Finite Group Databasebeta

← Group #72312546

Character table — Group #72312546

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106
size111111112222444444444444444444444444888888888888888888888888888888888888888888888888881616161616161616323232323232323232323232
order1222444422442222222222444444444488884444444444444444444488888888888888888888888888888822224444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ611111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ91111111111111111-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ111111111111111111-1-1-1-11111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ121111111111111111-1-1-1-11111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ131111111111111111-1-1-1-11111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111
χ141111111111111111-1-1-1-11111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1
χ151111111111111111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1
χ161111111111111111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1-1-111
χ171-1-1111-1-11-1-1111-1-111-1-11-1111-1-111-1-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−iii−i−iii−i−i111-1-1-111-1-11-11-11-11-11-11-1i−ii−ii−ii−i
χ181-1-1111-1-11-1-1111-1-111-1-11-1111-1-111-1-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−iii−i−iii−i−i111-1-1-111-1-1-11-11-11-11-11-11−ii−ii−ii−ii
χ191-1-1111-1-11-1-1111-1-111-1-11-1111-1-111-1-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii−i−iii−i−iii111-1-1-111-1-11-11-11-11-11-11-1−ii−ii−ii−ii
χ201-1-1111-1-11-1-1111-1-111-1-11-1111-1-111-1-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii−i−iii−i−iii111-1-1-111-1-1-11-11-11-11-11-11i−ii−ii−ii−i
χ211-1-1111-1-11-1-1111-1-111-1-11-1111-1-111-1-1-1-1-111ii−i−iii−i−i11-1-1ii−i−iii−i−i-1-111−i−iii−i−iii−i−iii−i−iii-1-1-1111-1-1111-1-111-1-111-1-11i−i−iii−i−ii
χ221-1-1111-1-11-1-1111-1-111-1-11-1111-1-111-1-1-1-1-111ii−i−iii−i−i11-1-1ii−i−iii−i−i-1-111−i−iii−i−iii−i−iii−i−iii-1-1-1111-1-111-111-1-111-1-111-1−iii−i−iii−i
χ231-1-1111-1-11-1-1111-1-111-1-11-1111-1-111-1-1-1-1-111−i−iii−i−iii11-1-1−i−iii−i−iii-1-111ii−i−iii−i−iii−i−iii−i−i-1-1-1111-1-1111-1-111-1-111-1-11−iii−i−iii−i
χ241-1-1111-1-11-1-1111-1-111-1-11-1111-1-111-1-1-1-1-111−i−iii−i−iii11-1-1−i−iii−i−iii-1-111ii−i−iii−i−iii−i−iii−i−i-1-1-1111-1-111-111-1-111-1-111-1i−i−iii−i−ii
χ251-1-1111-1-11-1-1111-1-1-1-1111-1111-1-1-1-111-111-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii-1-111ii−i−i−i−iiiii−i−i−i−iii111-1-1-1-1-1111-11-11-11-1-11-11i−ii−i−ii−ii
χ261-1-1111-1-11-1-1111-1-1-1-1111-1111-1-1-1-111-111-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii-1-111ii−i−i−i−iiiii−i−i−i−iii111-1-1-1-1-111-11-11-11-111-11-1−ii−iii−ii−i
χ271-1-1111-1-11-1-1111-1-1-1-1111-1111-1-1-1-111-111-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i−i−iiiii−i−i111-1-1-1-1-1111-11-11-11-1-11-11−ii−iii−ii−i
χ281-1-1111-1-11-1-1111-1-1-1-1111-1111-1-1-1-111-111-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i−i−iiiii−i−i111-1-1-1-1-111-11-11-11-111-11-1i−ii−i−ii−ii
χ291-1-1111-1-11-1-1111-1-1-1-1111-1111-1-1-1-111-1-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i−i−iiiii−i−i-1-1-111111-1-11-1-111-1-11-111-1i−i−ii−iii−i
χ301-1-1111-1-11-1-1111-1-1-1-1111-1111-1-1-1-111-1-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i−i−iiiii−i−i-1-1-111111-1-1-111-1-111-11-1-11−iii−ii−i−ii
χ311-1-1111-1-11-1-1111-1-1-1-1111-1111-1-1-1-111-1-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iiiii−i−i−i−iii-1-1-111111-1-11-1-111-1-11-111-1−iii−ii−i−ii
