Finite Group Databasebeta

← Group #72235131

Character table — Group #72235131

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97
size11112222222244444444444444444448888888888888888888888888888888816161616161616161616161616161616161616161616161616163232323232323232
order1222222222222222222222222224444222222444444444444444444444444442224444444444444444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-11111-1-1-1-1-1-111111111111111111-1-1-11-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-111-1-111-1-1-1-111111111-1-1-1-11111
χ5111111111111111111111111111111111-1-111-1-1111111111111111111111111-11-1-1-1-11-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111111111-1-111-11-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-1-111-1-1-1-111111111111111-1-1-1-1
χ91111111-1-111111111-1-1-1-1-1-1-11111111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-11-11-1-1-1-11-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1
χ101111111-1-111111111-1-1-1-1-1-1-11111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-11-1-1-1-11-1-1-1-111-1-111-1-1-1-11111-1-111-1-111
χ111111111-1-111111111-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-11-111-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111
χ121111111-1-111111111-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-111-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1
χ131111111-1-111111111-1-1-1-1-1-1-11111111-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ141111111-1-111111111-1-1-1-1-1-1-11111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1
χ151111111-1-111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ161111111-1-111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-11-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ171111-1-1-11111-11111-1111-1-1-1-1-1-1-111-1-11-11111111-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-111-1-11-1-11-11-11-11-11-1ii−i−iii−i−ii−ii−ii−ii−i
χ181111-1-1-11111-11111-1111-1-1-1-1-1-1-111-1-11-11111111-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-111-1-11-1-11-11-11-11-11-1−i−iii−i−iii−ii−ii−ii−ii
χ191111-1-1-11111-11111-1111-1-1-1-1-1-1-111-1-11-111-1-1111-111-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1-11-1-1111-1-111-1-11-11−i−iii−i−iiii−ii−i−ii−ii
χ201111-1-1-11111-11111-1111-1-1-1-1-1-1-111-1-11-111-1-1111-111-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1-11-1-1111-1-111-1-11-11ii−i−iii−i−i−ii−iii−ii−i
χ211111-1-1-11111-11111-1111-1-1-1-1-1-1-111-1-11-1-1-111-1-11-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-111-1-11-11-11-111-1-11ii−i−iii−i−i−ii−ii−ii−ii
χ221111-1-1-11111-11111-1111-1-1-1-1-1-1-111-1-11-1-1-111-1-11-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-111-1-11-11-11-111-1-11−i−iii−i−iiii−ii−ii−ii−i
χ231111-1-1-11111-11111-1111-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-11-111-1-111iiii−i−i−i−iiiii−i−i−i−i1-11-1111-1-111-1-11-111-1−i−iii−i−iii−ii−iii−ii−i
χ241111-1-1-11111-11111-1111-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-11-111-1-111−i−i−i−iiiii−i−i−i−iiiii1-11-1111-1-111-1-11-111-1ii−i−iii−i−ii−ii−i−ii−ii
χ251111-1-1-1-1-111-11111-1-1-1-11111-1-1-111-1-1-111111-1-1-11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1111-11-1-11-111-1-111-1ii−i−i−i−iiii−i−iii−i−ii
χ261111-1-1-1-1-111-11111-1-1-1-11111-1-1-111-1-1-111111-1-1-11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1111-11-1-11-111-1-111-1−i−iiiii−i−i−iii−i−iii−i
χ271111-1-1-1-1-111-11111-1-1-1-11111-1-1-111-1-1-1111-1-1-1-1-1111-1-111iiii−i−i−i−i−i−i−i−iiiii-11-1-111-11-111-11-11-1-11−i−iiiii−i−ii−i−ii−iii−i
χ281111-1-1-1-1-111-11111-1-1-1-11111-1-1-111-1-1-1111-1-1-1-1-1111-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-1-111-11-111-11-11-1-11ii−i−i−i−iii−iii−ii−i−ii
χ291111-1-1-1-1-111-11111-1-1-1-11111-1-1-111-1-1-11-1-11111-11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-11111-11-1-11-11-11ii−i−i−i−iii−iii−i−iii−i
χ301111-1-1-1-1-111-11111-1-1-1-11111-1-1-111-1-1-11-1-11111-11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-11111-11-1-11-11-11−i−iiiii−i−ii−i−iii−i−ii
