Finite Group Databasebeta

← Group #148307

Character table — Group #148307

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order122222222222444444448888888822448888161616161616161616161616161616164444444488888888
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
χ9111-1-1-11-111-1-1111-1-11-1-111-1-1-1-1111-11-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111-1-1-11-111-1-1111-1-11-1-111-1-1-1-1111-11-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111-1-1-11-111-1-1111-1-11-1-111-1-1-1-1111-11-111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111-1-1-11-111-1-1111-1-11-1-111-1-1-1-1111-11-111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111-1-1-11-111-1-1111-1-11-1-111-1-1-1-111-11-11-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ14111-1-1-11-111-1-1111-1-11-1-111-1-1-1-111-11-11-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ15111-1-1-11-111-1-1111-1-11-1-111-1-1-1-111-11-11-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111-1-1-11-111-1-1111-1-11-1-111-1-1-1-111-11-11-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-20000000022-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ20222222222222-2-2-2-2-2-2-2-20000000022-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ2322222222-2-2-2-22-2-2222-2-22-222-2-22-20000000000000000000000000000000000002i−2i2i−2i
χ2422222222-2-2-2-22-2-2222-2-22-222-2-22-2000000000000000000000000000000000000−2i2i−2i2i
χ2522222222-2-2-2-22-2-2222-2-2-22-2-222-22000000000000000000000000000000002i−2i2i−2i0000
χ2622222222-2-2-2-22-2-2222-2-2-22-2-222-2200000000000000000000000000000000−2i2i−2i2i0000
χ27222-2-2-22-222-2-2222-2-22-2-2-2-22222-2-22-22-2-2-22200000000000000000000000000000000
χ28222-2-2-22-222-2-2222-2-22-2-2-2-22222-2-2-22-2222-2-200000000000000000000000000000000
χ29222-2-2-22-222-2-2-2-2-222-222000000002-2-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ30222-2-2-22-222-2-2-2-2-222-222000000002-2-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ31222-2-2-22-222-2-2-2-2-222-22200000000-222-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ32222-2-2-22-222-2-2-2-2-222-22200000000-222-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ33222-2-2-22-2-2-2222-2-2-2-22222-2-2-2222-20000000000000000000000000000000000002-2-22
χ34222-2-2-22-2-2-2222-2-2-2-22222-2-2-2222-2000000000000000000000000000000000000-222-2
χ35222-2-2-22-2-2-2222-2-2-2-2222-2222-2-2-22000000000000000000000000000000002-2-220000
χ36222-2-2-22-2-2-2222-2-2-2-2222-2222-2-2-2200000000000000000000000000000000-222-20000
χ372-2-222-22-22-22-2-22-22-222-22-22-22-2-2200000000000000000000000000002i−2i2i−2i00000000
χ382-2-222-22-22-22-2-22-22-222-22-22-22-2-220000000000000000000000000000−2i2i−2i2i00000000
χ392-2-222-22-22-22-2-22-22-222-2-22-22-222-20000000000000000000000002i−2i2i−2i000000000000
χ402-2-222-22-22-22-2-22-22-222-2-22-22-222-2000000000000000000000000−2i2i−2i2i000000000000
χ412-2-222-22-2-22-2222-2-22-22-20000000000002i−2i2i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ422-2-222-22-2-22-2222-2-22-22-20000000000002i−2i2i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ432-2-222-22-2-22-2222-2-22-22-2000000000000−2i2i−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ442-2-222-22-2-22-2222-2-22-22-2000000000000−2i2i−2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ452-2-222-22-2-22-22-2-222-22-22222-2-22-2-2000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ462-2-222-22-2-22-22-2-222-22-22222-2-22-2-200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ472-2-222-22-2-22-22-2-222-22-22-2-2-222-22200000000000000002-2-222-2-220000000000000000
χ482-2-222-22-2-22-22-2-222-22-22-2-2-222-2220000000000000000-222-2-222-20000000000000000
χ492-2-2-2-22222-2-22-22-2-222-222-2-22-22-2200000000000000000000000000002-2-2200000000
χ502-2-2-2-22222-2-22-22-2-222-222-2-22-22-220000000000000000000000000000-222-200000000
χ512-2-2-2-22222-2-22-22-2-222-22-222-22-22-20000000000000000000000002-2-22000000000000
χ522-2-2-2-22222-2-22-22-2-222-22-222-22-22-2000000000000000000000000-222-2000000000000
χ532-2-2-2-2222-222-222-22-2-2-220000000000002i−2i−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ542-2-2-2-2222-222-222-22-2-2-220000000000002i−2i−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ552-2-2-2-2222-222-222-22-2-2-22000000000000−2i2i2i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ562-2-2-2-2222-222-222-22-2-2-22000000000000−2i2i2i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ572-2-2-2-2222-222-2-2-22-2222-222-222-2-2-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ582-2-2-2-2222-222-2-2-22-2222-222-222-2-2-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ592-2-2-2-2222-222-2-2-22-2222-2-2-22-2-222200000000000000002-2-22-222-20000000000000000
χ602-2-2-2-2222-222-2-2-22-2222-2-2-22-2-22220000000000000000-222-22-2-220000000000000000
χ6144444444-4-4-4-4-444-4-4-444000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-4-444-44444-4-4-4000000000000000000000000000000000000000000000000
χ634-4-444-44-44-44-44-44-44-4-44000000000000000000000000000000000000000000000000
χ644-4-4-4-44444-4-444-444-4-44-4000000000000000000000000000000000000000000000000
χ6588-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ6688-8-88-8-88000000000000000000000000000000000000000000000000000000000000
χ678-888-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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