Finite Group Databasebeta

← Group #490892

Character table — Group #490892

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222444444444444488888888888888816161616161616161616161632323232
order12224444888824444888888888888888161616161616161622448888161616164444
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1
χ9111111111111-1-1-1-1111-1-11111-1-1-111-1-11111-1-1-1-11-11-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1111-1-11111-1-1-111-1-11111-1-1-1-1-11-11-1-11111-1-1-1-111
χ11111111111111-1-1-1-1111-1-11111-1-1-111-1-1-1-1-1-111111-11-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1111-1-11111-1-1-111-1-1-1-1-1-11111-11-11-1-111-1-11111-1-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-111-1-1111111-1-1-1-11-11-1-1-111-1-111-11-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-111-1-1111111-1-1-1-1-11-1111-1-1-1-1111-11-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-111-1-111-1-1-1-111111-11-1-1-11111-1-11-11-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-111-1-111-1-1-1-11111-11-1111-1-111-1-1-11-11
χ1722222222-2-2-2-222222-2-2-2-22222-222-2-2-2-2000000000000000000000000
χ1822222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ1922222222-2-2-2-2-2-2-2-22-2-22222222-2-2-2-222000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-22-2-222-2-2-2-222222-2-2000000000000000000000000
χ21222222-2-222222-22-2-2-2-2-2-200002000000000000002-2-22000000000000
χ22222222-2-222222-22-2-2-2-2-2-20000200000000000000-222-2000000000000
χ23222222-2-22222-22-22-2-2-2220000-20000000000000022-2-2000000000000
χ24222222-2-22222-22-22-2-2-2220000-200000000000000-2-222000000000000
χ25222222-2-2-2-2-2-22-22-2-222220000-20000000000000000002i−2i2i−2i00000000
χ26222222-2-2-2-2-2-22-22-2-222220000-2000000000000000000−2i2i−2i2i00000000
χ27222222-2-2-2-2-2-2-22-22-222-2-2000020000000000000000002i−2i−2i2i00000000
χ28222222-2-2-2-2-2-2-22-22-222-2-200002000000000000000000−2i2i2i−2i00000000
χ292222-2-22200002-2-22-2000022-2-202-2000022−2−222−2−2000000002−22−20000
χ302222-2-22200002-2-22-2000022-2-202-20000−2−222−2−22200000000−22−220000
χ312222-2-22200002-2-22-20000-2-2220-22000022−2−222−2−200000000−22−220000
χ322222-2-22200002-2-22-20000-2-2220-220000−2−222−2−222000000002−22−20000
χ332222-2-2220000-222-2-2000022-2-20-22000022−2−2−2−222000000002−2−220000
χ342222-2-2220000-222-2-2000022-2-20-220000−2−22222−2−200000000−222−20000
χ352222-2-2220000-222-2-20000-2-22202-2000022−2−2−2−22200000000−222−20000
χ362222-2-2220000-222-2-20000-2-22202-20000−2−22222−2−2000000002−2−220000
χ374444-4-4-4-4000044-4-44000000000000000000000000000000000000000
χ384444-4-4-4-40000-4-4444000000000000000000000000000000000000000
χ394-44-4004-42222−22−220000022−22000000000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000
χ404-44-4004-42222−22−220000022−2200000000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000
χ414-44-4004-4−22−22222200000−2222000000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000
χ424-44-4004-4−22−22222200000−222200000000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000
χ434-44-400-442222−22−2200000−222200000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000
χ444-44-400-442222−22−2200000−22220000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000
χ454-44-400-44−22−2222220000022−2200000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000
χ464-44-400-44−22−2222220000022−220000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000
χ474-4-444-400000000000004-42i2−2i22i2−2i2000002i2−2i2000000000000000000000000
χ484-4-444-400000000000004-4−2i22i2−2i22i200000−2i22i2000000000000000000000000
χ494-4-444-40000000000000-442i2−2i22i2−2i200000−2i22i2000000000000000000000000
χ504-4-444-40000000000000-44−2i22i2−2i22i2000002i2−2i2000000000000000000000000
χ514-4-44-44004-44-40000000002i2−2i2−2i22i20002i2−2i200000000000000000000000000
χ524-4-44-44004-44-4000000000−2i22i22i2−2i2000−2i22i200000000000000000000000000
χ534-4-44-4400-44-440000000002i2−2i2−2i22i2000−2i22i200000000000000000000000000
χ544-4-44-4400-44-44000000000−2i22i22i2−2i20002i2−2i200000000000000000000000000
χ5588-8-8000042−42−424200000000000000000000000000000000000000000000
χ5688-8-80000−424242−4200000000000000000000000000000000000000000000

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