χ321-1-1111-1-11-1-1111-1-1-1-1111-1111-1-1-1-111-1-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iiiii−i−i−i−iii-1-1-111111-1-1-111-1-111-11-1-11i−i−ii−iii−i
χ332222222222222-22-20000-2-22-2-2-2-20000222220000222200000000-2-2-2-200000000-2-2-2-2000022222-2-22-2-2000000000000000000000000
χ342222222222222-22-20000-2-22-2-2-2-20000222220000-2-2-2-20000000022220000000022220000-2-2-2-22-2-22-2-2000000000000000000000000
χ352222222222222-22-20000-2-22-2-2-2-200002-2-2-2-20000222200000000-2-2-2-20000000022220000-2-2-2-2-222-222000000000000000000000000
χ362222222222222-22-20000-2-22-2-2-2-200002-2-2-2-20000-2-2-2-200000000222200000000-2-2-2-200002222-222-222000000000000000000000000
χ37222222222222-22-2-20000-22-22-22-20000-22222222200000000-2-2-2-200000000-2-2-2-2000022220000-22-2-22-2000000000000000000000000
χ38222222222222-22-2-20000-22-22-22-20000-22222-2-2-2-20000000022220000000022220000-2-2-2-20000-22-2-22-2000000000000000000000000
χ39222222222222-22-2-20000-22-22-22-20000-2-2-2-2-2222200000000-2-2-2-20000000022220000-2-2-2-200002-222-22000000000000000000000000
χ40222222222222-22-2-20000-22-22-22-20000-2-2-2-2-2-2-2-2-200000000222200000000-2-2-2-20000222200002-222-22000000000000000000000000
χ41222222222222-2-2-2222222-2-2-22-222222-2222200000000-2-2-2-200000000-2-2-2-20000000000000000-2-22-2-22222200000000000000000000
χ42222222222222-2-2-2222222-2-2-22-222222-2-2-2-2-200000000-2-2-2-2000000002222000000000000000022-222-2-2-2-2-200000000000000000000
χ43222222222222-2-2-22-2-2-2-22-2-2-22-22-2-2-2-2-222220000000022220000000022220000000000000000-2-22-2-22-2-2-2-200000000000000000000
χ44222222222222-2-2-22-2-2-2-22-2-2-22-22-2-2-2-2-2-2-2-2-200000000222200000000-2-2-2-2000000000000000022-222-2222200000000000000000000
χ452222-2-2-2-222-2-2222-20000-22-2-22-220000-200002-22-2000000002-22-200002i−2i2i−2i00002i−2i2i−2i00002i−2i2i−2i0000002i−2i2i−2i00000000000000000000
χ462222-2-2-2-222-2-2222-20000-22-2-22-220000-200002-22-2000000002-22-20000−2i2i−2i2i0000−2i2i−2i2i0000−2i2i−2i2i000000−2i2i−2i2i00000000000000000000
χ472222-2-2-2-222-2-2222-20000-22-2-22-220000-20000-22-2200000000-22-2200002i−2i2i−2i0000−2i2i−2i2i0000−2i2i−2i2i0000002i−2i2i−2i00000000000000000000
χ482222-2-2-2-222-2-2222-20000-22-2-22-220000-20000-22-2200000000-22-220000−2i2i−2i2i00002i−2i2i−2i00002i−2i2i−2i000000−2i2i−2i2i00000000000000000000
χ492222-2-2-2-222-2-22-22222222-2-22-22-2-2-2-2-2-20000000000002-22-20000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ502222-2-2-2-222-2-22-22222222-2-22-22-2-2-2-2-2-20000000000002-22-2000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ512222-2-2-2-222-2-22-222-2-2-2-22-2-22-22-22222-2000000000000-22-220000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ522222-2-2-2-222-2-22-222-2-2-2-22-2-22-22-22222-2000000000000-22-22000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
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χ542222-2-2-2-222-2-2-22-222222222-2-2-2-2-2-2-2-220000-22-22-22-22-22-222-22-2-22-2200000000000000000000000000000000000000000000000000
χ552222-2-2-2-222-2-2-22-22-2-2-2-2222-2-2-2-22222200002-22-2-22-222-22-2-22-22-22-2200000000000000000000000000000000000000000000000000
χ562222-2-2-2-222-2-2-22-22-2-2-2-2222-2-2-2-2222220000-22-222-22-22-22-22-22-22-22-200000000000000000000000000000000000000000000000000
χ572222-2-2-2-222-2-2-2-2-2-20000-2-22222200002000000002-22-200000000-22-222i−2i2i−2i−2i2i−2i2i00002i−2i2i−2i0000000000−2i2i−2i2i00000000000000000000
