Finite Group Databasebeta

← Group #512108

Character table — Group #512108

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222222444488882444444444488882222444444444444888881616161616161616161616164488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111
χ611111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-111-1-1
χ811111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ9111111-1-111111111-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-1-111-1-11111-1-1-1-111-1-11-11-1
χ10111111-1-111111111-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-111-11-11
χ11111111-1-111111111-111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-111-1-11111-1-1-1-111-1-1-11-11
χ12111111-1-111111111-111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-111-1-1-1-1-1-11111-1-1111-11-1
χ13111111-1-111111111-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-111-111-1
χ14111111-1-111111111-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-111-1-1-1-1111111-1-11-1-11
χ15111111-1-111111111-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-11
χ16111111-1-111111111-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-111-1
χ17222222222222-2-2-2-222222222222-2-2-2-20000000000000000-2-2-2-2-20000000000000000
χ18222222222222-2-2-2-22-2-2-2-222-2-2-2-2-2-2-2-20000000000000000-222220000000000000000
χ19222222-2-22222-2-2-2-2-222-2-2-2-222-2-222-2-200000000000000002-2-2220000000000000000
χ20222222-2-22222-2-2-2-2-2-2-222-2-2-2-22222-2-20000000000000000222-2-20000000000000000
χ212222-2-22222-2-20000-222222-2-2-2-2-2000000000000000000000000022−2−222−2−22−22−20000
χ222222-2-22222-2-20000-222222-2-2-2-2-20000000000000000000000000−2−222−2−222−22−220000
χ232222-2-22222-2-20000-2-2-2-2-22-22222000000000000000000000000022−2−222−2−2−22−220000
χ242222-2-22222-2-20000-2-2-2-2-22-222220000000000000000000000000−2−222−2−2222−22−20000
χ252222-2-222-2-2222222-20000-22000022-2-22222-2-2-2-200000000-200000000000000000000
χ262222-2-222-2-2222222-20000-22000022-2-2-2-2-2-2222200000000-200000000000000000000
χ272222-2-222-2-222-2-2-2-2-20000-220000-2-2220000000022-2-222-2-2200000000000000000000
χ282222-2-222-2-222-2-2-2-2-20000-220000-2-22200000000-2-222-2-222200000000000000000000
χ292222-2-2-2-222-2-20000222-2-2-22-2-222000000000000000000000000022−2−2−2−2222−2−220000
χ302222-2-2-2-222-2-20000222-2-2-22-2-2220000000000000000000000000−2−22222−2−2−222−20000
χ312222-2-2-2-222-2-200002-2-222-2222-2-2000000000000000000000000022−2−2−2−222−222−20000
χ322222-2-2-2-222-2-200002-2-222-2222-2-20000000000000000000000000−2−22222−2−22−2−220000
χ332222-2-2-2-2-2-2222222200002-20000-2-2-2-222-2-2-2-22200000000200000000000000000000
χ342222-2-2-2-2-2-2222222200002-20000-2-2-2-2-2-22222-2-200000000200000000000000000000
χ352222-2-2-2-2-2-222-2-2-2-2200002-2000022220000000022-2-2-2-222-200000000000000000000
χ362222-2-2-2-2-2-222-2-2-2-2200002-20000222200000000-2-22222-2-2-200000000000000000000
χ372-22-22-2002-22-222-2-20002i−2i00002i−2i002-2002-2002-22i−2i2i−2i00000002i−2i0000000000000000
χ382-22-22-2002-22-222-2-20002i−2i00002i−2i002-200-2200-22−2i2i−2i2i00000002i−2i0000000000000000
χ392-22-22-2002-22-222-2-2000−2i2i0000−2i2i002-2002-2002-2−2i2i−2i2i0000000−2i2i0000000000000000
χ402-22-22-2002-22-222-2-2000−2i2i0000−2i2i002-200-2200-222i−2i2i−2i0000000−2i2i0000000000000000
χ412-22-22-2002-22-2-2-2220002i−2i00002i−2i00-222-2002-20000002i−2i2i−2i000−2i2i0000000000000000
χ422-22-22-2002-22-2-2-2220002i−2i00002i−2i00-22-2200-22000000−2i2i−2i2i000−2i2i0000000000000000
χ432-22-22-2002-22-2-2-222000−2i2i0000−2i2i00-222-2002-2000000−2i2i−2i2i0002i−2i0000000000000000
χ442-22-22-2002-22-2-2-222000−2i2i0000−2i2i00-22-2200-220000002i−2i2i−2i0002i−2i0000000000000000
χ452-22-2-2200-222-222-2-202i−2i00002i−2i0000-22002-200-2200002i−2i−2i2i02i−2i000000000000000000
χ462-22-2-2200-222-222-2-202i−2i00002i−2i0000-2200-22002-20000−2i2i2i−2i02i−2i000000000000000000
χ472-22-2-2200-222-222-2-20−2i2i0000−2i2i0000-22002-200-220000−2i2i2i−2i0−2i2i000000000000000000
χ482-22-2-2200-222-222-2-20−2i2i0000−2i2i0000-2200-22002-200002i−2i−2i2i0−2i2i000000000000000000
χ492-22-2-2200-222-2-2-22202i−2i00002i−2i00002-22-200-22002i−2i−2i2i00000−2i2i000000000000000000
χ502-22-2-2200-222-2-2-22202i−2i00002i−2i00002-2-22002-200−2i2i2i−2i00000−2i2i000000000000000000
χ512-22-2-2200-222-2-2-2220−2i2i0000−2i2i00002-22-200-2200−2i2i2i−2i000002i−2i000000000000000000
χ522-22-2-2200-222-2-2-2220−2i2i0000−2i2i00002-2-22002-2002i−2i−2i2i000002i−2i000000000000000000
χ5344444444-4-4-4-4000040000-4-4000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-40000-4000044000000000000000000000000000000000000000000000
χ5544-4-4004-4000022−2222−220000000000022−2200000000000000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000
χ5644-4-4004-4000022−2222−220000000000022−2200000000000000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000
χ5744-4-4004-40000−2222−222200000000000−222200000000000000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000
χ5844-4-4004-40000−2222−222200000000000−222200000000000000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000
χ5944-4-400-44000022−2222−2200000000000−222200000000000000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000
χ6044-4-400-44000022−2222−2200000000000−222200000000000000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000
χ6144-4-400-440000−2222−22220000000000022−2200000000000000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000
χ6244-4-400-440000−2222−22220000000000022−2200000000000000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000
χ634-44-44-400-44-44000004i−4i0000−4i4i0000000000000000000000000000000000000000000
χ644-44-44-400-44-4400000−4i4i00004i−4i0000000000000000000000000000000000000000000
χ654-44-4-44004-4-4400000004i−4i0000−4i4i00000000000000000000000000000000000000000
χ664-44-4-44004-4-440000000−4i4i00004i−4i00000000000000000000000000000000000000000
χ678-8-880000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-8-8800000000−424242−420000000000000000000000000000000000000000000000000000

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