Finite Group Databasebeta

← Group #72262115

Character table — Group #72262115

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106
size111122222244444444444444444444444444448888888888888888888888888888888888888888888888881616161616161616323232323232323232323232
order1222222222222222224444444444444444444422222222444444444444444444444444444444444444444422444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ9111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ10111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ11111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ12111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ13111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ14111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ15111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ16111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ171-11-111-1-11-111-1-111-1-1ii−i−i1-1ii−i−i11-1-1ii−i−i1-111-1-11-11-1i−ii−i1-11-1ii−i−iii−i−ii−ii−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i1-11-1ii−i−i1-1i−i1-1i−i1-1i−i
χ181-11-111-1-11-111-1-111-1-1ii−i−i1-1ii−i−i11-1-1ii−i−i1-111-1-11-11-1i−ii−i1-11-1ii−i−iii−i−ii−ii−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i-11-11−i−iii-11−ii-11−ii-11−ii
χ191-11-111-1-11-111-1-111-1-1ii−i−i1-1ii−i−i11-1-1ii−i−i1-111-1-1-11-11−ii−ii-11-11ii−i−iii−i−i−ii−ii1-1i−i-1-111−i−iii-1-111−i−iii1-11-1ii−i−i-11−ii-11−ii1-1i−i
χ201-11-111-1-11-111-1-111-1-1ii−i−i1-1ii−i−i11-1-1ii−i−i1-111-1-1-11-11−ii−ii-11-11ii−i−iii−i−i−ii−ii1-1i−i-1-111−i−iii-1-111−i−iii-11-11−i−iii1-1i−i1-1i−i-11−ii
χ211-11-111-1-11-111-1-111-1-1ii−i−i1-1ii−i−i-1-111−i−iii1-1-1-1111-1-11i−i−ii1-1-11ii−i−i−i−iiii−i−ii-11−ii11-1-1ii−i−i-1-111−i−iii1-11-1ii−i−i1-1i−i-11−ii-11−ii
χ221-11-111-1-11-111-1-111-1-1ii−i−i1-1ii−i−i-1-111−i−iii1-1-1-1111-1-11i−i−ii1-1-11ii−i−i−i−iiii−i−ii-11−ii11-1-1ii−i−i-1-111−i−iii-11-11−i−iii-11−ii1-1i−i1-1i−i
χ231-11-111-1-11-111-1-111-1-1ii−i−i1-1ii−i−i-1-111−i−iii1-1-1-111-111-1−iii−i-111-1ii−i−i−i−iii−iii−i-11−ii-1-111−i−iii11-1-1ii−i−i1-11-1ii−i−i-11−ii1-1i−i-11−ii
χ241-11-111-1-11-111-1-111-1-1ii−i−i1-1ii−i−i-1-111−i−iii1-1-1-111-111-1−iii−i-111-1ii−i−i−i−iii−iii−i-11−ii-1-111−i−iii11-1-1ii−i−i-11-11−i−iii1-1i−i-11−ii1-1i−i
χ251-11-111-1-11-111-1-111-1-1−i−iii1-1−i−iii11-1-1−i−iii1-111-1-11-11-1−ii−ii1-11-1−i−iii−i−iii−ii−ii1-1−ii11-1-1−i−iii11-1-1−i−iii1-11-1−i−iii1-1−ii1-1−ii1-1−ii
χ261-11-111-1-11-111-1-111-1-1−i−iii1-1−i−iii11-1-1−i−iii1-111-1-11-11-1−ii−ii1-11-1−i−iii−i−iii−ii−ii1-1−ii11-1-1−i−iii11-1-1−i−iii-11-11ii−i−i-11i−i-11i−i-11i−i
χ271-11-111-1-11-111-1-111-1-1−i−iii1-1−i−iii11-1-1−i−iii1-111-1-1-11-11i−ii−i-11-11−i−iii−i−iiii−ii−i1-1−ii-1-111ii−i−i-1-111ii−i−i1-11-1−i−iii-11i−i-11i−i1-1−ii
χ281-11-111-1-11-111-1-111-1-1−i−iii1-1−i−iii11-1-1−i−iii1-111-1-1-11-11i−ii−i-11-11−i−iii−i−iiii−ii−i1-1−ii-1-111ii−i−i-1-111ii−i−i-11-11ii−i−i1-1−ii1-1−ii-11i−i
χ291-11-111-1-11-111-1-111-1-1−i−iii1-1−i−iii-1-111ii−i−i1-1-1-1111-1-11−iii−i1-1-11−i−iiiii−i−i−iii−i-11i−i11-1-1−i−iii-1-111ii−i−i1-11-1−i−iii1-1−ii-11i−i-11i−i
χ301-11-111-1-11-111-1-111-1-1−i−iii1-1−i−iii-1-111ii−i−i1-1-1-1111-1-11−iii−i1-1-11−i−iiiii−i−i−iii−i-11i−i11-1-1−i−iii-1-111ii−i−i-11-11ii−i−i-11i−i1-1−ii1-1−ii