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χ592222-2-2-2-222-2-2-2-2-2-20000-2-2222220000200000000-22-22000000002-22-22i−2i2i−2i2i−2i2i−2i0000−2i2i−2i2i0000000000−2i2i−2i2i00000000000000000000
χ602222-2-2-2-222-2-2-2-2-2-20000-2-2222220000200000000-22-22000000002-22-2−2i2i−2i2i−2i2i−2i2i00002i−2i2i−2i00000000002i−2i2i−2i00000000000000000000
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χ632-2-2222-2-22-2-222-2-220000-222-2-2220000-2-2-22200002i2i−2i−2i00000000−2i−2i2i2i000000002i2i−2i−2i0000−2i−2i2i2i-2222-2-2000000000000000000000000
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χ652-2-2222-2-22-2-22-22220000-2-2-22-2-220000222-2-22i2i−2i−2i00000000−2i−2i2i2i00000000−2i−2i2i2i00002i2i−2i−2i0000-22-22-22000000000000000000000000
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χ762-2-22-2-2222-22-222-220000-2-2-2-222-2000020000−2i2i2i−2i00000000−2i2i2i−2i0000−2i2i2i−2i0000-222-20000-222-2000000−2i2i2i−2i00000000000000000000
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χ782-2-22-2-2222-22-22-2-2-222-2-222-22-2-22-2-22220000000000002-2-22000000000000-222-2-222-2-222-22-2-22000000000000000000000000000000
χ792-2-22-2-2222-22-22-2-2-2-2-22222-22-2-2222-2-22000000000000-222-20000000000002-2-22-222-22-2-222-2-22000000000000000000000000000000
χ802-2-22-2-2222-22-22-2-2-2-2-22222-22-2-2222-2-22000000000000-222-2000000000000-222-22-2-22-222-2-222-2000000000000000000000000000000
χ812-2-22-2-2222-22-2-222-222-2-22-22-2-222-2-222-200002i−2i−2i2i2i−2i−2i2i-222-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000000000000000
χ822-2-22-2-2222-22-2-222-222-2-22-22-2-222-2-222-20000−2i2i2i−2i−2i2i2i−2i-222-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000000000000000
χ832-2-22-2-2222-22-2-222-2-2-2222-22-2-22222-2-2-200002i−2i−2i2i−2i2i2i−2i2-2-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000000000000000000000
χ842-2-22-2-2222-22-2-222-2-2-2222-22-2-22222-2-2-20000−2i2i2i−2i2i−2i−2i2i2-2-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000000000000000000000
χ852-2-22-2-2222-22-2-2-2220000-22222-2-20000-2000000002i−2i−2i2i00000000−2i2i2i−2i2i−2i−2i2i2-2-220000-222-20000000000−2i2i2i−2i00000000000000000000
χ862-2-22-2-2222-22-2-2-2220000-22222-2-20000-2000000002i−2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i-222-200002-2-2200000000002i−2i−2i2i00000000000000000000
χ872-2-22-2-2222-22-2-2-2220000-22222-2-20000-200000000−2i2i2i−2i000000002i−2i−2i2i2i−2i−2i2i-222-200002-2-220000000000−2i2i2i−2i00000000000000000000
χ882-2-22-2-2222-22-2-2-2220000-22222-2-20000-200000000−2i2i2i−2i000000002i−2i−2i2i−2i2i2i−2i2-2-220000-222-200000000002i−2i−2i2i00000000000000000000
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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−8i000000004-44-400000004i−4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-88i−8i8i−8i00000000-44-440000000−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8−8i8i−8i8i000000004-44-40000000−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8−8i8i−8i8i00000000-44-4400000004i−4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-88i−8i−8i8i000000004-4-4400000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-88i−8i−8i8i00000000-444-40000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8−8i8i8i−8i000000004-4-440000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8−8i8i8i−8i00000000-444-400000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-8888-8-8-888-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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