Finite Group Databasebeta

← Group #152828

Character table — Group #152828

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222444488888888881616161616161616441616161632323232323232323232323232323232444488882244
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-111-1-11111-1ii−i−i-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111-1-111-1-11111-1ii−i−i-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-11−ii
χ111111-1-111-1-11111-1ii−i−i-111-1-111-1-1i−iii−i−i-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121111-1-111-1-11111-1ii−i−i-111-1-111-1-1i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131111-1-111-1-11111-1−i−iii-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141111-1-111-1-11111-1−i−iii-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151111-1-111-1-11111-1−i−iii-111-1-111-1-1−ii−i−iii-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111-1-111-1-11111-1−i−iii-111-1-111-1-1−ii−i−iii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i1-1−ii
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ192222222222-2-2-2-2-22222-200000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ202222222222-2-2-2-2-22222-200000000-2-20000−2−222−2−222−2−222−2−222000000000000
χ212222222222-2-2-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−222000000000000
χ222222222222-2-2-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−2000000000000
χ232222-2-222-2-22222-22i2i−2i−2i-2-2-222-2-2222i−2i−2i−2i2i2i0000000000000000000000000000
χ242222-2-222-2-22222-2−2i−2i2i2i-2-2-222-2-222−2i2i2i2i−2i−2i0000000000000000000000000000
χ252222-2-222-2-2-2-2-2-222i2i−2i−2i200000000−2i2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ262222-2-222-2-2-2-2-2-222i2i−2i−2i200000000−2i2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ272222-2-222-2-2-2-2-2-22−2i−2i2i2i2000000002i−2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ282222-2-222-2-2-2-2-2-22−2i−2i2i2i2000000002i−2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ2922-2-22-22-2-22000002i−2i2i−2i02−22−22−22−200i2−i2i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ3022-2-22-22-2-22000002i−2i2i−2i02−22−22−22−200i2−i2i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ3122-2-22-22-2-22000002i−2i2i−2i0−22−22−22−2200−i2i2−i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3222-2-22-22-2-22000002i−2i2i−2i0−22−22−22−2200−i2i2−i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3322-2-22-22-2-2200000−2i2i−2i2i02−22−22−22−200−i2i2−i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ3422-2-22-22-2-2200000−2i2i−2i2i02−22−22−22−200−i2i2−i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ3522-2-22-22-2-2200000−2i2i−2i2i0−22−22−22−2200i2−i2i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3622-2-22-22-2-2200000−2i2i−2i2i0−22−22−22−2200i2−i2i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3722-2-22-2-222-2-2-222-20000222-2-2-2-22200000000000000000000002i−2i2i−2i00000000
χ3822-2-22-2-222-2-2-222-20000222-2-2-2-2220000000000000000000000−2i2i−2i2i00000000
χ3922-2-22-2-222-2-2-222-200002-2-22222-2-2000000000000000000000000002i−2i2i−2i0000
χ4022-2-22-2-222-2-2-222-200002-2-22222-2-200000000000000000000000000−2i2i−2i2i0000
χ4122-2-2-222-22-2000002-2-2202−2−222−2−22002−2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4222-2-2-222-22-2000002-2-2202−2−222−2−22002−2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4322-2-2-222-22-2000002-2-220−222−2−222−200−222−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ4422-2-2-222-22-2000002-2-220−222−2−222−200−222−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ4522-2-2-222-22-200000-222-202−2−222−2−2200−222−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4622-2-2-222-22-200000-222-202−2−222−2−2200−222−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4722-2-2-222-22-200000-222-20−222−2−222−2002−2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ4822-2-2-222-22-200000-222-20−222−2−222−2002−2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ4922-2-2-22-22-22-2-22220000-22222-2-2-2-200000000000000000000002i−2i−2i2i00000000
χ5022-2-2-22-22-22-2-22220000-22222-2-2-2-20000000000000000000000−2i2i2i−2i00000000
χ5122-2-2-22-22-22-2-22220000-2-2-2-2-22222000000000000000000000000002-2-220000
χ5222-2-2-22-22-22-2-22220000-2-2-2-2-2222200000000000000000000000000-222-20000
χ53444444-4-4-4-4000000000022−22−2222−222222−220000000000000000000000000000000000
χ54444444-4-4-4-40000000000−222222−2222−22−22220000000000000000000000000000000000
χ554444-4-4-4-444000000000022−2222−22−2222−22220000000000000000000000000000000000
χ564444-4-4-4-4440000000000−2222−222222−2222−220000000000000000000000000000000000
χ5744-4-44-4-444-444-4-440000-4000000000000000000000000000000000000000000
χ5844-4-4-44-44-4444-4-4-400004000000000000000000000000000000000000000000
χ598-88-800000042−4242−42000000000000000000000000000000000000000000000000
χ608-88-8000000−4242−4242000000000000000000000000000000000000000000000000
χ618-8-8800000042−42−4242000000000000000000000000000000000000000000000000
χ628-8-88000000−424242−42000000000000000000000000000000000000000000000000

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