χ311-11-111-1-11-111-1-111-1-1−i−iii1-1−i−iii-1-111ii−i−i1-1-1-111-111-1i−i−ii-111-1−i−iiiii−i−ii−i−ii-11i−i-1-111ii−i−i11-1-1−i−iii1-11-1−i−iii-11i−i1-1−ii-11i−i
χ321-11-111-1-11-111-1-111-1-1−i−iii1-1−i−iii-1-111ii−i−i1-1-1-111-111-1i−i−ii-111-1−i−iiiii−i−ii−i−ii-11i−i-1-111ii−i−i11-1-1−i−iii-11-11ii−i−i1-1−ii-11i−i1-1−ii
χ3322222222222-22-22-22-22222-2-2-2-2-2-200000000-2-200000022002200222-22-200000022000000000000-2-2-2-2-2-2-2-200000000000000000000
χ3422222222222-22-22-22-22222-2-2-2-2-2-200000000-2-2000000-2-200-2-200-2-22-22-2000000-2-20000000000002222222200000000000000000000
χ3522222222222-22-22-22-2-2-2-2-2-2-2222200000000-2-20000002200-2-20022-22-22000000-2-2000000000000-2-2-2-2222200000000000000000000
χ3622222222222-22-22-22-2-2-2-2-2-2-2222200000000-2-2000000-2-2002200-2-2-22-22000000220000000000002222-2-2-2-200000000000000000000
χ372222222222-22-22-22-222222-2-2-2-2-2-200000000-2-20000220022002200-22-22000022000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ382222222222-22-22-22-222222-2-2-2-2-2-200000000-2-20000-2-200-2-200-2-200-22-220000-2-2000000222222220000000000000000000000000000
χ392222222222-22-22-22-22-2-2-2-2-2-2222200000000-2-200002200-2-20022002-22-20000-2-2000000-2-2-2-222220000000000000000000000000000
χ402222222222-22-22-22-22-2-2-2-2-2-2222200000000-2-20000-2-2002200-2-2002-22-20000220000002222-2-2-2-20000000000000000000000000000
χ412222222222-2-2-2-2-2-2-2-222222222222222222222-2-2-2-2000000000000-2-2-2-2-2-2-2-200002222000000000000000000000000000000000000
χ422222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2222222000000000000-2-2-2-222220000-2-2-2-2000000000000000000000000000000000000
χ432222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-222-2-2-2-200000000000022222222000022-2-2000000000000000000000000000000000000
χ442222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222220000000000002222-2-2-2-20000-2-222000000000000000000000000000000000000
χ452222-2-2-2-22222-2-2-2-2220000-220000222200002-22-22-200002222000000000000-2-2-2-2-2-20000002-22-200002-22-200000000000000000000
χ462222-2-2-2-22222-2-2-2-2220000-220000222200002-22-22-20000-2-2-2-20000000000002222-2-2000000-22-220000-22-2200000000000000000000
χ472222-2-2-2-22222-2-2-2-2220000-220000-2-2-2-200002-2-22-22000022-2-2000000000000-2-222220000002-22-20000-22-2200000000000000000000
χ482222-2-2-2-22222-2-2-2-2220000-220000-2-2-2-200002-2-22-220000-2-22200000000000022-2-222000000-22-2200002-22-200000000000000000000
χ492222-2-2-2-2222-2-22-222-200002-2000000002222-220000220000-2-2-2-20000002-22-2002200-2-22-22-2000000002-22-200000000000000000000
χ502222-2-2-2-2222-2-22-222-200002-2000000002222-220000-2-2000022220000002-22-200-2-200-2-2-22-2200000000-22-2200000000000000000000
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χ522222-2-2-2-2222-2-22-222-200002-200000000-2-2-2-2-220000-2-20000-2-222000000-22-2200220022-22-22000000002-22-200000000000000000000
χ532222-2-2-2-222-222-22-2-2200002-2000000002222-2200000022-2-20000-2-20000-22-22220000-2-200002-22-22-22-2000000000000000000000000
χ542222-2-2-2-222-222-22-2-2200002-2000000002222-22000000-2-2220000220000-22-22-2-20000-2-20000-22-22-22-22000000000000000000000000
χ552222-2-2-2-222-222-22-2-2200002-200000000-2-2-2-2-2200000022220000-2-200002-22-2-2-20000220000-22-222-22-2000000000000000000000000
