2-2-22-2-2-22200000000000000000000000000000000
χ322222-2-2-2-222-2-2-222-2-2-22-2222222-2-2-2-2-2222-2-200000000000000000000000000000000
χ332222-2-2-2-2-2-22-2-222200-220022-2-2-2-2220000000000000000000000000000002i−2i−2i2i0000
χ342222-2-2-2-2-2-22-2-222200-220022-2-2-2-222000000000000000000000000000000−2i2i2i−2i0000
χ352222-2-2-2-2-2-22-2-222200-2200-2-22222-2-2000000000000000000000000002i−2i−2i2i00000000
χ362222-2-2-2-2-2-22-2-222200-2200-2-22222-2-200000000000000000000000000−2i2i2i−2i00000000
χ3722-2-222-2-22-2-2000022-2002-22−22−22−22−2002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ3822-2-222-2-22-2-2000022-2002-22−22−22−22−2002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ3922-2-222-2-22-2-2000022-2002-2−22−22−22−2200−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ4022-2-222-2-22-2-2000022-2002-2−22−22−22−2200−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ4122-2-222-2-22-2-200002-2200-222−22−22−22−200−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ4222-2-222-2-22-2-200002-2200-222−22−22−22−200−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ4322-2-222-2-22-2-200002-2200-22−22−22−22−22002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ4422-2-222-2-22-2-200002-2200-22−22−22−22−22002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ4522-2-2-2-2222-220000-22-200-222−22−2−22−2200−222−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ4622-2-2-2-2222-220000-22-200-222−22−2−22−2200−222−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ4722-2-2-2-2222-220000-22-200-22−22−222−22−2002−2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ4822-2-2-2-2222-220000-22-200-22−22−222−22−2002−2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ4922-2-2-2-2222-220000-2-22002-22−22−2−22−22002−2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ5022-2-2-2-2222-220000-2-22002-22−22−2−22−22002−2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ5122-2-2-2-2222-220000-2-22002-2−22−222−22−200−222−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ5222-2-2-2-2222-220000-2-22002-2−22−222−22−200−222−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ5344444444-4-4-4-4-4-4-4-40044000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4444-4-44004-4000000000000000000000000000000000000000000000000
χ5544-4-444-4-4-4440000-400000022−22−222222−22−222200000000000000000000000000000000000000
χ5644-4-444-4-4-4440000-4000000−222222−22−222222−2200000000000000000000000000000000000000
χ5744-4-4-4-444-44-40000400000022−22−2222−222222−2200000000000000000000000000000000000000
χ5844-4-4-4-444-44-400004000000−222222−2222−22−222200000000000000000000000000000000000000
χ594-44-44i−4i4i−4i0004i−4i4-400000000000000000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ6
χ604-44-44i−4i4i−4i0004i−4i4-40000000000000000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ6
χ614-44-44i−4i4i−4i000−4i4i-4400000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ6000000000000
χ624-44-44i−4i4i−4i000−4i4i-440000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ6000000000000
χ634-44-4−4i4i−4i4i0004i−4i-4400000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ2000000000000
χ644-44-4−4i4i−4i4i0004i−4i-440000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ2000000000000
χ654-44-4−4i4i−4i4i000−4i4i4-400000000000000000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ2
χ664-44-4−4i4i−4i4i000−4i4i4-40000000000000000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ2
χ678-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.