Finite Group Databasebeta

← Group #72271486

Character table — Group #72271486

Order 12288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size1111222248888888812121212161616161616161624242424484848484848484848484848484864646464646464649696128128128128128128128128128128128128128128128128128128128128128128128128192192192192192192192256256256256256256256256256256256256256256256256256256384384384384
order12222222222224444444422244444444424444444444444336666664466666666666666661212121212121212244888866666666121212121212121212128888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111
χ311111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111
χ411111111111-1-111-1-111111-1-11-1-1-1-11111-111-1-1-1-11111-1-1-11111111111111111-1-1111111-1-111-1-111-1-111111-1-111-1-111-1-1-1-11-1-1-11-1-1-11-1-1-1
χ511111111111-1-111-1-111111-1-11-1-1-1-11111-111-1-1-1-11111-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211111-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321−i32−1−i321+i321+i321+i32−1+i321−i321−i321−i321-1-1-1
χ611111111111-1-111-1-111111-1-11-1-1-1-11111-111-1-1-1-11111-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211111-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321+i32−1+i321−i321−i321−i32−1−i321+i321+i321+i321-1-1-1
χ7111111111-1-111-1-1111111-11-1-11-1-1-11111-1-1-111-1-111-1-111-111111111111111-1-1111111-1-111-1-111-1-111111-1-1111-11-11-11-1-1-1-11-1-1-11-1-1-11-1-1
χ8111111111-1-111-1-1111111-11-1-11-1-1-11111-1-1-111-1-111-1-111-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32111-1-111−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i321−i321+i32−1−i321+i321+i321−i32−1+i321−i321−i32-11-1-1
χ9111111111-1-111-1-1111111-11-1-11-1-1-11111-1-1-111-1-111-1-111-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32111-1-111−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i321+i321−i32−1+i321−i321−i321+i32−1−i321+i321+i32-11-1-1
χ10111111111-1-1-1-1-1-1-1-11111-1-11-1-111111111-1-1-1-11111-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-1111-1-111-1-111-1-111
χ11111111111-1-1-1-1-1-1-1-11111-1-11-1-111111111-1-1-1-11111-1-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32111-1-1-1-1−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-111
χ12111111111-1-1-1-1-1-1-1-11111-1-11-1-111111111-1-1-1-11111-1-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32111-1-1-1-1−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-111
χ133333333333333333333333333333333333333333333333300000000-1-1000000000000000000000000-1-1-1-1-1-1-1000000000000000000-1-1-1-1
χ1433333333333-3-333-3-333333-3-33-3-3-3-33333-333-3-3-3-33333-3-3-300000000-1-1000000000000000000000000-1-1-1-1-111000000000000000000-1111
χ15333333333-3-333-3-3333333-33-3-33-3-3-33333-3-3-333-3-333-3-333-300000000-1-1000000000000000000000000-1-1-111-1-10000000000000000001-111
χ16333333333-3-3-3-3-3-3-3-33333-3-33-3-333333333-3-3-3-33333-3-3-3-3300000000-1-1000000000000000000000000-1-1-1111100000000000000000011-1-1
χ1744444-44-4-42244-2-24404042-42-2-42-2-20-400222002-200-2-200-2111111110011-1-1-1-11111-1-1-1-111111111110000000-1-1-1-1-1-1-1-1111-11-11-11-10000
χ1844444-44-4-42244-2-24404042-42-2-42-2-20-400222002-200-2-200-2−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3200−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200000001+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i320000
χ1944444-44-4-42244-2-24404042-42-2-42-2-20-400222002-200-2-200-2−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3200−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3200000001−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i320000
χ2044444-44-4-422-4-4-2-2-4-4040424-2-24-2220-400-22200-2200-2-2002111111110011-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-10000000-1-111-1-111-1-111-1111-110000
χ2144444-44-4-422-4-4-2-2-4-4040424-2-24-2220-400-22200-2200-2-2002−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3200−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3200000001+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321−i32−1−i32−1−i321+i32−1−i32−1+i32−1+i321−i32−1+i320000
χ2244444-44-4-422-4-4-2-2-4-4040424-2-24-2220-400-22200-2200-2-2002−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3200−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3200000001−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321+i32−1+i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i320000
χ2344444-44-4-4-2-24422440404-2-4-22-4-2220-400-2-2-200-220022002111111110011-1-1111111-1-11111-1-111-1-1110000000-11-11-11-11-1-1-1-1-11-1-1-110000
