Finite Group Databasebeta

← Group #146554

Character table — Group #146554

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222222222222222444444444444448888888888888888888888888888888888881616161616161616
order122222222244444444888822224444888888888888888888888888881616161616161616161616161616161644448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-1-1-1111-1-11-1-1111111-1-111-1-11-1-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ10111111-1-1-1-1111-1-11-1-1111111-1-111-1-11-1-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−iii−i−iii
χ11111111-1-1-1-1111-1-11-1-1111111-1-111-1-11-1-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ12111111-1-1-1-1111-1-11-1-1111111-1-111-1-11-1-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ii−i−iii−i−i
χ13111111-1-1-1-1111-1-11-1-11111-1-111-1-1111-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ14111111-1-1-1-1111-1-11-1-11111-1-111-1-1111-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i
χ15111111-1-1-1-1111-1-11-1-11111-1-111-1-1111-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ16111111-1-1-1-1111-1-11-1-11111-1-111-1-1111-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii
χ171-1-111-111-1-11-1-11-11-1111-1-11-11-11-11-1111-1-1-11-11-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−ii−ii−ii−ii−i
χ181-1-111-111-1-11-1-11-11-1111-1-11-11-11-11-1111-1-1-11-11-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−ii−ii−ii−ii
χ191-1-111-111-1-11-1-11-11-1111-1-11-11-11-11-1111-1-1-11-11-1-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−ii−ii−ii−ii
χ201-1-111-111-1-11-1-11-11-1111-1-11-11-11-11-1111-1-1-11-11-1-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iiii−ii−ii−ii−i
χ211-1-111-111-1-11-1-11-11-1111-1-1-11-11-11-11111-1-1-1-11-1111-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iiii−ii−i−ii−ii
χ221-1-111-111-1-11-1-11-11-1111-1-1-11-11-11-11111-1-1-1-11-1111-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−ii−iii−ii−i
χ231-1-111-111-1-11-1-11-11-1111-1-1-11-11-11-11111-1-1-1-11-11-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii−ii−iii−ii−i
χ241-1-111-111-1-11-1-11-11-1111-1-1-11-11-11-11111-1-1-1-11-11-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−ii−ii−i−ii−ii
χ251-1-111-1-1-1111-1-1-1111-111-1-11-1-111-1-111-1-111-11-1-11ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii-111-1-111-1
χ261-1-111-1-1-1111-1-1-1111-111-1-11-1-111-1-111-1-111-11-1-11ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-11
χ271-1-111-1-1-1111-1-1-1111-111-1-11-1-111-1-111-1-111-11-1-11−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii1-1-111-1-11
χ281-1-111-1-1-1111-1-1-1111-111-1-11-1-111-1-111-1-111-11-1-11−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i-111-1-111-1
χ291-1-111-1-1-1111-1-1-1111-111-1-1-111-1-111-11-1-111-1-111-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i-111-11-1-11
χ301-1-111-1-1-1111-1-1-1111-111-1-1-111-1-111-11-1-111-1-111-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii1-1-11-111-1
χ311-1-111-1-1-1111-1-1-1111-111-1-1-111-1-111-11-1-111-1-111-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i1-1-11-111-1
χ321-1-111-1-1-1111-1-1-1111-111-1-1-111-1-111-11-1-111-1-111-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii-111-11-1-11
χ33222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ34222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ35222222-2-2-2-2222-2-22-2-2-2-2-2-222-2-222-2-2-22222-2-2-2220000000000000000000000000000000000000000
χ36222222-2-2-2-2222-2-22-2-2-2-2-2-2-2-222-2-222-22222-222-2-20000000000000000000000000000000000000000