χ311111-1-1-1-1-111-11111-1-1-1-11111-1-1-111-1-1-11-1-1-1-111-1111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-11-1-11-111-11-1−i−iiiii−i−i−iii−ii−i−ii
χ321111-1-1-1-1-111-11111-1-1-1-11111-1-1-111-1-1-11-1-1-1-111-1111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-11-1-11-111-11-1ii−i−i−i−iiii−i−ii−iii−i
χ3322222222222222-2-222222222-2-22-2-2-2-2-2-2002200-2-222-2-2-2-2000000000000000002000020000000-2-2000000000000000000
χ3422222222222222-2-222222222-2-22-2-2-2-2-2-200-2-200-2-2-2-2222200000000000000000-20000-2000000022000000000000000000
χ35222222222222-2-222-22-2-222-2-222-2-2-2-2-222220022-2-2000000000000000000000020002000-2-200-2-200000000000000000000
χ36222222222222-2-222-22-2-222-2-222-2-2-2-2-222-2-200-2-2-2-20000000000000000000000-2000-200022002200000000000000000000
χ37222222222222-2-2-2-2-22-2-222-2-2-2-2-22222-2-20000002200000000000000000000000022020200-2-20000-2-20000000000000000
χ38222222222222-2-2-2-2-22-2-222-2-2-2-2-22222-2-200000022000000000000000000000000-2-20-20-200220000220000000000000000
χ392222222-2-222222-2-22-2-2-2-2-2-2-2-2-22-2-2-2-2220022002222-2-2-2-200000000000000000-20000-2000000022000000000000000000
χ402222222-2-222222-2-22-2-2-2-2-2-2-2-2-22-2-2-2-22200-2-20022-2-22222000000000000000002000020000000-2-2000000000000000000
χ412222222-2-2222-2-222-2-222-2-22222-2-2-2-2-2-2-22200-2-22200000000000000000000002000-20002200-2-200000000000000000000
χ422222222-2-2222-2-222-2-222-2-22222-2-2-2-2-2-2-2-2-20022220000000000000000000000-20002000-2-2002200000000000000000000
χ432222222-2-2222-2-2-2-2-2-222-2-222-2-2-2222222000000-2-20000000000000000000000002-20-20200220000-2-20000000000000000
χ442222222-2-2222-2-2-2-2-2-222-2-222-2-2-2222222000000-2-2000000000000000000000000-22020-200-2-20000220000000000000000
χ452222-2-2-22222-222-2-2-2222-2-2-2-222-2-2-222-22002200-22-2-2-2-2220000000000000000020000-20000000-22000000000000000000
χ462222-2-2-22222-222-2-2-2222-2-2-2-222-2-2-222-2200-2-200-222222-2-200000000000000000-20000200000002-2000000000000000000
χ472222-2-2-22222-2-2-22222-2-2-2-222-2-22-2-2222-2220022-220000000000000000000000-2000-2000-2200-2200000000000000000000
χ482222-2-2-22222-2-2-22222-2-2-2-222-2-22-2-2222-2-2-200-2-2-220000000000000000000000200020002-2002-200000000000000000000
χ492222-2-2-22222-2-2-2-2-222-2-2-2-22222222-2-2-220000002-20000000000000000000000002-2020-200-220000-220000000000000000
χ502222-2-2-22222-2-2-2-2-222-2-2-2-22222222-2-2-220000002-2000000000000000000000000-220-202002-200002-20000000000000000
χ512222-2-2-2-2-222-222-2-2-2-2-2-2222222-2-2-2222-20022002-2-2-2-2-22200000000000000000-20000200000002-2000000000000000000
χ522222-2-2-2-2-222-222-2-2-2-2-2-2222222-2-2-2222-200-2-2002-22222-2-20000000000000000020000-20000000-22000000000000000000
χ532222-2-2-2-2-222-2-2-2222-22222-2-2-2-22-2-222-222200-2-22-20000000000000000000000-200020002-200-2200000000000000000000
χ542222-2-2-2-2-222-2-2-2222-22222-2-2-2-22-2-222-22-2-200222-200000000000000000000002000-2000-22002-200000000000000000000
χ552222-2-2-2-2-222-2-2-2-2-22-22222-2-222222-2-22-2000000-22000000000000000000000000220-20-2002-20000-220000000000000000
χ562222-2-2-2-2-222-2-2-2-2-22-22222-2-222222-2-22-2000000-22000000000000000000000000-2-2020200-2200002-20000000000000000
χ572-2-2222-200-22-22-22-2200000002-2-22-22-200002-200002-22-22-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000002i−2i2i−2i00000000
χ582-2-2222-200-22-22-22-2200000002-2-22-22-200002-200002-22-22-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000−2i2i−2i2i00000000
χ592-2-2222-200-22-22-22-2200000002-2-22-22-20000-220000-22-22-22000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000−2i2i−2i2i00000000
χ602-2-2222-200-22-22-22-2200000002-2-22-22-20000-220000-22-22-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000002i−2i2i−2i00000000
χ612-2-2222-200-22-22-2-2220000000-22-2-22-2200002-200002-2-22-222i2i−2i−2i2i2i−2i−2i000000000000000000000000002i−2i2i−2i000000000000
