Finite Group Databasebeta

← Group #231566

Character table — Group #231566

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888844444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ1711-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i111-1-111-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ1811-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1ii−i−iii−i−i−i−iii−i−iii111-1-111-1-11111-1-1-1-1i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii-11-11-11-11
χ1911-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1−i−iii−i−iiiii−i−iii−i−i111-1-111-1-11111-1-1-1-1−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i-11-11-11-11
χ2011-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii111-1-111-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ2111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1ii−i−iii−i−iii−i−i−i−iii111-1-1-1-111-1-1-1-11111i−ii−ii−i−ii−i−iii−i−iiiii−i−i−i−iii1-11-1-11-11
χ2211-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1ii−i−iii−i−i−i−iiiii−i−i111-1-1-1-111-1-1-1-11111i−ii−i−iii−i−i−iii−i−iii−i−iiiii−i−i-11-111-11-1
χ2311-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1−i−iii−i−iiiii−i−i−i−iii111-1-1-1-111-1-1-1-11111−ii−iii−i−iiii−i−iii−i−iii−i−i−i−iii-11-111-11-1
χ2411-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1−i−iii−i−iii−i−iiiii−i−i111-1-1-1-111-1-1-1-11111−ii−ii−iii−iii−i−iii−i−i−i−iiiii−i−i1-11-1-11-11
χ2511-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1ii−i−i−i−iiiii−i−iii−i−i1-1-11111-1-1-1-1-1-11111i−i−iii−ii−iii−i−i−i−iii−i−iii−i−iii1-1-111-1-11
χ2611-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1ii−i−i−i−iii−i−iii−i−iii1-1-11111-1-1-1-1-1-11111i−i−ii−ii−iiii−i−i−i−iiiii−i−iii−i−i-111-1-111-1
χ2711-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1−i−iiiii−i−iii−i−iii−i−i1-1-11111-1-1-1-1-1-11111−iii−ii−ii−i−i−iiiii−i−i−i−iii−i−iii-111-1-111-1
χ2811-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1−i−iiiii−i−i−i−iii−i−iii1-1-11111-1-1-1-1-1-11111−iii−i−ii−ii−i−iiiii−i−iii−i−iii−i−i1-1-111-1-11
χ2911-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1ii−i−i−i−iiiii−i−i−i−iii1-1-111-1-1111111-1-1-1-1i−i−iii−i−ii−i−iiiii−i−i−i−iiiii−i−i1-1-11-111-1
χ3011-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1ii−i−i−i−iii−i−iiiii−i−i1-1-111-1-1111111-1-1-1-1i−i−ii−iii−i−i−iiiii−i−iii−i−i−i−iii-111-11-1-11
χ3111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1−i−iiiii−i−iii−i−i−i−iii1-1-111-1-1111111-1-1-1-1−iii−ii−i−iiii−i−i−i−iii−i−iiiii−i−i-111-11-1-11
χ3211-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-1111111-1-1-1-1−iii−i−iii−iii−i−i−i−iiiii−i−i−i−iii1-1-11-111-1
χ332222222222-2-222-2-20000000022222222-20000000022222222-20000-2-2-2-2000000000000-2-2-2-2000000000000000000000000
χ342222222222-2-222-2-20000000022222222-200000000-2-2-2-2-2-2-2-2-20000-2-2-2-20000000000002222000000000000000000000000
χ352222222222-2-222-2-200000000-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2-200002222000000000000-2-222000000000000000000000000
