Finite Group Databasebeta

← Group #494342

Character table — Group #494342

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222222222222222444444444444448888888888888888888888888888888888881616161616161616
order122222222244444444888844444444888888222244444444444488881616161616161616161616161616161644448888
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
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-1-1-1111-1-1-11-11111iiii−i−i−i−i1-1-1-11-111-1-111-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ10111111-1-1-1-1111-1-1-11-11111iiii−i−i−i−i1-1-1-11-111-1-111-1-1iiii−i−i−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ11111111-1-1-1-1111-1-1-11-11111iiii−i−i−i−i1-1-1-11-1-1-111-1-111−i−i−i−iiiiiii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ12111111-1-1-1-1111-1-1-11-11111iiii−i−i−i−i1-1-1-11-1-1-111-1-111−i−i−i−iiiiiii−i−i-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ13111111-1-1-1-1111-1-1-11-11111−i−i−i−iiiii1-1-1-11-111-1-111-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ14111111-1-1-1-1111-1-1-11-11111−i−i−i−iiiii1-1-1-11-111-1-111-1-1−i−i−i−iiiii−i−iii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ15111111-1-1-1-1111-1-1-11-11111−i−i−i−iiiii1-1-1-11-1-1-111-1-111iiii−i−i−i−i−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ16111111-1-1-1-1111-1-1-11-11111−i−i−i−iiiii1-1-1-11-1-1-111-1-111iiii−i−i−i−i−i−iii-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ171111-1-111-1-11-1-111-11-1-1-1-1-1ii−i−iii−i−i111-11-111-1-1-1-111ii−i−iii−i−ii−ii−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ181111-1-111-1-11-1-111-11-1-1-1-1-1ii−i−iii−i−i111-11-111-1-1-1-111ii−i−iii−i−ii−ii−i-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ191111-1-111-1-11-1-111-11-1-1-1-1-1ii−i−iii−i−i111-11-1-1-11111-1-1−i−iii−i−iiii−ii−i11-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ201111-1-111-1-11-1-111-11-1-1-1-1-1ii−i−iii−i−i111-11-1-1-11111-1-1−i−iii−i−iiii−ii−i-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ211111-1-111-1-11-1-111-11-1-1-1-1-1−i−iii−i−iii111-11-111-1-1-1-111−i−iii−i−iii−ii−ii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ221111-1-111-1-11-1-111-11-1-1-1-1-1−i−iii−i−iii111-11-111-1-1-1-111−i−iii−i−iii−ii−ii-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ231111-1-111-1-11-1-111-11-1-1-1-1-1−i−iii−i−iii111-11-1-1-11111-1-1ii−i−iii−i−i−ii−ii11-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ241111-1-111-1-11-1-111-11-1-1-1-1-1−i−iii−i−iii111-11-1-1-11111-1-1ii−i−iii−i−i−ii−ii-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ251111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-11111111-1-1-1-111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1111-1-111-1-11
χ261111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-11111111-1-1-1-111-1-1-1-1111-1-11-1-11111-1-1-1-11111-1-1-111-1-111-1
χ271111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-1111-1-1-1-11111-1-11111-1-11-1-1111-1-1-1-11111-1-1-1-111-111-1-111-1
χ281111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-1111-1-1-1-11111-1-11111-1-11-1-11-1-11111-1-1-1-11111-1-11-1-111-1-11
χ291111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111-1-11-1-11111111-1-1-1-1-1-11111-1-1-111-111-1-1-1-111-1-11111-1-11-1-11-111-1
χ301111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111-1-11-1-11111111-1-1-1-1-1-11111-1-1-111-1-1-11111-1-111-1-1-1-111-111-11-1-11
χ311111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111-1-11-1-1111-1-1-1-1111111-1-1-1-111-111-111-1-1-1-111-1-11111-1-1-111-11-1-11
χ321111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111-1-11-1-1111-1-1-1-1111111-1-1-1-111-111-1-1-11111-1-111-1-1-1-1111-1-11-111-1
χ33222222222222222222-2-2-2-222222222-2-2-2-2-2-20000000000000000-2-2-2-2000000000000000000000000
χ34222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222000000000000000000000000
χ35222222-2-2-2-2222-2-2-22-2-2-2-2-22i2i2i2i−2i−2i−2i−2i-2222-220000000000000000−2i−2i2i2i000000000000000000000000
χ36222222-2-2-2-2222-2-2-22-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2222-2200000000000000002i2i−2i−2i000000000000000000000000
