Finite Group Databasebeta

← Group #117113

Character table — Group #117113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444448888888888888888888888884444444444444444
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
χ9111-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-111-1-1
χ10111-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-1-111
χ11111-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111
χ12111-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1
χ13111-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1-1-111
χ14111-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-11111-1-1
χ15111-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-11111-1-1
χ16111-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i11-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222-2-22-22-2000000000000000022-2-222-2-20000000000000000
χ20222222222222-2-2-2-2-2-2-2-222-2-22-22-20000000000000000-2-222-2-2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-222-22-220000000022-2-222-2-2000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-222-22-2200000000-2-222-2-222000000000000000000000000
χ2322222222-2-2-2-22222-2-2-2-22-22-222-2-20000000000000000000000000000000000002i−2i2i−2i
χ2422222222-2-2-2-22222-2-2-2-22-22-222-2-2000000000000000000000000000000000000−2i2i−2i2i
χ2522222222-2-2-2-22222-2-2-2-2-22-22-2-222000000000000000000000000000000002-22-20000
χ2622222222-2-2-2-22222-2-2-2-2-22-22-2-22200000000000000000000000000000000-22-220000
χ2722222222-2-2-2-2-2-2-2-222222-2-222-2-220000000000000000000000002-22-2000000000000
χ2822222222-2-2-2-2-2-2-2-222222-2-222-2-22000000000000000000000000-22-22000000000000
χ2922222222-2-2-2-2-2-2-2-22222-222-2-222-200000000000000000000000000002-22-200000000
χ3022222222-2-2-2-2-2-2-2-22222-222-2-222-20000000000000000000000000000-22-2200000000
χ31222-2-2-2-222-2-2222-2-2-2-222-2-2-2-2222222-2-2-2-22200000000000000000000000000000000
χ32222-2-2-2-222-2-2222-2-2-2-222-2-2-2-22222-2-22222-2-200000000000000000000000000000000
χ33222-2-2-2-222-2-22-2-22222-2-222-2-2-22-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ34222-2-2-2-222-2-22-2-22222-2-222-2-2-22-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ35222-2-2-2-222-2-22-2-22222-2-2-2-2222-22-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ36222-2-2-2-222-2-22-2-22222-2-2-2-2222-22-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ37222-2-2-2-22-222-222-2-222-2-22-22-2-2-2220000000000000000000000000000000000002i−2i−2i2i
χ38222-2-2-2-22-222-222-2-222-2-22-22-2-2-222000000000000000000000000000000000000−2i2i2i−2i
χ39222-2-2-2-22-222-222-2-222-2-2-22-2222-2-2000000000000000000000000000000002-2-220000
χ40222-2-2-2-22-222-222-2-222-2-2-22-2222-2-200000000000000000000000000000000-222-20000
χ41222-2-2-2-22-222-2-2-222-2-2222-2-22-222-20000000000000000000000002i−2i−2i2i000000000000
χ42222-2-2-2-22-222-2-2-222-2-2222-2-22-222-2000000000000000000000000−2i2i2i−2i000000000000
χ43222-2-2-2-22-222-2-2-222-2-222-222-22-2-2200000000000000000000000000002i−2i−2i2i00000000
χ44222-2-2-2-22-222-2-2-222-2-222-222-22-2-220000000000000000000000000000−2i2i2i−2i00000000
χ452-2-222-2-2222-2-22-22-22-22-200000000002i−2i002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ462-2-222-2-2222-2-22-22-22-22-200000000002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ472-2-222-2-2222-2-22-22-22-22-20000000000−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ482-2-222-2-2222-2-22-22-22-22-20000000000−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ492-2-222-2-2222-2-2-22-22-22-22000000002i−2i002i−2i00i2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000000000
χ502-2-222-2-2222-2-2-22-22-22-22000000002i−2i002i−2i00−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000000000
χ512-2-222-2-2222-2-2-22-22-22-2200000000−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000000000
χ522-2-222-2-2222-2-2-22-22-22-2200000000−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000000000
χ532-2-2-2-22222-22-22-2-22-222-200000000002i−2i00−2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ542-2-2-2-22222-22-22-2-22-222-200000000002i−2i00−2i2i−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ552-2-2-2-22222-22-22-2-22-222-20000000000−2i2i002i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ562-2-2-2-22222-22-22-2-22-222-20000000000−2i2i002i−2i−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ572-2-2-2-22222-22-2-222-22-2-22000000002i−2i00−2i2i002−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ582-2-2-2-22222-22-2-222-22-2-22000000002i−2i00−2i2i00−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ592-2-2-2-22222-22-2-222-22-2-2200000000−2i2i002i−2i002−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ602-2-2-2-22222-22-2-222-22-2-2200000000−2i2i002i−2i00−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ614-4-444-4-44-4-4444-44-4-44-44000000000000000000000000000000000000000000000000
χ624-4-444-4-44-4-444-44-444-44-4000000000000000000000000000000000000000000000000
χ634-4-4-4-4444-44-444-4-444-4-44000000000000000000000000000000000000000000000000
χ644-4-4-4-4444-44-44-444-4-444-4000000000000000000000000000000000000000000000000
χ6588-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ6688-8-88-88-8000000000000000000000000000000000000000000000000000000000000
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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