χ362222222222-2-222-2-200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-22222-20000222200000000000022-2-2000000000000000000000000
χ3722222222-2-222-2-2222222222200000000-22222222200000000-2-2-2-2-2000000000000-2-2-2-20000000000000000000000000000
χ3822222222-2-222-2-2222222222200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-2-200000000000022220000000000000000000000000000
χ3922222222-2-222-2-222-2-2-2-2-2-2-2-200000000-22222-2-2-2-200000000-22222000000000000-2-2220000000000000000000000000000
χ4022222222-2-222-2-222-2-2-2-2-2-2-2-200000000-2-2-2-2-2222200000000-2222200000000000022-2-20000000000000000000000000000
χ4122-2-2-2-22222-2-2-2-222000000002222-2-2-2-22000000002i2i−2i−2i2i2i−2i−2i-20000-2-222000000000000−2i2i−2i2i000000000000000000000000
χ4222-2-2-2-22222-2-2-2-222000000002222-2-2-2-2200000000−2i−2i2i2i−2i−2i2i2i-20000-2-2220000000000002i−2i2i−2i000000000000000000000000
χ4322-2-2-2-22222-2-2-2-22200000000-2-2-2-222222000000002i2i−2i−2i−2i−2i2i2i-2000022-2-2000000000000−2i2i2i−2i000000000000000000000000
χ4422-2-2-2-22222-2-2-2-22200000000-2-2-2-22222200000000−2i−2i2i2i2i2i−2i−2i-2000022-2-20000000000002i−2i−2i2i000000000000000000000000
χ4522-2-2-2-222-2-22222-2-22222-2-2-2-20000000022i2i−2i−2i2i2i−2i−2i00000000-2-2-222000000000000−2i2i−2i2i0000000000000000000000000000
χ4622-2-2-2-222-2-22222-2-22222-2-2-2-2000000002−2i−2i2i2i−2i−2i2i2i00000000-2-2-2220000000000002i−2i2i−2i0000000000000000000000000000
χ4722-2-2-2-222-2-22222-2-2-2-2-2-222220000000022i2i−2i−2i−2i−2i2i2i00000000-222-2-2000000000000−2i2i2i−2i0000000000000000000000000000
χ4822-2-2-2-222-2-22222-2-2-2-2-2-22222000000002−2i−2i2i2i2i2i−2i−2i00000000-222-2-20000000000002i−2i−2i2i0000000000000000000000000000
χ492-222-2-22-2002-2002-22i2i−2i−2i2i2i−2i−2ii2i2−i2−i2i2i2−i2−i202-22-22i−2i2i−2i0000000000000i2−i2i2−i222−2−222−2−200000000i2−i2i2−i22−22−20000000000000000
χ502-222-2-22-2002-2002-22i2i−2i−2i2i2i−2i−2ii2i2−i2−i2i2i2−i2−i20-22-22−2i2i−2i2i0000000000000i2−i2i2−i222−2−222−2−200000000−i2i2−i2i2−22−220000000000000000
χ512-222-2-22-2002-2002-22i2i−2i−2i2i2i−2i−2i−i2−i2i2i2−i2−i2i2i202-22-22i−2i2i−2i0000000000000−i2i2−i2i2−2−222−2−22200000000−i2i2−i2i2−22−220000000000000000
χ522-222-2-22-2002-2002-22i2i−2i−2i2i2i−2i−2i−i2−i2i2i2−i2−i2i2i20-22-22−2i2i−2i2i0000000000000−i2i2−i2i2−2−222−2−22200000000i2−i2i2−i22−22−20000000000000000
χ532-222-2-22-2002-2002-2−2i−2i2i2i−2i−2i2i2ii2i2−i2−i2i2i2−i2−i202-22-2−2i2i−2i2i0000000000000i2−i2i2−i2−2−222−2−22200000000i2−i2i2−i2−22−220000000000000000
χ542-222-2-22-2002-2002-2−2i−2i2i2i−2i−2i2i2ii2i2−i2−i2i2i2−i2−i20-22-222i−2i2i−2i0000000000000i2−i2i2−i2−2−222−2−22200000000−i2i2−i2i22−22−20000000000000000
χ552-222-2-22-2002-2002-2−2i−2i2i2i−2i−2i2i2i−i2−i2i2i2−i2−i2i2i202-22-2−2i2i−2i2i0000000000000−i2i2−i2i222−2−222−2−200000000−i2i2−i2i22−22−20000000000000000
χ562-222-2-22-2002-2002-2−2i−2i2i2i−2i−2i2i2i−i2−i2i2i2−i2−i2i2i20-22-222i−2i2i−2i0000000000000−i2i2−i2i222−2−222−2−200000000i2−i2i2−i2−22−220000000000000000
