Finite Group Databasebeta

← Group #117574

Character table — Group #117574

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222224444444444444444448888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ9111111-1-1-1-1-1-1111-1-1-1-1-11-1111-1-11iiii−i−i−i−iii−i−iii−i−i1111-1-1-1-111-1-1ii−i−i11-1-1ii−i−i
χ10111111-1-1-1-1-1-1111-1-1-1-1-11-1111-1-11iiii−i−i−i−iii−i−iii−i−i1111-1-1-1-1-1-111−i−iii-1-111−i−iii
χ11111111-1-1-1-1-1-1111-1-1-1-1-11-1111-1-11iiii−i−i−i−i−i−iii−i−iii-1-1-1-1111111-1-1−i−iii-1-111ii−i−i
χ12111111-1-1-1-1-1-1111-1-1-1-1-11-1111-1-11iiii−i−i−i−i−i−iii−i−iii-1-1-1-11111-1-111ii−i−i11-1-1−i−iii
χ13111111-1-1-1-1-1-1111-1-1-1-1-11-1111-1-11−i−i−i−iiiiiii−i−iii−i−i-1-1-1-1111111-1-1ii−i−i-1-111−i−iii
χ14111111-1-1-1-1-1-1111-1-1-1-1-11-1111-1-11−i−i−i−iiiiiii−i−iii−i−i-1-1-1-11111-1-111−i−iii11-1-1ii−i−i
χ15111111-1-1-1-1-1-1111-1-1-1-1-11-1111-1-11−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-111-1-1−i−iii11-1-1−i−iii
χ16111111-1-1-1-1-1-1111-1-1-1-1-11-1111-1-11−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-1-1-111ii−i−i-1-111ii−i−i
χ17222222222222-2-2-2-2-2-2-2-2-2-22-2-22-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2-2-22-2-22-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ192222222222-2-222222-2-2222-2-2-2-2-2-2000000002222-2-2-2-2000000000000000000000000
χ202222222222-2-222222-2-2222-2-2-2-2-2-200000000-2-2-2-22222000000000000000000000000
χ212222222222-2-2-2-2-2-2-222-2-2-2-222-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ222222222222-2-2-2-2-2-2-222-2-2-2-222-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ23222222-2-2-2-222222-2-222-22-2-2-2-222-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ24222222-2-2-2-222222-2-222-22-2-2-2-222-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ25222222-2-2-2-222-2-2-222-2-22-22-2222-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ26222222-2-2-2-222-2-2-222-2-22-22-2222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ27222222-2-2-2-2-2-2-2-2-222222-222-2-2-22222-2-2-2-22200000000000000000000000000000000
χ28222222-2-2-2-2-2-2-2-2-222222-222-2-2-222-2-22222-2-200000000000000000000000000000000
χ292222-2-222-2-22222-22222-2-2-2-22-2-2-2200000000000000000000000000002i−2i2i−2i00000000
χ302222-2-222-2-22222-22222-2-2-2-22-2-2-220000000000000000000000000000−2i2i−2i2i00000000
χ312222-2-222-2-222-2-22-2-2-2-2222-2-22-222000000000000000000000000000000002-22-20000
χ322222-2-222-2-222-2-22-2-2-2-2222-2-22-22200000000000000000000000000000000-22-220000
χ332222-2-222-2-2-2-222-222-2-2-2-2-22-2222-20000000000000000000000002-22-2000000000000
χ342222-2-222-2-2-2-222-222-2-2-2-2-22-2222-2000000000000000000000000-22-22000000000000
χ352222-2-222-2-2-2-2-2-22-2-22222222-22-2-20000000000000000000000000000000000002-22-2
χ362222-2-222-2-2-2-2-2-22-2-22222222-22-2-2000000000000000000000000000000000000-22-22
χ372222-2-2-2-2222222-2-2-2222-222-22-2-2-20000000000000000000000002-2-22000000000000
