Finite Group Databasebeta

← Group #139019

Character table — Group #139019

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222244444444448888888888888888816161616161616161616161632323232
order12222244444444888888888888888161616161616161644448888161616164488
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ5111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ7111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911111111-1-11-1-1-1-1-1-111-11ii−i−iii−i−iiiii−i−i−i−i1-11-1i−ii−i11-1-11-1i−i
χ1011111111-1-11-1-1-1-1-1-111-11ii−i−iii−i−i−i−i−i−iiiii1-11-1i−ii−i-1-111-11−ii
χ1111111111-1-11-1-1-1-1-1-111-11ii−i−i−i−iiiiiii−i−i−i−i-11-11i−i−ii-1-1111-1−ii
χ1211111111-1-11-1-1-1-1-1-111-11ii−i−i−i−iii−i−i−i−iiiii-11-11i−i−ii11-1-1-11i−i
χ1311111111-1-11-1-1-1-1-1-111-11−i−iiiii−i−iiiii−i−i−i−i-11-11−iii−i11-1-1-11−ii
χ1411111111-1-11-1-1-1-1-1-111-11−i−iiiii−i−i−i−i−i−iiiii-11-11−iii−i-1-1111-1i−i
χ1511111111-1-11-1-1-1-1-1-111-11−i−iii−i−iiiiiii−i−i−i−i1-11-1−ii−ii-1-111-11i−i
χ1611111111-1-11-1-1-1-1-1-111-11−i−iii−i−iii−i−i−i−iiiii1-11-1−ii−ii11-1-11-1−ii
χ1722222222222222-2-2-2-2-2-2-20000222200000000000000-2-200000000
χ1822222222222222-2-2-2-2-2-2-20000-2-2-2-2000000000000002200000000
χ1922222222-2-22-2-2-2222-2-22-200002i2i−2i−2i00000000000000−2i2i00000000
χ2022222222-2-22-2-2-2222-2-22-20000−2i−2i2i2i000000000000002i−2i00000000
χ212222-2-22222-2-22-222-222-2-200000000000000002-2-22000000000000
χ222222-2-22222-2-22-222-222-2-20000000000000000-222-2000000000000
χ232222-2-22222-2-22-2-2-22-2-22222220000000000000000-2-20000000000
χ242222-2-22222-2-22-2-2-22-2-222-2-2-2-20000000000000000220000000000
χ252222-2-222-2-2-22-2222-2-2-2-222i2i−2i−2i0000000000000000−2i2i0000000000
χ262222-2-222-2-2-22-2222-2-2-2-22−2i−2i2i2i00000000000000002i−2i0000000000
χ272222-2-222-2-2-22-22-2-22222-2000000000000000022-2-2000000000000
χ282222-2-222-2-2-22-22-2-22222-20000000000000000-2-222000000000000
χ292222-2-2-2-2222-2-22000000000002-22-222−2−222−2−2000000002−22−20000
χ302222-2-2-2-2222-2-22000000000002-22-2−2−222−2−22200000000−22−220000
χ312222-2-2-2-2222-2-2200000000000-22-2222−2−222−2−200000000−22−220000
χ322222-2-2-2-2222-2-2200000000000-22-22−2−222−2−222000000002−22−20000
χ332222-2-2-2-2-2-2222-2000000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2000000002−2−220000
χ342222-2-2-2-2-2-2222-2000000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i200000000−222−20000
χ352222-2-2-2-2-2-2222-200000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i200000000−222−20000
χ362222-2-2-2-2-2-2222-200000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2000000002−2−220000
χ37444444-4-444-44-4-4000000000000000000000000000000000000000
χ38444444-4-4-4-4-4-444000000000000000000000000000000000000000
χ3944-4-4004-400000000400-4022−2222−220000000000000000000000000000
χ4044-4-4004-400000000400-40−2222−22220000000000000000000000000000
χ4144-4-4004-400000000-400402i2−2i2−2i22i20000000000000000000000000000
χ4244-4-4004-400000000-40040−2i22i22i2−2i20000000000000000000000000000
χ434-4-4400004i−4i00002i2−2i2022−220000000000ζ−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+ζ70000000000000000
χ444-4-4400004i−4i00002i2−2i2022−220000000000−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−ζ70000000000000000
χ454-4-4400004i−4i0000−2i22i20−22220000000000ζ−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−ζ70000000000000000
χ464-4-4400004i−4i0000−2i22i20−22220000000000−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+ζ70000000000000000
χ474-4-440000−4i4i00002i2−2i20−22220000000000ζ+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+ζ70000000000000000
χ484-4-440000−4i4i00002i2−2i20−22220000000000−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−ζ70000000000000000
χ494-4-440000−4i4i0000−2i22i2022−220000000000ζ+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−ζ70000000000000000
χ504-4-440000−4i4i0000−2i22i2022−220000000000−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+ζ70000000000000000
χ5188-8-800-88000000000000000000000000000000000000000000000
χ528-88-88-800000000000000000000000000000000000000000000000
χ538-88-8-8800000000000000000000000000000000000000000000000

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