Finite Group Databasebeta

← Group #72312131

Character table — Group #72312131

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106
size111111112222444444444444444444444444888888888888888888888888888888888888888888888888881616161616161616323232323232323232323232
order1222444422442222224444444444444488882244444444444444444488888888888888888888888888888822224444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111
χ711111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1
χ811111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111
χ911111111111111111111111-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-1
χ1011111111111111111111111-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ1111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111111111-1-111-1-111-1-1-1-1
χ1211111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ1311111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-111
χ1411111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1
χ1511111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111
χ1611111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1
χ171-1-1111-1-11-1-11111-1-1-111-1-1-11111-1-1-1-1111-1-11-1ii−i−iii−i−i1-1ii−i−iii−i−i11-1-1ii−i−iii−i−iii−i−iii−i−i111-1-1-111-1-11-11-11-11-1i−ii−ii−ii−i1-11-1
χ181-1-1111-1-11-1-11111-1-1-111-1-1-11111-1-1-1-1111-1-11-1ii−i−iii−i−i1-1ii−i−iii−i−i11-1-1ii−i−iii−i−iii−i−iii−i−i111-1-1-111-1-1-11-11-11-11−ii−ii−ii−ii-11-11
χ191-1-1111-1-11-1-11111-1-1-111-1-1-11111-1-1-1-1111-1-11-1−i−iii−i−iii1-1−i−iii−i−iii11-1-1−i−iii−i−iii−i−iii−i−iii111-1-1-111-1-11-11-11-11-1−ii−ii−ii−ii1-11-1
χ201-1-1111-1-11-1-11111-1-1-111-1-1-11111-1-1-1-1111-1-11-1−i−iii−i−iii1-1−i−iii−i−iii11-1-1−i−iii−i−iii−i−iii−i−iii111-1-1-111-1-1-11-11-11-11i−ii−ii−ii−i-11-11
χ211-1-1111-1-11-1-11111-1-1-111-1-1-11111-1-1-1-11-1-1111-1ii−i−iii−i−i1-1ii−i−iii−i−i-1-111−i−iii−i−iii−i−iii−i−iii-1-1-1111-1-1111-1-111-1-11i−ii−i−ii−ii1-1-11
χ221-1-1111-1-11-1-11111-1-1-111-1-1-11111-1-1-1-11-1-1111-1ii−i−iii−i−i1-1ii−i−iii−i−i-1-111−i−iii−i−iii−i−iii−i−iii-1-1-1111-1-111-111-1-111-1−ii−iii−ii−i-111-1
χ231-1-1111-1-11-1-11111-1-1-111-1-1-11111-1-1-1-11-1-1111-1−i−iii−i−iii1-1−i−iii−i−iii-1-111ii−i−iii−i−iii−i−iii−i−i-1-1-1111-1-1111-1-111-1-11−ii−iii−ii−i1-1-11
χ241-1-1111-1-11-1-11111-1-1-111-1-1-11111-1-1-1-11-1-1111-1−i−iii−i−iii1-1−i−iii−i−iii-1-111ii−i−iii−i−iii−i−iii−i−i-1-1-1111-1-111-111-1-111-1i−ii−i−ii−ii-111-1
χ251-1-1111-1-11-1-11111-1-1-111-1-1-1-1-1-1-11111111-1-1-11ii−i−i−i−iii-11ii−i−i−i−iii-1-111ii−i−i−i−iiiii−i−i−i−iii111-1-1-1-1-1111-11-11-11-1i−i−iii−i−ii-11-11
χ261-1-1111-1-11-1-11111-1-1-111-1-1-1-1-1-1-11111111-1-1-11ii−i−i−i−iii-11ii−i−i−i−iii-1-111ii−i−i−i−iiiii−i−i−i−iii111-1-1-1-1-111-11-11-11-11−iii−i−iii−i1-11-1
χ271-1-1111-1-11-1-11111-1-1-111-1-1-1-1-1-1-11111111-1-1-11−i−iiiii−i−i-11−i−iiiii−i−i-1-111−i−iiiii−i−i−i−iiiii−i−i111-1-1-1-1-1111-11-11-11-1−iii−i−iii−i-11-11
χ281-1-1111-1-11-1-11111-1-1-111-1-1-1-1-1-1-11111111-1-1-11−i−iiiii−i−i-11−i−iiiii−i−i-1-111−i−iiiii−i−i−i−iiiii−i−i111-1-1-1-1-111-11-11-11-11i−i−iii−i−ii1-11-1
