Finite Group Databasebeta

← Group #119253

Character table — Group #119253

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444488888888888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-1-1-1-11-1-111-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ10111111111-1-1-1-1-1-11-1-111-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-1-111−i−iii
χ11111111111-1-1-1-1-1-11-1-111-1-111-1-11-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-1-111−i−iii
χ12111111111-1-1-1-1-1-11-1-111-1-111-1-11-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii11-1-1ii−i−i
χ13111111111-1-1-1-1-1-11-1-111-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii
χ14111111111-1-1-1-1-1-11-1-111-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-1-111ii−i−i
χ15111111111-1-1-1-1-1-11-1-111-1-111-1-11-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-1-111ii−i−i
χ16111111111-1-1-1-1-1-11-1-111-1-111-1-11-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i11-1-1−i−iii
χ17222222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222-2-2-2-2-2-22-2-2-2-222-2-222-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ20222222222-2-2-2-2-2-22-2-2-2-222-2-222-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ21222222-2-2-2222-2-2-2-22-222-2-22-22-2-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ22222222-2-2-2222-2-2-2-22-222-2-22-22-2-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ23222222-2-2-2222-2-2-2-22-2-2-222-22-222-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ24222222-2-2-2222-2-2-2-22-2-2-222-22-222-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ25222222-2-2-2-2-2-2222-2-2222222-2-22-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ26222222-2-2-2-2-2-2222-2-2222222-2-22-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ27222222-2-2-2-2-2-2222-2-22-2-2-2-2-222-222000000000000000022-2-2-2-2220000000000000000
χ28222222-2-2-2-2-2-2222-2-22-2-2-2-2-222-2220000000000000000-2-22222-2-20000000000000000
χ292222-2-222-222-2-222-2-2-22222-22-2-2-22000000000000000000000000000000002i−2i2i−2i0000
χ302222-2-222-222-2-222-2-2-22222-22-2-2-2200000000000000000000000000000000−2i2i−2i2i0000
χ312222-2-222-222-2-222-2-2-2-2-2-2-22-2222-20000000000000000000000000000000000002i−2i2i−2i
χ322222-2-222-222-2-222-2-2-2-2-2-2-22-2222-2000000000000000000000000000000000000−2i2i−2i2i
χ332222-2-222-2-2-222-2-2-22222-2-2-2222-2-2000000000000000000000000000000002i−2i−2i2i0000
χ342222-2-222-2-2-222-2-2-22222-2-2-2222-2-200000000000000000000000000000000−2i2i2i−2i0000
χ352222-2-222-2-2-222-2-2-222-2-2222-2-2-2220000000000000000000000000000000000002-2-22
χ362222-2-222-2-2-222-2-2-222-2-2222-2-2-222000000000000000000000000000000000000-222-2
χ372222-2-2-2-2222-22-2-22-2222-2-2-2-2-22220000000000000000000000002-22-2000000000000
χ382222-2-2-2-2222-22-2-22-2222-2-2-2-2-2222000000000000000000000000-22-22000000000000
χ392222-2-2-2-2222-22-2-22-22-2-222222-2-2-200000000000000000000000000002i−2i2i−2i00000000
χ402222-2-2-2-2222-22-2-22-22-2-222222-2-2-20000000000000000000000000000−2i2i−2i2i00000000
χ412222-2-2-2-22-2-22-22222-22222-2-22-22-20000000000000000000000002-2-22000000000000
χ422222-2-2-2-22-2-22-22222-22222-2-22-22-2000000000000000000000000-222-2000000000000
χ432222-2-2-2-22-2-22-22222-2-2-2-2-222-22-2200000000000000000000000000002-2-2200000000
χ442222-2-2-2-22-2-22-22222-2-2-2-2-222-22-220000000000000000000000000000-222-200000000
χ452-22-22-22-222-22-22-2-2-220000000000002i−2i002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ462-22-22-22-222-22-22-2-2-220000000000002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ472-22-22-22-222-22-22-2-2-22000000000000−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ482-22-22-22-222-22-22-2-2-22000000000000−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ492-22-22-22-22-22-22-22-22-20000000000002-200-22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ502-22-22-22-22-22-22-22-22-20000000000002-200-22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ512-22-22-22-22-22-22-22-22-2000000000000-22002-2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ522-22-22-22-22-22-22-22-22-2000000000000-22002-2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ532-22-22-2-22-22-222-222-2-200000000002i−2i002i−2i002−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ542-22-22-2-22-22-222-222-2-200000000002i−2i002i−2i00−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ552-22-22-2-22-22-222-222-2-20000000000−2i2i00−2i2i002−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ562-22-22-2-22-22-222-222-2-20000000000−2i2i00−2i2i00−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ572-22-22-2-22-2-22-2-22-222200000000002-200-22002−2−22−222−22−2−22−222−20000000000000000
χ582-22-22-2-22-2-22-2-22-222200000000002-200-2200−222−22−2−22−222−22−2−220000000000000000
χ592-22-22-2-22-2-22-2-22-22220000000000-22002-2002−2−22−222−2−222−22−2−220000000000000000
χ602-22-22-2-22-2-22-2-22-22220000000000-22002-200−222−22−2−222−2−22−222−20000000000000000
χ614-44-4-444-4-44-4-444-444-400000000000000000000000000000000000000000000000000
χ624-44-4-444-4-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ634-44-4-44-4444-4-4-4-44-44400000000000000000000000000000000000000000000000000
χ644-44-4-44-444-44444-4-4-4-400000000000000000000000000000000000000000000000000
χ6588-8-800000000000000008i−8i0000000000000000000000000000000000000000000000
χ6688-8-80000000000000000−8i8i0000000000000000000000000000000000000000000000
χ678-8-88000000000000008-8000000000000000000000000000000000000000000000000
χ688-8-8800000000000000-88000000000000000000000000000000000000000000000000

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