χ562222-2-2-2-222-222-22-2-2200002-200000000-2-2-2-2-22000000-2-2-2-200002200002-22-22200002200002-22-2-22-22000000000000000000000000
χ572222-2-2-2-222-2-22222-2-20000-220000222200002-2-22-2222220000-2-2-2-2000000000000-2-200-22-220000-22-22000000000000000000000000
χ582222-2-2-2-222-2-22222-2-20000-220000222200002-2-22-22-2-2-2-200002222000000000000-2-2002-22-200002-22-2000000000000000000000000
χ592222-2-2-2-222-2-22222-2-20000-220000-2-2-2-200002-22-22-222-2-20000-2-2220000000000002200-22-2200002-22-2000000000000000000000000
χ602222-2-2-2-222-2-22222-2-20000-220000-2-2-2-200002-22-22-2-2-222000022-2-200000000000022002-22-20000-22-22000000000000000000000000
χ612-22-222-2-22-22-2-222-2-222i2i−2i−2i-22−2i−2i2i2i00000000-220000002-2002i−2i002-22i−2i−2i2i0000002i−2i000000000000-2-222−2i−2i2i2i00000000000000000000
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χ632-22-222-2-22-22-2-222-2-22−2i−2i2i2i-222i2i−2i−2i00000000-220000002-200−2i2i002-2−2i2i2i−2i000000−2i2i000000000000-2-2222i2i−2i−2i00000000000000000000
χ642-22-222-2-22-22-2-222-2-22−2i−2i2i2i-222i2i−2i−2i00000000-22000000-22002i−2i00-22−2i2i2i−2i0000002i−2i00000000000022-2-2−2i−2i2i2i00000000000000000000
χ652-22-222-2-22-2-222-2-222-22i2i−2i−2i-22−2i−2i2i2i00000000-2200002-2002i−2i002-200−2i2i2i−2i00002i−2i000000-2-222−2i−2i2i2i0000000000000000000000000000
χ662-22-222-2-22-2-222-2-222-22i2i−2i−2i-22−2i−2i2i2i00000000-220000-2200−2i2i00-2200−2i2i2i−2i0000−2i2i00000022-2-22i2i−2i−2i0000000000000000000000000000
χ672-22-222-2-22-2-222-2-222-2−2i−2i2i2i-222i2i−2i−2i00000000-2200002-200−2i2i002-2002i−2i−2i2i0000−2i2i000000-2-2222i2i−2i−2i0000000000000000000000000000
χ682-22-222-2-22-2-222-2-222-2−2i−2i2i2i-222i2i−2i−2i00000000-220000-22002i−2i00-22002i−2i−2i2i00002i−2i00000022-2-2−2i−2i2i2i0000000000000000000000000000
χ692-22-222-2-22-2-2-222-2-2222i2i−2i−2i2-22i2i−2i−2i22-2-22i2i−2i−2i2-2-2-222000000000000−2i−2i2i2i−2i−2i2i2i00002-22i−2i000000000000000000000000000000000000
χ702-22-222-2-22-2-2-222-2-2222i2i−2i−2i2-22i2i−2i−2i-2-222−2i−2i2i2i2-222-2-2000000000000−2i−2i2i2i2i2i−2i−2i0000-22−2i2i000000000000000000000000000000000000
χ712-22-222-2-22-2-2-222-2-222−2i−2i2i2i2-2−2i−2i2i2i22-2-2−2i−2i2i2i2-2-2-2220000000000002i2i−2i−2i2i2i−2i−2i00002-2−2i2i000000000000000000000000000000000000
χ722-22-222-2-22-2-2-222-2-222−2i−2i2i2i2-2−2i−2i2i2i-2-2222i2i−2i−2i2-222-2-20000000000002i2i−2i−2i−2i−2i2i2i0000-222i−2i000000000000000000000000000000000000
χ732-22-2-2-2222-22222-2-2-2-20000-2-2000022-2-20000222-2-2200002i−2i2i−2i000000000000−2i2i−2i2i-220000002i−2i−2i2i00002i−2i−2i2i00000000000000000000
χ742-22-2-2-2222-22222-2-2-2-20000-2-2000022-2-20000222-2-220000−2i2i−2i2i0000000000002i−2i2i−2i-22000000−2i2i2i−2i0000−2i2i2i−2i00000000000000000000
χ752-22-2-2-2222-22222-2-2-2-20000-2-20000-2-222000022-222-200002i−2i−2i2i000000000000−2i2i2i−2i2-20000002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ762-22-2-2-2222-22222-2-2-2-20000-2-20000-2-222000022-222-20000−2i2i2i−2i0000000000002i−2i−2i2i2-2000000−2i2i2i−2i00002i−2i−2i2i00000000000000000000
χ772-22-2-2-2222-22-22-2-22-22000022000000002i2i−2i−2i-2-200002-20000−2i2i-220000002i−2i−2i2i002i−2i00−2i2i2-2-22000000002i−2i−2i2i00000000000000000000
χ782-22-2-2-2222-22-22-2-22-22000022000000002i2i−2i−2i-2-20000-2200002i−2i2-20000002i−2i−2i2i00−2i2i00−2i2i-222-200000000−2i2i2i−2i00000000000000000000