χ291-1-1111-1-11-1-11111-1-1-111-1-1-1-1-1-1-111111-1-111-11ii−i−i−i−iii-11ii−i−i−i−iii11-1-1−i−iiiii−i−i−i−iiiii−i−i-1-1-111111-1-11-1-111-1-11i−i−ii−iii−i-111-1
χ301-1-1111-1-11-1-11111-1-1-111-1-1-1-1-1-1-111111-1-111-11ii−i−i−i−iii-11ii−i−i−i−iii11-1-1−i−iiiii−i−i−i−iiiii−i−i-1-1-111111-1-1-111-1-111-1−iii−ii−i−ii1-1-11
χ311-1-1111-1-11-1-11111-1-1-111-1-1-1-1-1-1-111111-1-111-11−i−iiiii−i−i-11−i−iiiii−i−i11-1-1ii−i−i−i−iiiii−i−i−i−iii-1-1-111111-1-11-1-111-1-11−iii−ii−i−ii-111-1
χ321-1-1111-1-11-1-11111-1-1-111-1-1-1-1-1-1-111111-1-111-11−i−iiiii−i−i-11−i−iiiii−i−i11-1-1ii−i−i−i−iiiii−i−i−i−iii-1-1-111111-1-1-111-1-111-1i−i−ii−iii−i1-1-11
χ332222222222222-2-22-2-2-2-22-2-22222222222222-2-200000000-2-200000000222200000000000000002-2-22-2-2-2-2-2-200000000000000000000
χ342222222222222-2-22-2-2-2-22-2-2222222222-2-2-2-2-2-200000000-2-200000000-2-2-2-20000000000000000-222-222222200000000000000000000
χ352222222222222-2-22-2-2-2-22-2-2-2-2-2-2-2-2-2-22222222000000002200000000-2-2-2-200000000000000002-2-22-2-2222200000000000000000000
χ362222222222222-2-22-2-2-2-22-2-2-2-2-2-2-2-2-2-22-2-2-2-22200000000220000000022220000000000000000-222-222-2-2-2-200000000000000000000
χ37222222222222-22-2-22-22-2-22-200000000-222220000002222000000-2-2-2-200000000-2-2-2-200002222-22-2-22-2000000000000000000000000
χ38222222222222-22-2-22-22-2-22-200000000-22222000000-2-2-2-200000022220000000022220000-2-2-2-2-22-2-22-2000000000000000000000000
χ39222222222222-22-2-22-22-2-22-200000000-2-2-2-2-20000002222000000-2-2-2-20000000022220000-2-2-2-22-222-22000000000000000000000000
χ40222222222222-22-2-22-22-2-22-200000000-2-2-2-2-2000000-2-2-2-2000000222200000000-2-2-2-2000022222-222-22000000000000000000000000
χ41222222222222-2-22-2-22-22-2-2200000000-22222002222000000-2-2-2-200000000-2-2-2-2000022220000-2-22-2-22000000000000000000000000
χ42222222222222-2-22-2-22-22-2-2200000000-2222200-2-2-2-200000022220000000022220000-2-2-2-20000-2-22-2-22000000000000000000000000
χ43222222222222-2-22-2-22-22-2-2200000000-2-2-2-2-2002222000000-2-2-2-20000000022220000-2-2-2-2000022-222-2000000000000000000000000
χ44222222222222-2-22-2-22-22-2-2200000000-2-2-2-2-200-2-2-2-2000000222200000000-2-2-2-200002222000022-222-2000000000000000000000000
χ452222-2-2-2-222-2-222-222-2-22-2-2200000000-200000000002-22-20000002-22-22i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i00000000002i−2i2i−2i00000000000000000000
χ462222-2-2-2-222-2-222-222-2-22-2-2200000000-200000000002-22-20000002-22-2−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i0000000000−2i2i−2i2i00000000000000000000
χ472222-2-2-2-222-2-222-222-2-22-2-2200000000-20000000000-22-22000000-22-222i−2i2i−2i−2i2i−2i2i0000−2i2i−2i2i00000000002i−2i2i−2i00000000000000000000
χ482222-2-2-2-222-2-222-222-2-22-2-2200000000-20000000000-22-22000000-22-22−2i2i−2i2i2i−2i2i−2i00002i−2i2i−2i0000000000−2i2i−2i2i00000000000000000000
χ492222-2-2-2-222-2-22-222-222-2-22-200000000-20000002-22-20000002-22-200002i−2i2i−2i00002i−2i2i−2i00002i−2i2i−2i000000−2i2i−2i2i00000000000000000000
χ502222-2-2-2-222-2-22-222-222-2-22-200000000-20000002-22-20000002-22-20000−2i2i−2i2i0000−2i2i−2i2i0000−2i2i−2i2i0000002i−2i2i−2i00000000000000000000
