Finite Group Databasebeta

← Group #137513

Character table — Group #137513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488884448888888844448888888161616161616161622448888881616161644
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111-1-1-1-111-1-1-1-11-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111-1-1-111-1-1-1-1-1-1-111-111ii−i−i11ii−i−i-1i−iii−i−i1111-1-1-1-11-11-1i−iii−i−iii−i−i1-1
χ101111-1-1-111-1-1-1-1-1-1-111-111ii−i−i11ii−i−i-1i−iii−i−i-1-1-1-111111-11-1i−i−i−iii−i−iii-11
χ111111-1-1-111-1-1-1-1-1-1-111-111ii−i−i11ii−i−i-1i−i−i−iii1111-1-1-1-1-11-11−ii−i−iiiii−i−i-11
χ121111-1-1-111-1-1-1-1-1-1-111-111ii−i−i11ii−i−i-1i−i−i−iii-1-1-1-11111-11-11−iiii−i−i−i−iii1-1
χ131111-1-1-111-1-1-1-1-1-1-111-111−i−iii11−i−iii-1−iiii−i−i1111-1-1-1-1-11-11i−iii−i−i−i−iii-11
χ141111-1-1-111-1-1-1-1-1-1-111-111−i−iii11−i−iii-1−iiii−i−i-1-1-1-11111-11-11i−i−i−iiiii−i−i1-1
χ151111-1-1-111-1-1-1-1-1-1-111-111−i−iii11−i−iii-1−ii−i−iii1111-1-1-1-11-11-1−ii−i−iii−i−iii1-1
χ161111-1-1-111-1-1-1-1-1-1-111-111−i−iii11−i−iii-1−ii−i−iii-1-1-1-111111-11-1−iiii−i−iii−i−i-11
χ17222222222222-2-2-2-2222-2-22222-2-2-2-2-2-2-2220000000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-22222-2-2-20000000000000000000000000000
χ19222222-2222-222222-2-2-2220000-2-20000-2002222000000000000-2-20000000000
χ20222222-2222-222222-2-2-2220000-2-20000-200-2-2-2-2000000000000220000000000
χ21222222-2222-22-2-2-2-2-2-2-2-2-200002200002000000000000002-2-22000000000000
χ22222222-2222-22-2-2-2-2-2-2-2-2-20000220000200000000000000-222-2000000000000
χ23222222-2-2-2-2-2-20000-222002i2i−2i−2i0000000−2i2i000022−2−222−2−20000000000i2−i2i2−i200
χ24222222-2-2-2-2-2-20000-222002i2i−2i−2i0000000−2i2i0000−2−222−2−2220000000000−i2i2−i2i200
χ25222222-2-2-2-2-2-20000-22200−2i−2i2i2i00000002i−2i000022−2−222−2−20000000000−i2i2−i2i200
χ26222222-2-2-2-2-2-20000-22200−2i−2i2i2i00000002i−2i0000−2−222−2−2220000000000i2−i2i2−i200
χ272222-2-2222-22-22222-2-22-2-20000220000-20000000000000022-2-2000000000000
χ282222-2-2222-22-22222-2-22-2-20000220000-200000000000000-2-222000000000000
χ292222-2-2222-22-2-2-2-2-2-2-22220000-2-200002002i2i−2i−2i000000000000−2i2i0000000000
χ302222-2-2222-22-2-2-2-2-2-2-22220000-2-20000200−2i−2i2i2i0000000000002i−2i0000000000
χ312222-2-22-2-22220000-22-20022220000000-2-2000022−2−2−2−22200000000002−2−2200
χ322222-2-22-2-22220000-22-20022220000000-2-20000−2−22222−2−20000000000−222−200
χ332222-2-22-2-22220000-22-200-2-2-2-2000000022000022−2−2−2−2220000000000−222−200
χ342222-2-22-2-22220000-22-200-2-2-2-20000000220000−2−22222−2−200000000002−2−2200
χ352222-2-2-222-2-2-2222222-2-2-22i2i−2i−2i-2-2−2i−2i2i2i22i−2i0000000000000000000000000000
χ362222-2-2-222-2-2-2222222-2-2-2−2i−2i2i2i-2-22i2i−2i−2i2−2i2i0000000000000000000000000000
χ372-22-22-202-220-2-2-2220002-200000000000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000002−22−2000000
χ382-22-22-202-220-2-2-2220002-200000000000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000−22−22000000
χ392-22-22-202-220-2-2-2220002-20000000000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000−22−22000000
χ402-22-22-202-220-2-2-2220002-20000000000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000002−22−2000000
χ412-22-2-2202-2-20222-2-20002-200000000000002-2-22i2−i2i2−i2−i2i2−i2i2000000−i2i2i2−i2000000
χ422-22-2-2202-2-20222-2-20002-200000000000002-2-22−i2i2−i2i2i2−i2i2−i2000000i2−i2−i2i2000000
χ432-22-2-2202-2-20222-2-20002-20000000000000-222-2i2−i2i2−i2−i2i2−i2i2000000i2−i2−i2i2000000
χ442-22-2-2202-2-20222-2-20002-20000000000000-222-2−i2i2−i2i2i2−i2i2−i2000000−i2i2i2−i2000000
χ454444444-4-4-44-400004-4-40000000000000000000000000000000000000000000
χ464444-4-4-4-4-44-4400004-440000000000000000000000000000000000000000000
χ4744-4-4004000-4022−2222−220000022−2222−2222−222-22-20000000000000000000000000000000
χ4844-4-4004000-4022−2222−2200000−2222−222222−22-22-220000000000000000000000000000000
χ4944-4-4004000-40−2222−22220000022−2222−22−2222-22-220000000000000000000000000000000
χ5044-4-4004000-40−2222−222200000−2222−2222−22222-22-20000000000000000000000000000000
χ5144-4-400-40004022−2222−22000002i2−2i2−2i22i2−2222−2i2i2i−2i0000000000000000000000000000000
χ5244-4-400-40004022−2222−2200000−2i22i22i2−2i2−22222i−2i−2i2i0000000000000000000000000000000
χ5344-4-400-400040−2222−2222000002i2−2i2−2i22i222−222i−2i−2i2i0000000000000000000000000000000
χ5444-4-400-400040−2222−222200000−2i22i22i2−2i222−22−2i2i2i−2i0000000000000000000000000000000
χ554-44-44-404-440-444-4-4000-4400000000000000000000000000000000000000000
χ564-44-44-40-44-404000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ574-44-44-40-44-40400000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ584-44-4-4404-4-404-4-444000-4400000000000000000000000000000000000000000
χ594-44-4-440-4440-4000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ604-44-4-440-4440-400000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ618-8-880000000042−42−42420000000000000000000000000000000000000000000000
χ628-8-8800000000−424242−420000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).