Finite Group Databasebeta

← Group #153598

Character table — Group #153598

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1122222222244444444444444488888888888888888888883232323232323232
order12244881616161644888161632323232323232321616323232326464646464646464646464646464646422244488
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ911-11-1111111i−ii−i-1-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−ii−i
χ1011-11-1111111i−ii−i-1-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii
χ1111-11-1111111i−ii−i-1-1-11111-1-1-1-1i−iii−i−i-1-1-1-11111−i−i−i−iiiii1-1-11i−i−ii
χ1211-11-1111111i−ii−i-1-1-11111-1-1-1-1i−iii−i−i-1-1-1-11111−i−i−i−iiiii-111-1−iii−i
χ1311-11-1111111−ii−ii-1-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii
χ1411-11-1111111−ii−ii-1-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i
χ1511-11-1111111−ii−ii-1-1-11111-1-1-1-1−ii−i−iii-1-1-1-11111iiii−i−i−i−i1-1-11−iii−i
χ1611-11-1111111−ii−ii-1-1-11111-1-1-1-1−ii−i−iii-1-1-1-11111iiii−i−i−i−i-111-1i−i−ii
χ17222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ192222222-2-2-2-222222-2-200000000-2-2000022−2−222−2−222−2−222−2−200000000
χ202222222-2-2-2-222222-2-200000000-2-20000−2−222−2−222−2−222−2−22200000000
χ212222222-2-2-2-2-2-2-2-22-2-20000000022000022−2−222−2−2−2−222−2−22200000000
χ222222222-2-2-2-2-2-2-2-22-2-200000000220000−2−222−2−22222−2−222−2−200000000
χ2322222-2-2000022-2-2-20022−2−222−2−2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000
χ2422222-2-2000022-2-2-20022−2−222−2−2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000
χ2522222-2-2000022-2-2-200−2−222−2−22200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000
χ2622222-2-2000022-2-2-200−2−222−2−22200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000
χ2722222-2-20000-2-222-20022−2−222−2−200−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000
χ2822222-2-20000-2-222-20022−2−222−2−200−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000
χ2922222-2-20000-2-222-200−2−222−2−222002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000
χ3022222-2-20000-2-222-200−2−222−2−222002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000
χ3122-22-22222222i−2i2i−2i-2-2-2-2-2-2-222222i−2i−2i−2i2i2i000000000000000000000000
χ3222-22-2222222−2i2i−2i2i-2-2-2-2-2-2-22222−2i2i2i2i−2i−2i000000000000000000000000
χ3322-22-222-2-2-2-22i−2i2i−2i-22200000000−2i2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000
χ3422-22-222-2-2-2-22i−2i2i−2i-22200000000−2i2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000
χ3522-22-222-2-2-2-2−2i2i−2i2i-222000000002i−2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000
χ3622-22-222-2-2-2-2−2i2i−2i2i-222000000002i−2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000
χ3722-22-2-2-200002i−2i−2i2i20022−2−2−2−22200i2−i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ3822-22-2-2-200002i−2i−2i2i20022−2−2−2−22200i2−i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ3922-22-2-2-200002i−2i−2i2i200−2−22222−2−200−i2i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ4022-22-2-2-200002i−2i−2i2i200−2−22222−2−200−i2i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ4122-22-2-2-20000−2i2i2i−2i20022−2−2−2−22200−i2i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ4222-22-2-2-20000−2i2i2i−2i20022−2−2−2−22200−i2i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ4322-22-2-2-20000−2i2i2i−2i200−2−22222−2−200i2−i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ4422-22-2-2-20000−2i2i2i−2i200−2−22222−2−200i2−i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ45444-4-4002222−22−220000022−222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000
χ46444-4-4002222−22−220000022−22−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000
χ47444-4-400−22−22222200000−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000
χ48444-4-400−22−22222200000−2222−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000
χ4944-4-44002222−22−2200000−22222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000
χ5044-4-44002222−22−2200000−2222−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000
χ5144-4-4400−22−2222220000022−222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000
χ5244-4-4400−22−2222220000022−22−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000
χ538-800042−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ5000000000000000000000000000000000000000000000
χ548-800042−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ5000000000000000000000000000000000000000000000
χ558-8000−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ7000000000000000000000000000000000000000000000
χ568-8000−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ7000000000000000000000000000000000000000000000

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