Finite Group Databasebeta

← Group #509286

Character table — Group #509286

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444448888888888888888888161616161616161616161632323232
order122222444488888888161616162244448881616161616161616161624444488816162448
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-11-1-111-1-1-1-1
χ31111111111111111111111-1-1-1-111-1-1111-1-1-1-111111111-1-1-111-1-1-1-1-11
χ41111111111111111111111-1-1-1-111-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-1111-1
χ5111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1111-1-1-111-1
χ6111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11-1-11
χ7111111111111111111-1-1-1-1-1-1-1-111-1-11-1-11111-1-1-1-11-11-111-111111-1-1-1
χ8111111111111111111-1-1-1-1-1-1-1-111-1-11-1-11111-1-1-1-1-11-11-1-1-1-1-111-1111
χ9111111111111111-1-1111111-11-1-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-111-1-1
χ10111111111111111-1-1111111-11-1-1-111-1111111-1-1-1-1-1-1-1-111-111-1-1-1-111
χ11111111111111111-1-111111-11-11-1-1-1-1-111-1-1-1-1-1-1-1-11111111-1-111-1-11-1
χ12111111111111111-1-111111-11-11-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-11
χ13111111111111111-1-11-1-1-1-11-11-1-1-111-1-1-1-1-1-1-111111-11-111-1-1-111-11-11
χ14111111111111111-1-11-1-1-1-11-11-1-1-111-1-1-1-1-1-1-11111-11-11-1-1-111111-11-1
χ15111111111111111-1-11-1-1-1-1-11-11-1-1-1-1-1-1-1111111111-11-1-1-11-1-1-1-11-111
χ16111111111111111-1-11-1-1-1-1-11-11-1-1-1-1-1-1-111111111-11-1111111-1-1-11-1-1
χ172222222222-2-2-2-2-222-200002222-2-2-2-220000000000000000-200000000
χ182222222222-2-2-2-2-222-20000-2-2-2-2-2-22220000000000000000200000000
χ192222222222-2-2-2-2-2-2-2-200002-22-222-2-2-20000000000000000200000000
χ202222222222-2-2-2-2-2-2-2-20000-22-222222-20000000000000000-200000000
χ212222-2-22-22-22222-200-22222000000000-2-2000000002-2-2200000000000
χ222222-2-22-22-22222-200-22222000000000-2-200000000-222-200000000000
χ232222-2-22-22-22222-200-2-2-2-2-2000000000220000000022-2-200000000000
χ242222-2-22-22-22222-200-2-2-2-2-20000000002200000000-2-22200000000000
χ252222-2-2-22-220000022022−2−222-2-20000-22−222−2−222−2−20000000002−20000
χ262222-2-2-22-220000022022−2−2-2-2220000-22−2−2−22222−2−2000000000−220000
χ272222-2-2-22-2200000220−2−22222-2-20000-2−22−2−222−2−222000000000−220000
χ282222-2-2-22-2200000220−2−222-2-2220000-2−2222−2−2−2−2220000000002−20000
χ292222-2-2-22-2200000-2-2022−2−22-2-22000022−222−2−2−2−222000000000−220000
χ302222-2-2-22-2200000-2-2022−2−2-222-2000022−2−2−222−2−2220000000002−20000
χ312222-2-2-22-2200000-2-20−2−2222-2-2200002−22−2−22222−2−20000000002−20000
χ322222-2-2-22-2200000-2-20−2−222-222-200002−2222−2−222−2−2000000000−220000
χ332-22-22-2-222-2-2-222-20020000000000000002-22-2000000002i−2i02i−2i000000
χ342-22-22-2-222-2-2-222-20020000000000000002-22-200000000−2i2i0−2i2i000000
χ352-22-22-2-222-2-2-222-2002000000000000000-22-22000000002i−2i0−2i2i000000
χ362-22-22-2-222-2-2-222-2002000000000000000-22-2200000000−2i2i02i−2i000000
χ37444444-4-4-4-4000000002222−22−22000000000−222200000000000000000000000
χ38444444-4-4-4-400000000−22−22222200000000022−2200000000000000000000000
χ394444-4-44-44-4-4-4-4-4400400000000000000000000000000000000000000
χ404-44-44-44-4-440000000000000000004i−4i00000000000000000000000000
χ414-44-44-44-4-44000000000000000000−4i4i00000000000000000000000000
χ424-44-44-4-444-444-4-4400-400000000000000000000000000000000000000
χ434-44-4-4444-4-40000000000000000000000022−22−22220000000000000000000
χ444-44-4-4444-4-400000000000000000000000−222222−220000000000000000000
χ454-44-4-44-4-44444-4-4-400400000000000000000000000000000000000000
χ464-44-4-44-4-444-4-444400-400000000000000000000000000000000000000
χ474-4-4400000022−2222−22022−2202ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500002-2000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000
χ484-4-4400000022−2222−22022−220−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500002-2000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000
χ494-4-4400000022−2222−220−222202ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000-22000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000
χ504-4-4400000022−2222−220−22220−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000-22000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000
χ514-4-44000000−2222−2222022−2202ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000-22000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000
χ524-4-44000000−2222−2222022−220−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000-22000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000
χ534-4-44000000−2222−22220−222202ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700002-2000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000
χ544-4-44000000−2222−22220−22220−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700002-2000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000
χ5588-8-800000042−42−4242000000000000000000000000000000000000000000
χ5688-8-8000000−424242−42000000000000000000000000000000000000000000

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