χ372222-2-222-2-22-2-222-22-222222i2i−2i−2i2i2i−2i−2i-2-2-22-220000000000000000−2i2i−2i2i000000000000000000000000
χ382222-2-222-2-22-2-222-22-22222−2i−2i2i2i−2i−2i2i2i-2-2-22-2200000000000000002i−2i2i−2i000000000000000000000000
χ392222-2-2-2-2222-2-2-2-2222222222-2-2-2-222-222-2-2-20000000000000000-222-2000000000000000000000000
χ402222-2-2-2-2222-2-2-2-22222222-2-22222-2-2-222-2-2-200000000000000002-2-22000000000000000000000000
χ412-2-222-22-22-222-22-2-2-2200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000
χ422-2-222-22-22-222-22-2-2-2200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000
χ432-2-222-22-22-222-22-2-2-220000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000
χ442-2-222-22-22-222-22-2-2-220000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000
χ452-2-222-22-22-2-2-22-2222-222-2-20000000022-22-2-22-22-22-22-2000000000000000000000000000000000000
χ462-2-222-22-22-2-2-22-2222-222-2-20000000022-22-2-2-22-22-22-22000000000000000000000000000000000000
χ472-2-222-22-22-2-2-22-2222-2-2-22200000000-2-22-222000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ482-2-222-22-22-2-2-22-2222-2-2-22200000000-2-22-22200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ492-2-222-2-22-2222-2-222-2-200002-22-2-22-2200000000000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ502-2-222-2-22-2222-2-222-2-200002-22-2-22-2200000000000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ512-2-222-2-22-2222-2-222-2-20000-22-222-22-200000000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ522-2-222-2-22-2222-2-222-2-20000-22-222-22-200000000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ532-2-222-2-22-22-2-222-2-22222-2-2000000002-22-2-222-2-222-2-22000000000000000000000000000000000000
χ542-2-222-2-22-22-2-222-2-22222-2-2000000002-22-2-22-222-2-222-2000000000000000000000000000000000000
χ552-2-222-2-22-22-2-222-2-222-2-22200000000-22-222-2000000002-22-2-22-220000000000000000000000000000
χ562-2-222-2-22-22-2-222-2-222-2-22200000000-22-222-200000000-22-222-22-20000000000000000000000000000
χ572-2-22-222-2-222-222-22-2-200002-2-222-2-2200000000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ582-2-22-222-2-222-222-22-2-200002-2-222-2-2200000000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ592-2-22-222-2-222-222-22-2-20000-222-2-222-200000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ602-2-22-222-2-222-222-22-2-20000-222-2-222-200000000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ612-2-22-222-2-22-22-2-22-22222-2-200000000-2-2222-2000000002-2-222-2-220000000000000000000000000000
χ622-2-22-222-2-22-22-2-22-22222-2-200000000-2-2222-200000000-222-2-222-20000000000000000000000000000
χ632-2-22-222-2-22-22-2-22-222-2-2220000000022-2-2-222-2-22-222-2000000000000000000000000000000000000
χ642-2-22-222-2-22-22-2-22-222-2-2220000000022-2-2-22-222-22-2-22000000000000000000000000000000000000
χ652-2-22-22-222-22-22-22-2-2200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000i2−i2−i2i2−i2i2i2−i22−2−22−222−200000000
χ662-2-22-22-222-22-22-22-2-2200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000−i2i2i2−i2i2−i2−i2i2−222−22−2−2200000000
χ672-2-22-22-222-22-22-22-2-220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000i2−i2−i2i2−i2i2i2−i2−222−22−2−2200000000
χ682-2-22-22-222-22-22-22-2-220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000−i2i2i2−i2i2−i2−i2i22−2−22−222−200000000
χ692-2-22-22-222-2-22-22-222-222-2-200000000-22-2-222000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ702-2-22-22-222-2-22-22-222-222-2-200000000-22-2-22200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ712-2-22-22-222-2-22-22-222-2-2-222000000002-222-2-22-22-2-22-22000000000000000000000000000000000000
χ722-2-22-22-222-2-22-22-222-2-2-222000000002-222-2-2-22-222-22-2000000000000000000000000000000000000
χ734444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000000000
χ74444444-4-4-4-4-4-4-4444-4400000000000000000000000000000000000000000000000000000000000000
χ754444-4-444-4-4-444-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ764444-4-4-4-444-44444-4-4-400000000000000000000000000000000000000000000000000000000000000
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).