Finite Group Databasebeta

← Group #146129

Character table — Group #146129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222222222244444444888888888888888881616161616161616323232323232
order12224444448888244488884444888881616161616161616888816161616888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ92222222222-2-2-2-22222-2-2-2-22222-2-2-2-2-20000000000000000000000
χ102222222222-2-2-2-22222-2-2-2-2-2-2-2-2-222220000000000000000000000
χ1122222222-2-222222-2-2-222-2-20000-20000000000000000000000002i−2i
χ1222222222-2-222222-2-2-222-2-20000-2000000000000000000000000−2i2i
χ1322222222-2-2-2-2-2-22-2-2-2-2-2220000200000000000000000000002i−2i00
χ1422222222-2-2-2-2-2-22-2-2-2-2-222000020000000000000000000000−2i2i00
χ1522222-2-22222222-22-2-2-2-2220000-200002222-2-2-2-200000000000000
χ1622222-2-22222222-22-2-2-2-2220000-20000-2-2-2-2222200000000000000
χ1722222-2-2222-2-2-2-2-22-2-222-2-20000200000000000000002i2i−2i−2i000000
χ1822222-2-2222-2-2-2-2-22-2-222-2-2000020000000000000000−2i−2i2i2i000000
χ1922222-2-22-2-22222-2-222-2-2-2-200002000000000000000000002i−2i0000
χ2022222-2-22-2-22222-2-222-2-2-2-20000200000000000000000000−2i2i0000
χ2122222-2-22-2-2-2-2-2-2-2-22222220000-20000000000002i2i−2i−2i0000000000
χ2222222-2-22-2-2-2-2-2-2-2-22222220000-2000000000000−2i−2i2i2i0000000000
χ232222-222-2-2-20000-22-220000000002i2i−2i−2i22−2−222−2−20000i2−i2i2−i2000000
χ242222-222-2-2-20000-22-220000000002i2i−2i−2i−2−222−2−2220000−i2i2−i2i2000000
χ252222-222-2-2-20000-22-22000000000−2i−2i2i2i22−2−222−2−20000−i2i2−i2i2000000
χ262222-222-2-2-20000-22-22000000000−2i−2i2i2i−2−222−2−2220000i2−i2i2−i2000000
χ272222-2-2-2-2-2-20000222-2000022-2-20000022−2−2−2−22200002−2−22000000
χ282222-2-2-2-2-2-20000222-2000022-2-200000−2−22222−2−20000−222−2000000
χ292222-2-2-2-2-2-20000222-20000-2-2220000022−2−2−2−2220000−222−2000000
χ302222-2-2-2-2-2-20000222-20000-2-22200000−2−22222−2−200002−2−22000000
χ314444-444-4440000-4-44-400000000000000000000000000000000000
χ324444-4-4-4-44400004-4-4400000000000000000000000000000000000
χ3344-4-4-4004004i4i−4i−4i00000000000000000000000002ζ2−2ζ22ζ6−2ζ60000000000
χ3444-4-4-4004004i4i−4i−4i0000000000000000000000000−2ζ22ζ2−2ζ62ζ60000000000
χ3544-4-4-400400−4i−4i4i4i00000000000000000000000002ζ6−2ζ62ζ2−2ζ20000000000
χ3644-4-4-400400−4i−4i4i4i0000000000000000000000000−2ζ62ζ6−2ζ22ζ20000000000
χ374-44-400004i−4i2i2−2i22i2−2i200000022−222-22i−2i02ζ2−2ζ22ζ6−2ζ60000000000000000000000
χ384-44-400004i−4i2i2−2i22i2−2i200000022−22-22−2i2i0−2ζ22ζ2−2ζ62ζ60000000000000000000000
χ394-44-400004i−4i−2i22i2−2i22i2000000−22222-22i−2i0−2ζ22ζ2−2ζ62ζ60000000000000000000000
χ404-44-400004i−4i−2i22i2−2i22i2000000−2222-22−2i2i02ζ2−2ζ22ζ6−2ζ60000000000000000000000
χ414-44-40000−4i4i2i2−2i22i2−2i2000000−22222-2−2i2i02ζ6−2ζ62ζ2−2ζ20000000000000000000000
χ424-44-40000−4i4i2i2−2i22i2−2i2000000−2222-222i−2i0−2ζ62ζ6−2ζ22ζ20000000000000000000000
χ434-44-40000−4i4i−2i22i2−2i22i200000022−222-2−2i2i0−2ζ62ζ6−2ζ22ζ20000000000000000000000
χ444-44-40000−4i4i−2i22i2−2i22i200000022−22-222i−2i02ζ6−2ζ62ζ2−2ζ20000000000000000000000
χ454-4-4404i−4i00022−22−222200002i2−2i200000000000ζ−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−ζ700000000000000
χ464-4-4404i−4i00022−22−222200002i2−2i200000000000−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+ζ700000000000000
χ474-4-4404i−4i000−222222−220000−2i22i200000000000ζ+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−ζ700000000000000
χ484-4-4404i−4i000−222222−220000−2i22i200000000000−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+ζ700000000000000
χ494-4-440−4i4i00022−22−22220000−2i22i200000000000ζ−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+ζ700000000000000
χ504-4-440−4i4i00022−22−22220000−2i22i200000000000−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−ζ700000000000000
χ514-4-440−4i4i000−222222−2200002i2−2i200000000000ζ+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+ζ700000000000000
χ524-4-440−4i4i000−222222−2200002i2−2i200000000000−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−ζ700000000000000
χ5388-8-8800-8000000000000000000000000000000000000000000000

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