χ2444444-44-4-4-2-24422440404-2-4-22-4-2220-400-2-2-200-220022002−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3200−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200000001+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321+i321−i321+i321+i321+i32−1−i321−i321−i321−i32−1+i320000
χ2544444-44-4-4-2-24422440404-2-4-22-4-2220-400-2-2-200-220022002−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3200−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200000001−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321−i321+i321−i321−i321−i32−1+i321+i321+i321+i32−1−i320000
χ2644444-44-4-4-2-2-4-422-4-40404-242242-2-20-4002-2-2002-2002200-2111111110011-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-10000000-111-1-111-111-111-1-111-10000
χ2744444-44-4-4-2-2-4-422-4-40404-242242-2-20-4002-2-2002-2002200-2−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3200−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i3200000001+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32−1−i32−1+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i320000
χ2844444-44-4-4-2-2-4-422-4-40404-242242-2-20-4002-2-2002-2002200-2−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3200−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i3200000001−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32−1+i32−1−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i320000
χ294444-44-44-4442244-2-24040-422-4-2-22-2-400020022-220000-2-2-21111111100-1-11111-1-1-1-11111-1-1111111110000000-1-1-1-1-1-1-1-111-11-11-11-110000
χ304444-44-44-4442244-2-24040-422-4-2-22-2-400020022-220000-2-2-2−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32001+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200000001+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i320000
χ314444-44-44-4442244-2-24040-422-4-2-22-2-400020022-220000-2-2-2−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32001−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3200000001−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i320000
χ324444-44-44-444-2-244224040-4-2-2-422-22-4000-200-2-22-200002221111111100-1-1111111-1-111111111-1-111-1-10000000-1-111-1-111-1-1-1-11-1-1-11-10000
χ334444-44-44-444-2-244224040-4-2-2-422-22-4000-200-2-22-20000222−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32001+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3200000001+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321−i321+i321+i32−1−i321+i321−i321−i32−1+i321−i320000
χ344444-44-44-444-2-244224040-4-2-2-422-22-4000-200-2-22-20000222−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32001−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3200000001−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321+i321−i321−i32−1+i321−i321+i321+i32−1−i321+i320000
χ354444-44-44-4-4-422-4-4-2-2404042-24-22-22-4000-200222-20000-2-221111111100-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1110000000-11-11-11-11-1-1111-1111-10000
χ364444-44-44-4-4-422-4-4-2-2404042-24-22-22-4000-200222-20000-2-22−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32001+i321+i32−1−i32−1−i321+i321+i321+i321+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200000001+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321+i321−i32−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i321−i320000
χ374444-44-44-4-4-422-4-4-2-2404042-24-22-22-4000-200222-20000-2-22−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32001−i321−i32−1+i32−1+i321−i321−i321−i321−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200000001−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321−i321+i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i320000
χ384444-44-44-4-4-4-2-2-4-42240404-2242-22-2-4000200-2-2-22000022-21111111100-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-10000000-111-1-111-1111-1-111-1-110000
χ394444-44-44-4-4-4-2-2-4-42240404-2242-22-2-4000200-2-2-22000022-2−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32001+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3200000001+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32−1−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i320000
χ404444-44-44-4-4-4-2-2-4-42240404-2242-22-2-4000200-2-2-22000022-2−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32001−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3200000001−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32−1+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i320000
χ414444-4-4-4-442222-2-2-2-20000-2-2422-4-44004-402-22-200002-22-201111111100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111100000001111111111-1-1-1-1-1-1-1-10000
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Here i is the imaginary unit (i² = −1).