χ512222-2-2-2-222-2-22-222-222-2-22-200000000-2000000-22-22000000-22-2200002i−2i2i−2i0000−2i2i−2i2i0000−2i2i−2i2i000000−2i2i−2i2i00000000000000000000
χ522222-2-2-2-222-2-22-222-222-2-22-200000000-2000000-22-22000000-22-220000−2i2i−2i2i00002i−2i2i−2i00002i−2i2i−2i0000002i−2i2i−2i00000000000000000000
χ532222-2-2-2-222-2-2-222-222-2-22-2-222-2-222-2-220000222-22-22-22-2-2-2-22-22-22-2200000000000000000000000000000000000000000000000000
χ542222-2-2-2-222-2-2-222-222-2-22-2-222-2-222-2-22000022-22-22-22-22-2-22-22-22-22-200000000000000000000000000000000000000000000000000
χ552222-2-2-2-222-2-2-222-222-2-22-2-2-2-222-2-22220000-2-22-22-2-22-2222-22-222-22-200000000000000000000000000000000000000000000000000
χ562222-2-2-2-222-2-2-222-222-2-22-2-2-2-222-2-22220000-2-2-22-222-22-2222-22-2-22-2200000000000000000000000000000000000000000000000000
χ572222-2-2-2-222-2-2-2-2-2-2-2-22222222-2-222-2-220000-2-200000000220000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ582222-2-2-2-222-2-2-2-2-2-2-2-22222222-2-222-2-220000-2-20000000022000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ592222-2-2-2-222-2-2-2-2-2-2-2-222222-2-222-2-222200002200000000-2-20000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ602222-2-2-2-222-2-2-2-2-2-2-2-222222-2-222-2-222200002200000000-2-2000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ612-2-2222-2-22-2-222-2-2-222-2-2-2222222-2-2-2-2222-2-2-2200000000-220000000022-2-200000000000000002-2-2-222-2-22200000000000000000000
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χ632-2-2222-2-22-2-222-2-2-222-2-2-222-2-2-2-22222222-2-22-2000000002-200000000-2-22200000000000000002-2-2-22222-2-200000000000000000000
χ642-2-2222-2-22-2-222-2-2-222-2-2-222-2-2-2-222222-2-2222-2000000002-20000000022-2-20000000000000000-2222-2-2-2-22200000000000000000000
χ652-2-2222-2-22-2-22-22-22-222-22-2200000000-222-2-20000002i2i−2i−2i000000−2i−2i2i2i00000000−2i−2i2i2i00002i2i−2i−2i-22-22-22000000000000000000000000
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χ702-2-2222-2-22-2-22-2-2222-2-2222-200000000-222-2-200−2i−2i2i2i0000002i2i−2i−2i000000002i2i−2i−2i0000−2i−2i2i2i0000-2-2222-2000000000000000000000000
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χ742-2-22-2-2222-22-222-2-2-22-2222-200000000-200000000002i−2i−2i2i0000002i−2i−2i2i−2i2i2i−2i2-2-2200002-2-220000000000−2i2i2i−2i00000000000000000000
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χ762-2-22-2-2222-22-222-2-2-22-2222-200000000-20000000000−2i2i2i−2i000000−2i2i2i−2i−2i2i2i−2i-222-20000-222-20000000000−2i2i2i−2i00000000000000000000
χ772-2-22-2-2222-22-22-22-22-22-22-2200000000-20000002i−2i−2i2i0000002i−2i−2i2i00002i−2i−2i2i0000-222-20000-222-2000000−2i2i2i−2i00000000000000000000
χ782-2-22-2-2222-22-22-22-22-22-22-2200000000-20000002i−2i−2i2i0000002i−2i−2i2i0000−2i2i2i−2i00002-2-2200002-2-220000002i−2i−2i2i00000000000000000000
χ792-2-22-2-2222-22-22-22-22-22-22-2200000000-2000000−2i2i2i−2i000000−2i2i2i−2i00002i−2i−2i2i00002-2-2200002-2-22000000−2i2i2i−2i00000000000000000000