χ622-2-2222-200-22-22-2-2220000000-22-2-22-2200002-200002-2-22-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000−2i2i−2i2i000000000000
χ632-2-2222-200-22-22-2-2220000000-22-2-22-220000-220000-222-22-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000−2i2i−2i2i000000000000
χ642-2-2222-200-22-22-2-2220000000-22-2-22-220000-220000-222-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000002i−2i2i−2i000000000000
χ652-2-22-2-2200-2222-22-2-20000000-2222-2-2200002-20000-222-2-220000000022-2-2-2-22200000000000000000000002-2-2200000000
χ662-2-22-2-2200-2222-22-2-20000000-2222-2-2200002-20000-222-2-2200000000-2-22222-2-20000000000000000000000-222-200000000
χ672-2-22-2-2200-2222-22-2-20000000-2222-2-220000-2200002-2-222-20000000022-2-2-2-2220000000000000000000000-222-200000000
χ682-2-22-2-2200-2222-22-2-20000000-2222-2-220000-2200002-2-222-200000000-2-22222-2-200000000000000000000002-2-2200000000
χ692-2-22-2-2200-2222-2-22-200000002-22-222-200002-20000-22-222-222-2-2-2-222000000000000000000000000002-2-22000000000000
χ702-2-22-2-2200-2222-2-22-200000002-22-222-200002-20000-22-222-2-2-22222-2-200000000000000000000000000-222-2000000000000
χ712-2-22-2-2200-2222-2-22-200000002-22-222-20000-2200002-22-2-2222-2-2-2-22200000000000000000000000000-222-2000000000000
χ722-2-22-2-2200-2222-2-22-200000002-22-222-20000-2200002-22-2-22-2-22222-2-2000000000000000000000000002-2-22000000000000
χ7344444-4444-4-4-400000-4004-400000000000000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000
χ7444444-4444-4-4-400000-4004-40000000000000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ7544444-44-4-4-4-4-400000400-4400000000000000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ7644444-44-4-4-4-4-400000400-440000000000000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000
χ774444-44-444-4-4400000-400-4400000000000000000000000002-22-2-22-222-22-2-22-220000000000000000000000000000000000
χ784444-44-444-4-4400000-400-440000000000000000000000000-22-222-22-2-22-222-22-20000000000000000000000000000000000
χ794444-44-4-4-4-4-44000004004-400000000000000000000000002-22-2-22-22-22-222-22-20000000000000000000000000000000000
χ804444-44-4-4-4-4-44000004004-40000000000000000000000000-22-222-22-22-22-2-22-220000000000000000000000000000000000
χ814-4-4444-400-44-4-444-4-400000004-44-44-44000000000000000000000000000000000000000000000000000000000000000000
χ824-4-4444-400-44-4-44-44-40000000-4444-44-4000000000000000000000000000000000000000000000000000000000000000000
χ834-4-444-4-4004-440000004-4004-4000000000000000000000002-2-222-2-222-2-222-2-220000000000000000000000000000000000
χ844-4-444-4-4004-440000004-4004-400000000000000000000000-222-2-222-2-222-2-222-20000000000000000000000000000000000
χ854-4-444-4-4004-44000000-4400-44000000000000000000000002-2-222-2-22-222-2-222-20000000000000000000000000000000000
χ864-4-444-4-4004-44000000-4400-4400000000000000000000000-222-2-222-22-2-222-2-220000000000000000000000000000000000
χ874-4-44-444004-4-40000004-400-44000000000000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000
χ884-4-44-444004-4-40000004-400-4400000000000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000
χ894-4-44-444004-4-4000000-44004-4000000000000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000
χ904-4-44-444004-4-4000000-44004-400000000000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000
χ914-4-44-4-4400-444-444-440000000-44-4-444-4000000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-4400-444-44-44400000004-4-44-4-44000000000000000000000000000000000000000000000000000000000000000000
χ938-88-80008-80000000000000000000000004-4004-40000000000000000000000000000000000000000000000000000000000
χ948-88-80008-8000000000000000000000000-4400-440000000000000000000000000000000000000000000000000000000000
χ958-88-8000-880000000000000000000000004-400-440000000000000000000000000000000000000000000000000000000000
χ968-88-8000-88000000000000000000000000-44004-40000000000000000000000000000000000000000000000000000000000
χ971616-16-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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