χ572-22-22-2-222-2002-200i2−i2i2−i2i2−i2i2−i22i−2i2i−2i2i−2i2i−2i0000000002i−2i2i−2i2-22-20i2−i2i2−i200002−22−22−22−200000000000000002−22−2i2−i2i2−i200000000
χ582-22-22-2-222-2002-200i2−i2i2−i2i2−i2i2−i22i−2i2i−2i2i−2i2i−2i000000000−2i2i−2i2i-22-220i2−i2i2−i200002−22−22−22−20000000000000000−22−22−i2i2−i2i200000000
χ592-22-22-2-222-2002-200i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i−2i2i−2i2i0000000002i−2i2i−2i-22-220i2−i2i2−i20000−22−22−22−2200000000000000002−22−2−i2i2−i2i200000000
χ602-22-22-2-222-2002-200i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i−2i2i−2i2i000000000−2i2i−2i2i2-22-20i2−i2i2−i20000−22−22−22−220000000000000000−22−22i2−i2i2−i200000000
χ612-22-22-2-222-2002-200−i2i2−i2i2−i2i2−i2i22i−2i2i−2i2i−2i2i−2i0000000002i−2i2i−2i2-22-20−i2i2−i2i20000−22−22−22−220000000000000000−22−22−i2i2−i2i200000000
χ622-22-22-2-222-2002-200−i2i2−i2i2−i2i2−i2i22i−2i2i−2i2i−2i2i−2i000000000−2i2i−2i2i-22-220−i2i2−i2i20000−22−22−22−2200000000000000002−22−2i2−i2i2−i200000000
χ632-22-22-2-222-2002-200−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i−2i2i−2i2i0000000002i−2i2i−2i-22-220−i2i2−i2i200002−22−22−22−20000000000000000−22−22i2−i2i2−i200000000
χ642-22-22-2-222-2002-200−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i−2i2i−2i2i000000000−2i2i−2i2i2-22-20−i2i2−i2i200002−22−22−22−200000000000000002−22−2−i2i2−i2i200000000
χ652-2-22-22-222-200-2200i2−i2i2−i2−i2i2−i2i22i−2i2i−2i−2i2i−2i2i0000000002-2-22−2i2i2i−2i0i2−i2−i2i200002−22−2−22−220000000000000000−i2i2i2−i22−2−2200000000
χ662-2-22-22-222-200-2200i2−i2i2−i2−i2i2−i2i22i−2i2i−2i−2i2i−2i2i000000000-222-22i−2i−2i2i0i2−i2−i2i200002−22−2−22−220000000000000000i2−i2−i2i2−222−200000000
χ672-2-22-22-222-200-2200i2−i2i2−i2−i2i2−i2i2−2i2i−2i2i2i−2i2i−2i0000000002-2-222i−2i−2i2i0i2−i2−i2i20000−22−222−22−20000000000000000−i2i2i2−i2−222−200000000
χ682-2-22-22-222-200-2200i2−i2i2−i2−i2i2−i2i2−2i2i−2i2i2i−2i2i−2i000000000-222-2−2i2i2i−2i0i2−i2−i2i20000−22−222−22−20000000000000000i2−i2−i2i22−2−2200000000
χ692-2-22-22-222-200-2200−i2i2−i2i2i2−i2i2−i22i−2i2i−2i−2i2i−2i2i0000000002-2-22−2i2i2i−2i0−i2i2i2−i20000−22−222−22−20000000000000000i2−i2−i2i2−222−200000000
χ702-2-22-22-222-200-2200−i2i2−i2i2i2−i2i2−i22i−2i2i−2i−2i2i−2i2i000000000-222-22i−2i−2i2i0−i2i2i2−i20000−22−222−22−20000000000000000−i2i2i2−i22−2−2200000000
χ712-2-22-22-222-200-2200−i2i2−i2i2i2−i2i2−i2−2i2i−2i2i2i−2i2i−2i0000000002-2-222i−2i−2i2i0−i2i2i2−i200002−22−2−22−220000000000000000i2−i2−i2i22−2−2200000000
χ722-2-22-22-222-200-2200−i2i2−i2i2i2−i2i2−i2−2i2i−2i2i2i−2i2i−2i000000000-222-2−2i2i2i−2i0−i2i2i2−i200002−22−2−22−220000000000000000−i2i2i2−i2−222−200000000
χ732-2-2-2222-2002-200-222i2i−2i−2i−2i−2i2i2ii2i2−i2−i2−i2−i2i2i202i−2i−2i2i-222-20000000000000i2−i2−i2i222−2−2−2−22200000000−222−2i2−i2−i2i20000000000000000
χ742-2-2-2222-2002-200-222i2i−2i−2i−2i−2i2i2ii2i2−i2−i2−i2−i2i2i20−2i2i2i−2i2-2-220000000000000i2−i2−i2i222−2−2−2−222000000002−2−22−i2i2i2−i20000000000000000