χ792-22-2-2-2222-22-22-2-22-2200002200000000−2i−2i2i2i-2-200002-200002i−2i-22000000−2i2i2i−2i00−2i2i002i−2i2-2-2200000000−2i2i2i−2i00000000000000000000
χ802-22-2-2-2222-22-22-2-22-2200002200000000−2i−2i2i2i-2-20000-220000−2i2i2-2000000−2i2i2i−2i002i−2i002i−2i-222-2000000002i−2i−2i2i00000000000000000000
χ812-22-2-2-2222-2-22-222-22-2000022000000002i2i−2i−2i-2-20000002-2−2i2i0000-220000−2i2i2i−2i2i−2i0000−2i2i00002i−2i−2i2i2-2-22000000000000000000000000
χ822-22-2-2-2222-2-22-222-22-2000022000000002i2i−2i−2i-2-2000000-222i−2i00002-20000−2i2i2i−2i−2i2i0000−2i2i0000−2i2i2i−2i-222-2000000000000000000000000
χ832-22-2-2-2222-2-22-222-22-200002200000000−2i−2i2i2i-2-20000002-22i−2i0000-2200002i−2i−2i2i−2i2i00002i−2i0000−2i2i2i−2i2-2-22000000000000000000000000
χ842-22-2-2-2222-2-22-222-22-200002200000000−2i−2i2i2i-2-2000000-22−2i2i00002-200002i−2i−2i2i2i−2i00002i−2i00002i−2i−2i2i-222-2000000000000000000000000
χ852-22-2-2-2222-2-2-2-2-222220000-2-2000022-2-2000022-222-22-22-20000-22-22000000000000-2200-222-20000-222-2000000000000000000000000
χ862-22-2-2-2222-2-2-2-2-222220000-2-2000022-2-2000022-222-2-22-2200002-22-2000000000000-22002-2-2200002-2-22000000000000000000000000
χ872-22-2-2-2222-2-2-2-2-222220000-2-20000-2-2220000222-2-222-2-220000-222-20000000000002-200-222-200002-2-22000000000000000000000000
χ882-22-2-2-2222-2-2-2-2-222220000-2-20000-2-2220000222-2-22-222-200002-2-220000000000002-2002-2-220000-222-2000000000000000000000000
χ8944444-4-44-4-4000000004-44-4000000000000000000000000000000000000000000000000000000000000000022-2-22-22-2000000000000
χ9044444-4-44-4-4000000004-44-40000000000000000000000000000000000000000000000000000000000000000-2-222-22-22000000000000
χ9144444-4-44-4-400000000-44-44000000000000000000000000000000000000000000000000000000000000000022-2-2-22-22000000000000
χ9244444-4-44-4-400000000-44-440000000000000000000000000000000000000000000000000000000000000000-2-2222-22-2000000000000
χ934-44-44-44-4-44000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000002-2-222i−2i−2i2i000000000000
χ944-44-44-44-4-44000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000-222-2−2i2i2i−2i000000000000
χ954-44-44-44-4-4400000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000002-2-22−2i2i2i−2i000000000000
χ964-44-44-44-4-4400000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000-222-22i−2i−2i2i000000000000
χ978888-888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8000000000000000000004i−4i4i−4i4-44-44i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8000000000000000000004i−4i4i−4i-44-44−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-800000000000000000000−4i4i−4i4i4-44-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-800000000000000000000−4i4i−4i4i-44-444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88000000000000000000004-4-444-4-444-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88000000000000000000004-4-44-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-8800000000000000000000-444-44-4-44-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-8800000000000000000000-444-4-444-44-4-440000000000000000000000000000000000000000000000000000000000000000000000

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