χ802-2-22-2-2222-22-22-22-22-22-22-2200000000-2000000−2i2i2i−2i000000−2i2i2i−2i0000−2i2i2i−2i0000-222-20000-222-20000002i−2i−2i2i00000000000000000000
χ812-2-22-2-2222-22-2-2222-2-2-2-2-22222-2-2-2-222200002-22i−2i−2i2i2i−2i−2i2i-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000000000000000000000
χ822-2-22-2-2222-22-2-2222-2-2-2-2-22222-2-2-2-222200002-2−2i2i2i−2i−2i2i2i−2i-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000000000000000000000
χ832-2-22-2-2222-22-2-2222-2-2-2-2-222-2-22222-2-220000-222i−2i−2i2i−2i2i2i−2i2-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000000000000000
χ842-2-22-2-2222-22-2-2222-2-2-2-2-222-2-22222-2-220000-22−2i2i2i−2i2i−2i−2i2i2-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000000000000000
χ852-2-22-2-2222-22-2-2-2-222222-2-2-222-2-2-2-22220000-22000000002-20000000000002-2-222-2-22-222-2-222-2000000000000000000000000000000
χ862-2-22-2-2222-22-2-2-2-222222-2-2-222-2-2-2-22220000-22000000002-2000000000000-222-2-222-22-2-222-2-22000000000000000000000000000000
χ872-2-22-2-2222-22-2-2-2-222222-2-2-2-2-22222-2-2200002-200000000-220000000000002-2-22-222-2-222-22-2-22000000000000000000000000000000
χ882-2-22-2-2222-22-2-2-2-222222-2-2-2-2-22222-2-2200002-200000000-22000000000000-222-22-2-222-2-22-222-2000000000000000000000000000000
χ894444-4-4-4-4-4-444000000000000000000004-44-4000000000000000000000000000000000000000000000000002222-2-2-2-2000000000000
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χ914444-4-4-4-4-4-44400000000000000000000-44-440000000000000000000000000000000000000000000000000022-2-2-2-222000000000000
χ924444-4-4-4-4-4-44400000000000000000000-44-4400000000000000000000000000000000000000000000000000-2-22222-2-2000000000000
χ934-4-44-4-444-44-44000000000000000000004-4-44000000000000000000000000000000000000000000000000002-22-2-22-22000000000000
χ944-4-44-4-444-44-44000000000000000000004-4-4400000000000000000000000000000000000000000000000000-22-222-22-2000000000000
χ954-4-44-4-444-44-4400000000000000000000-444-4000000000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ964-4-44-4-444-44-4400000000000000000000-444-400000000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ9788888888-8-8-8-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-88i−8i8i−8i0000000000000004-44i−4i4-44i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-88i−8i8i−8i000000000000000-44−4i4i-44−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8−8i8i−8i8i0000000000000004-4−4i4i4-4−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8−8i8i−8i8i000000000000000-444i−4i-444i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-88i−8i−8i8i0000000000000004-44i−4i-44−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-88i−8i−8i8i000000000000000-44−4i4i4-44i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8−8i8i8i−8i0000000000000004-4−4i4i-444i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8−8i8i8i−8i000000000000000-444i−4i4-4−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-8888-8-8-888-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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