Finite Group Databasebeta

← Group #114178

Character table — Group #114178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222224444444444444444448888888888888888888888882222444444448888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ9111111-1-1-1-1-1-111-1-1-1-1-111-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1111-1-1-1ii−i−iii−i−i
χ10111111-1-1-1-1-1-111-1-1-1-1-111-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-1-1111−i−iii−i−iii
χ11111111-1-1-1-1-1-111-1-1-1-1-111-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1111-1-1-1−i−iii−i−iii
χ12111111-1-1-1-1-1-111-1-1-1-1-111-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-1-1111ii−i−iii−i−i
χ13111111-1-1-1-1-1-111-1-1-1-1-111-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1-11-111ii−i−i−i−iii
χ14111111-1-1-1-1-1-111-1-1-1-1-111-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1111-11-1-1−i−iiiii−i−i
χ15111111-1-1-1-1-1-111-1-1-1-1-111-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-11-111−i−iiiii−i−i
χ16111111-1-1-1-1-1-111-1-1-1-1-111-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1111-11-1-1ii−i−i−i−iii
χ17222222222222-2-2-2-2-2-2-2-2-2-222-2-22-20000000000000000000000000000000000002i−2i2i−2i
χ18222222222222-2-2-2-2-2-2-2-2-2-222-2-22-2000000000000000000000000000000000000−2i2i−2i2i
χ192222222222-2-222222-2-2222-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ202222222222-2-222222-2-2222-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ212222222222-2-2-2-2-2-2-222-2-2-2-2-222-22000000000000000000000000000000002-22-20000
χ222222222222-2-2-2-2-2-2-222-2-2-2-2-222-2200000000000000000000000000000000-22-220000
χ23222222-2-2-2-22222-2-2-22222-2-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ24222222-2-2-2-22222-2-2-22222-2-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ25222222-2-2-2-222-2-2222-2-2-2-22-2-2222-2000000000000000000000000000000002i−2i−2i2i0000
χ26222222-2-2-2-222-2-2222-2-2-2-22-2-2222-200000000000000000000000000000000−2i2i2i−2i0000
χ27222222-2-2-2-2-2-2-2-222222-2-2222-2-2-220000000000000000000000000000000000002-2-22
χ28222222-2-2-2-2-2-2-2-222222-2-2222-2-2-22000000000000000000000000000000000000-222-2
χ292222-2-222-2-2222222-2-2-2-2-2-22-22-2-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ302222-2-222-2-2222222-2-2-2-2-2-22-22-2-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ312222-2-222-2-222-2-2-2-22222222-2-22-2-2000000000000000000000000002-2002-200000000
χ322222-2-222-2-222-2-2-2-22222222-2-22-2-200000000000000000000000000-2200-2200000000
χ332222-2-222-2-2-2-22222-222-2-2-2-22-222-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ342222-2-222-2-2-2-22222-222-2-2-2-22-222-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ352222-2-222-2-2-2-2-2-2-2-22-2-2222-222-2220000000000000000000000002200-2-20000000000
χ362222-2-222-2-2-2-2-2-2-2-22-2-2222-222-222000000000000000000000000-2-200220000000000
χ372222-2-2-2-2222222-2-22-2-2-2-22-22-22-22000000000000000022-2-2-2-2220000000000000000
χ382222-2-2-2-2222222-2-22-2-2-2-22-22-22-220000000000000000-2-22222-2-20000000000000000
χ392222-2-2-2-22222-2-222-22222-2-222-2-2-20000000000000000000000002-200-220000000000
χ402222-2-2-2-22222-2-222-22222-2-222-2-2-2000000000000000000000000-22002-20000000000
χ412222-2-2-2-222-2-222-2-2222-2-222-22-22-20000000022-2-2-2-222000000000000000000000000
χ422222-2-2-2-222-2-222-2-2222-2-222-22-22-200000000-2-22222-2-2000000000000000000000000
χ432222-2-2-2-222-2-2-2-222-2-2-222-22-2-2222000000000000000000000000002-200-2200000000
χ442222-2-2-2-222-2-2-2-222-2-2-222-22-2-222200000000000000000000000000-22002-200000000
χ452-2-222-22-22-2002-22-22002-2-2000000002-2002-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ462-2-222-22-22-2002-22-22002-2-2000000002-2002-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ472-2-222-22-22-2002-22-22002-2-200000000-2200-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ482-2-222-22-22-2002-22-22002-2-200000000-2200-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ492-2-222-2-22-22002-2-22-2002-22000000002-200-222−22−2−22−222−22−2−22−220000000000000000
χ502-2-222-2-22-22002-2-22-2002-22000000002-200-22−22−222−22−2−22−222−22−20000000000000000
χ512-2-222-2-22-22002-2-22-2002-2200000000-22002-22−22−2−22−22−22−222−22−20000000000000000
χ522-2-222-2-22-22002-2-22-2002-2200000000-22002-2−22−222−22−22−22−2−22−220000000000000000
χ532-2-22-222-2-22002-22-2-200-2220000002-2002-2002−2−222−2−222−2−222−2−220000000000000000
χ542-2-22-222-2-22002-22-2-200-2220000002-2002-200−222−2−222−2−222−2−222−20000000000000000
χ552-2-22-222-2-22002-22-2-200-222000000-2200-22002−2−222−2−22−222−2−222−20000000000000000
χ562-2-22-222-2-22002-22-2-200-222000000-2200-2200−222−2−222−22−2−222−2−220000000000000000
χ572-2-22-22-222-2002-2-22200-22-20000002-200-2200i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ582-2-22-22-222-2002-2-22200-22-20000002-200-2200−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ592-2-22-22-222-2002-2-22200-22-2000000-22002-200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ602-2-22-22-222-2002-2-22200-22-2000000-22002-200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ614-4-444-44-44-400-44-44-400-4440000000000000000000000000000000000000000000000
χ624-4-444-4-44-4400-444-4400-44-40000000000000000000000000000000000000000000000
χ634-4-44-444-4-4400-44-444004-4-40000000000000000000000000000000000000000000000
χ644-4-44-44-444-400-444-4-4004-440000000000000000000000000000000000000000000000
χ6588-8-800000000000008i−8i0000000000000000000000000000000000000000000000000
χ6688-8-80000000000000−8i8i0000000000000000000000000000000000000000000000000
χ678-88-80000008i−8i00000000000000000000000000000000000000000000000000000000
χ688-88-8000000−8i8i00000000000000000000000000000000000000000000000000000000

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