Finite Group Databasebeta

← Group #509581

Character table — Group #509581

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444448888888888888888888161616161616161616161632323232
order122222444488888888161616164444448881616161616161616161624444488816164448
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-11-1-111-1-1-1-1
χ31111111111111111111111-1-1-1-1111-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-11
χ41111111111111111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1111-1
χ5111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-11-1-11
χ6111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-111-1
χ7111111111111111111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111-1111
χ8111111111111111111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-11111-111111-1-1-1
χ9111111111111111-1-1111111-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-11-11-1
χ10111111111111111-1-1111111-11-1-1-1-111111111-1-1-1-1-1-1-1-111-111-1-1-11-11
χ11111111111111111-1-111111-11-11-1-1-1-1-1-1-1-1-111-1-1-1-11111111-1-111-11-1-1
χ12111111111111111-1-111111-11-11-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-111
χ13111111111111111-1-11-1-1-1-11-11-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1111111-1-1
χ14111111111111111-1-11-1-1-1-11-11-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-111-1-111
χ15111111111111111-1-11-1-1-1-1-11-11-1-1-1-1-11111-1-1111111-1-111111-1-1-1-11-1
χ16111111111111111-1-11-1-1-1-1-11-11-1-1-1-1-11111-1-11111-1-111-1-11-1-1-1-111-11
χ172222222222-2-2-2-2-222-200002222-2-22-2-20000000000000000-200000000
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
χ202222222222-2-2-2-2-2-2-2-20000-22-2222-2220000000000000000-200000000
χ212222-2-22-22-22222-200-222220000000000000-2-200002-22-200000000000
χ222222-2-22-22-22222-200-222220000000000000-2-20000-22-2200000000000
χ232222-2-22-22-22222-200-2-2-2-2-200000000000002200002-2-2200000000000
χ242222-2-22-22-22222-200-2-2-2-2-20000000000000220000-222-200000000000
χ252222-2-2-22-220000022022−2−22-2-2200-20022−2−22−222−2−20000000002−20000
χ262222-2-2-22-220000022022−2−2-222-200-200−2−2222−222−2−2000000000−220000
χ272222-2-2-22-2200000220−2−2222-2-2200-200−2−222−22−2−222000000000−220000
χ282222-2-2-22-2200000220−2−222-222-200-20022−2−2−22−2−2220000000002−20000
χ292222-2-2-22-2200000-2-2022−2−222-2-20020022−2−22−2−2−222000000000−220000
χ302222-2-2-22-2200000-2-2022−2−2-2-22200200−2−2222−2−2−2220000000002−20000
χ312222-2-2-22-2200000-2-20−2−22222-2-200200−2−222−2222−2−20000000002−20000
χ322222-2-2-22-2200000-2-20−2−222-2-2220020022−2−2−2222−2−2000000000−220000
χ3322-2-22-22-2-22-2-222-200200000000000002i−2i2i−2i00000000002i−2i02-2000000
χ3422-2-22-22-2-22-2-222-200200000000000002i−2i2i−2i0000000000−2i2i0-22000000
χ3522-2-22-22-2-22-2-222-20020000000000000−2i2i−2i2i00000000002i−2i0-22000000
χ3622-2-22-22-2-22-2-222-20020000000000000−2i2i−2i2i0000000000−2i2i02-2000000
χ37444444-4-4-4-4000000002222−22−220000000000000−22220000000000000000000
χ38444444-4-4-4-400000000−22−222222000000000000022−220000000000000000000
χ394444-4-44-44-4-4-4-4-4400400000000000000000000000000000000000000
χ4044-4-44-44-4-4444-4-4400-400000000000000000000000000000000000000
χ4144-4-44-4-444-400000000000000000004-40000000000000000000000000
χ4244-4-44-4-444-40000000000000000000-440000000000000000000000000
χ4344-4-4-4444-4-444-4-4-400400000000000000000000000000000000000000
χ4444-4-4-4444-4-4-4-444400-400000000000000000000000000000000000000
χ4544-4-4-44-4-4440000000000000000000002i2−2i2−2i22i2000000000000000000000
χ4644-4-4-44-4-444000000000000000000000−2i22i22i2−2i2000000000000000000000
χ474-4-4400000022−2222−2202i2−2i202ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500002i−2i000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000
χ484-4-4400000022−2222−2202i2−2i20−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500002i−2i000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000
χ494-4-4400000022−2222−220−2i22i202ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000−2i2i000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000
χ504-4-4400000022−2222−220−2i22i20−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000−2i2i000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000
χ514-4-44000000−2222−222202i2−2i202ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000−2i2i000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000
χ524-4-44000000−2222−222202i2−2i20−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000−2i2i000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000
χ534-4-44000000−2222−22220−2i22i202ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700002i−2i000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000
χ544-4-44000000−2222−22220−2i22i20−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700002i−2i000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000
χ558-88-800000042−42−4242000000000000000000000000000000000000000000
χ568-88-8000000−424242−42000000000000000000000000000000000000000000

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