χ382222-2-2-2-2222222-2-2-2222-222-22-2-2-2000000000000000000000000-222-2000000000000
χ392222-2-2-2-22222-2-2222-2-2-22-222-2-22-20000000000000000000000000000000000002i−2i−2i2i
χ402222-2-2-2-22222-2-2222-2-2-22-222-2-22-2000000000000000000000000000000000000−2i2i2i−2i
χ412222-2-2-2-222-2-222-2-2-2-2-22-22-22-222200000000000000000000000000002-2-2200000000
χ422222-2-2-2-222-2-222-2-2-2-2-22-22-22-22220000000000000000000000000000-222-200000000
χ432222-2-2-2-222-2-2-2-222222-22-2-2-222-22000000000000000000000000000000002-2-220000
χ442222-2-2-2-222-2-2-2-222222-22-2-2-222-2200000000000000000000000000000000-222-20000
χ452-2-222-22-22-2002-222-200-2-220000002−22−22−22−22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i20000000000000000
χ462-2-222-22-22-2002-222-200-2-220000002−22−22−22−2−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i20000000000000000
χ472-2-222-22-22-2002-222-200-2-22000000−22−22−22−222i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i20000000000000000
χ482-2-222-22-22-2002-222-200-2-22000000−22−22−22−22−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i20000000000000000
χ492-2-222-22-22-200-22-2-220022-2000000i2−i2−i2i2i2−i2−i2i200002i−2i2i−2i2−2−222−2−220000000000000000
χ502-2-222-22-22-200-22-2-220022-2000000i2−i2−i2i2i2−i2−i2i20000−2i2i−2i2i−222−2−222−20000000000000000
χ512-2-222-22-22-200-22-2-220022-2000000−i2i2i2−i2−i2i2i2−i200002i−2i2i−2i−222−2−222−20000000000000000
χ522-2-222-22-22-200-22-2-220022-2000000−i2i2i2−i2−i2i2i2−i20000−2i2i−2i2i2−2−222−2−220000000000000000
χ532-2-222-2-22-22002-22-22002-2-2000000i2−i2i2−i2−i2i2−i2i22-2-220000−i2i2−i2i2i2−i2i2−i20000000000000000
χ542-2-222-2-22-22002-22-22002-2-2000000i2−i2i2−i2−i2i2−i2i2-222-20000i2−i2i2−i2−i2i2−i2i20000000000000000
χ552-2-222-2-22-22002-22-22002-2-2000000−i2i2−i2i2i2−i2i2−i22-2-220000i2−i2i2−i2−i2i2−i2i20000000000000000
χ562-2-222-2-22-22002-22-22002-2-2000000−i2i2−i2i2i2−i2i2−i2-222-20000−i2i2−i2i2i2−i2i2−i20000000000000000
χ572-2-222-2-22-2200-22-22-200-2220000002−2−22−222−200002-2-222−2−22−222−20000000000000000
χ582-2-222-2-22-2200-22-22-200-2220000002−2−22−222−20000-222-2−222−22−2−220000000000000000
χ592-2-222-2-22-2200-22-22-200-222000000−222−22−2−2200002-2-22−222−22−2−220000000000000000
χ602-2-222-2-22-2200-22-22-200-222000000−222−22−2−220000-222-22−2−22−222−20000000000000000
χ614-4-44-444-4-44004-4-44-40044-40000000000000000000000000000000000000000000000
χ624-4-44-444-4-4400-444-4400-4-440000000000000000000000000000000000000000000000
χ634-4-44-44-444-4004-4-4-4400-4440000000000000000000000000000000000000000000000
χ644-4-44-44-444-400-4444-4004-4-40000000000000000000000000000000000000000000000
χ6588-8-800000000000008-80000000000000000000000000000000000000000000000000
χ6688-8-80000000000000-880000000000000000000000000000000000000000000000000
χ678-88-80000008-800000000000000000000000000000000000000000000000000000000
χ688-88-8000000-8800000000000000000000000000000000000000000000000000000000

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