χ752-2-2-2222-2002-200-222i2i−2i−2i−2i−2i2i2i−i2−i2i2i2i2i2−i2−i202i−2i−2i2i-222-20000000000000−i2i2i2−i2−2−22222−2−2000000002−2−22−i2i2i2−i20000000000000000
χ762-2-2-2222-2002-200-222i2i−2i−2i−2i−2i2i2i−i2−i2i2i2i2i2−i2−i20−2i2i2i−2i2-2-220000000000000−i2i2i2−i2−2−22222−2−200000000−222−2i2−i2−i2i20000000000000000
χ772-2-2-2222-2002-200-22−2i−2i2i2i2i2i−2i−2ii2i2−i2−i2−i2−i2i2i202i−2i−2i2i2-2-220000000000000i2−i2−i2i2−2−22222−2−200000000−222−2−i2i2i2−i20000000000000000
χ782-2-2-2222-2002-200-22−2i−2i2i2i2i2i−2i−2ii2i2−i2−i2−i2−i2i2i20−2i2i2i−2i-222-20000000000000i2−i2−i2i2−2−22222−2−2000000002−2−22i2−i2−i2i20000000000000000
χ792-2-2-2222-2002-200-22−2i−2i2i2i2i2i−2i−2i−i2−i2i2i2i2i2−i2−i202i−2i−2i2i2-2-220000000000000−i2i2i2−i222−2−2−2−222000000002−2−22i2−i2−i2i20000000000000000
χ802-2-2-2222-2002-200-22−2i−2i2i2i2i2i−2i−2i−i2−i2i2i2i2i2−i2−i20−2i2i2i−2i-222-20000000000000−i2i2i2−i222−2−2−2−22200000000−222−2−i2i2i2−i20000000000000000
χ8144444444-4-4-4-4-4-4-4-40000000000000000400000000000000004000000000000000000000000000000000000000000000000
χ82444-4-44-4-40000000022−22−222222−22−222222−22−222222−22−2222000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ83444-4-44-4-40000000022−22−222222−22−2222−222222−22−222222−2200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ84444-4-44-4-400000000−222222−22−222222−2222−22−222222−22−222200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ85444-4-44-4-400000000−222222−22−222222−22−222222−22−222222−22000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ8644-444-4-4-40000000022−22−2222−222222−2222−22−2222−222222−22000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ8744-444-4-4-40000000022−22−2222−222222−22−222222−2222−22−222200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ8844-444-4-4-400000000−222222−2222−22−222222−22−2222−222222−2200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ8944-444-4-4-400000000−222222−2222−22−2222−222222−2222−22−2222000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ9044-4-4-4-444-4-4-4-444440000000000000000-400000000000000004000000000000000000000000000000000000000000000000
χ914-444-4-44-400-4400-44000000002i22i2−2i2−2i22i22i2−2i2−2i20000000000000000000000−2i22i2−2i22i20000000000000000000000000000000000000000
χ924-444-4-44-400-4400-4400000000−2i2−2i22i22i2−2i2−2i22i22i200000000000000000000002i2−2i22i2−2i20000000000000000000000000000000000000000
χ934-44-44-4-44-4400-44002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ944-44-44-4-44-4400-4400−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ954-4-44-44-44-44004-4002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ964-4-44-44-44-44004-400−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ974-4-4-4444-400-44004-4000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ984-4-4-4444-400-44004-400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000

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