χ372222-2-22-22-222-2-22-2-22000022-2-2-2-22200000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ382222-2-22-22-222-2-22-2-22000022-2-2-2-22200000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ392222-2-22-22-222-2-22-2-220000-2-22222-2-200000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ402222-2-22-22-222-2-22-2-220000-2-22222-2-200000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ412222-2-22-22-2-2-222-222-2222200000000-22-22-2-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ422222-2-22-22-2-2-222-222-2222200000000-22-22-2-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ432222-2-22-22-2-2-222-222-2-2-2-2-2000000002-22-2220000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ442222-2-22-22-2-2-222-222-2-2-2-2-2000000002-22-222000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ452222-2-2-22-2222-22-2-22-200002222-2-2-2-200000000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ462222-2-2-22-2222-22-2-22-200002222-2-2-2-200000000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ472222-2-2-22-2222-22-2-22-20000-2-2-2-2222200000000000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ482222-2-2-22-2222-22-2-22-20000-2-2-2-2222200000000000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ492222-2-2-22-22-2-22-222-22222200000000-2-22-22-200002-22-2-22-2200000000000000000000000000000000
χ502222-2-2-22-22-2-22-222-22222200000000-2-22-22-20000-22-222-22-200000000000000000000000000000000
χ512222-2-2-22-22-2-22-222-22-2-2-2-20000000022-22-220000000000002-22-2-22-22000000000000000000000000
χ522222-2-2-22-22-2-22-222-22-2-2-2-20000000022-22-22000000000000-22-222-22-2000000000000000000000000
χ532-2-222-222-2-22-2-22-22-22-2-2222-22-22-22-2-2-2-2222-22-220000000000000000000000000000000000000000
χ542-2-222-222-2-22-2-22-22-22-2-222-22-22-22-22-2-2-22222-22-20000000000000000000000000000000000000000
χ552-2-222-2-2-2222-2-2-2222-2-2-2222-2-222-2-22-222-2-22-222-20000000000000000000000000000000000000000
χ562-2-222-2-2-2222-2-2-2222-2-2-222-222-2-222-2-222-2-222-2-220000000000000000000000000000000000000000
χ572-2-22-222-2-222-22-2-2-22200002-2-22-222-2000000000000000000000000002−2−222−2−222−2−222−2−2200000000
χ582-2-22-222-2-222-22-2-2-22200002-2-22-222-200000000000000000000000000−222−2−222−2−222−2−222−200000000
χ592-2-22-222-2-222-22-2-2-2220000-222-22-2-22000000000000000000000000002−2−222−2−22−222−2−222−200000000
χ602-2-22-222-2-222-22-2-2-2220000-222-22-2-2200000000000000000000000000−222−2−222−22−2−222−2−2200000000
χ612-2-22-222-2-22-22-2222-2-222-2-200000000-22-2-22200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ622-2-22-222-2-22-22-2222-2-222-2-200000000-22-2-2220000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ632-2-22-222-2-22-22-2222-2-2-2-222000000002-222-2-20000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ642-2-22-222-2-22-22-2222-2-2-2-222000000002-222-2-2000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ652-2-22-22-222-22-2222-2-2-200002-22-2-22-22000000000000000000000000002−2−22−222−22−2−22−222−200000000
χ662-2-22-22-222-22-2222-2-2-200002-22-2-22-2200000000000000000000000000−222−22−2−22−222−22−2−2200000000
χ672-2-22-22-222-22-2222-2-2-20000-22-222-22-2000000000000000000000000002−2−22−222−2−222−22−2−2200000000
χ682-2-22-22-222-22-2222-2-2-20000-22-222-22-200000000000000000000000000−222−22−2−222−2−22−222−200000000
χ692-2-22-22-222-2-22-2-2-222222-2-200000000-2-222-2200002-2-22-222-200000000000000000000000000000000
χ702-2-22-22-222-2-22-2-2-222222-2-200000000-2-222-220000-222-22-2-2200000000000000000000000000000000
χ712-2-22-22-222-2-22-2-2-2222-2-2220000000022-2-22-20000000000002-2-22-222-2000000000000000000000000
χ722-2-22-22-222-2-22-2-2-2222-2-2220000000022-2-22-2000000000000-222-22-2-22000000000000000000000000
χ734444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000000000
χ74444444-4-4-4-4-4-4-444-44400000000000000000000000000000000000000000000000000000000000000
χ754-4-444-444-4-4-444-44-44-400000000000000000000000000000000000000000000000000000000000000
χ764-4-444-4-4-444-4444-4-4-4400000000000000000000000000000000000000000000000000000000000000
χ7788-8-8000000000000004i2−4i24i2−4i20000000000000000000000000000000000000000000000000000000000
χ7888-8-800000000000000−4i24i2−4i24i20000000000000000000000000000000000000000000000000000000000
χ798-88-8000000000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000000000000000
χ808-88-800000000000000−4i24i24i2−4i20000000000000000000000000000000000000000000000000000000000

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