Finite Group Databasebeta

← Group #72271332

Character table — Group #72271332

Order 12288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size11112244888812121616161616161616161624242424244848484848484848484848484848646464646464646496969696128128128128128128128128128128128128192192192192256256256256256256256256256256256256256256256256256256256256256256256256384384384384384
order12222222222222224444444424444224444444444443366666622446666666666664444666666661212121212121212121212121212121248888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−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+i3211111
χ31111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+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−i3211111
χ411111111111111-1-111-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-1111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-1-1-1
χ511111111111111-1-111-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1-1-1-1
χ611111111111111-1-111-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1-1-1-1
χ711111111-1-1-1-1111-1-1-11-111-1-1111111-11-111-1-1-1-111-1-111111111111111-1-1-1-111-1-1-1-111-1-1111-1111-111-1-111-1-1-1-11-1-1-11-1-111-1-1
χ811111111-1-1-1-1111-1-1-11-111-1-1111111-11-111-1-1-1-111-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i3211-1-1−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i32−1−i321+i321−i321−i32−1+i321−i32-111-1-1
χ911111111-1-1-1-1111-1-1-11-111-1-1111111-11-111-1-1-1-111-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i3211-1-1−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i32−1+i321−i321+i321+i32−1−i321+i32-111-1-1
χ1011111111-1-1-1-111-11-1-1-11-1-11111111-11-1111-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-111-1111-11-1-111-1-111-1-1-11-1-1-11-1-1-111
χ1111111111-1-1-1-111-11-1-1-11-1-11111111-11-1111-1-1-1-1-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i3211-1-1−1−i32−1−i321+i32−1−i32−1+i32−1+i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321+i32−1−i321−i321−i321−i32−1+i32-1-1-111
χ1211111111-1-1-1-111-11-1-1-11-1-11111111-11-1111-1-1-1-1-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i3211-1-1−1+i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321−i32−1+i321+i321+i321+i32−1−i32-1-1-111
χ13333333333333333333333333333333333333333333300000000-1-1-1-1000000000000-1-1-1-1000000000000000000000000-1-1-1-1-1
χ1433333333333333-3-333-3-3-3-3-3-333333-3-3-3-3333333-3-3-3-300000000-1-1-1-1000000000000-1-1-1-1000000000000000000000000-11111
χ1533333333-3-3-3-3333-3-3-33-333-3-3333333-33-333-3-3-3-333-3-300000000-1-1-1-1000000000000-1-1110000000000000000000000001-1-111
χ1633333333-3-3-3-333-33-3-3-33-3-33333333-33-3333-3-3-3-3-3-33300000000-1-1-1-1000000000000-1-111000000000000000000000000111-1-1
χ17444444-4-444444422-4-422-2-2-2-2-400002222000000-2-2-2-21111111100001111111111110000-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-100000
χ18444444-4-444444422-4-422-2-2-2-2-400002222000000-2-2-2-2−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i320000−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3200001+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3200000
χ19444444-4-444444422-4-422-2-2-2-2-400002222000000-2-2-2-2−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i320000−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3200001−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3200000
χ20444444-4-4444444-2-2-4-4-2-22222-40000-2-2-2-200000022221111111100001111111111110000-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-11100000
χ21444444-4-4444444-2-2-4-4-2-22222-40000-2-2-2-20000002222−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i320000−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3200001+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200000
χ22444444-4-4444444-2-2-4-4-2-22222-40000-2-2-2-20000002222−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i320000−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3200001−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200000
χ23444444-4-4-4-4-4-4442-2442-2-2-222-400002-22-2000000-2-22211111111000011-1-1-1-111-1-1-1-10000-1-1-11-1-1-1111-1-111-1-111-1111-1100000
χ24444444-4-4-4-4-4-4442-2442-2-2-222-400002-22-2000000-2-222−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i320000−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i3200001+i321+i321+i32−1−i321−i321−i321−i32−1+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+i3200000
χ25444444-4-4-4-4-4-4442-2442-2-2-222-400002-22-2000000-2-222−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i320000−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i3200001−i321−i321−i32−1+i321+i321+i321+i32−1−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−i3200000
χ26444444-4-4-4-4-4-444-2244-2222-2-2-40000-22-2200000022-2-211111111000011-1-1-1-111-1-1-1-10000-1-11-1-1-11-1-1-111-1-111111-1111-100000
χ27444444-4-4-4-4-4-444-2244-2222-2-2-40000-22-2200000022-2-2−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i320000−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i3200001+i321+i32−1−i321+i321−i321−i32−1+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i321−i3200000
χ28444444-4-4-4-4-4-444-2244-2222-2-2-40000-22-2200000022-2-2−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i320000−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i3200001−i321−i32−1+i321−i321+i321+i32−1−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i3200000
χ294444-4-44-422-2-200242-2-2-42-24-40004-4-20200022-2-22-200111111110000-1-111-1-1-1-111-1-100001-1-111-1-111-11-11-11-11-11-11-11-100000
χ304444-4-44-422-2-200242-2-2-42-24-40004-4-20200022-2-22-200−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3200001+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i320000−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i3200000
χ314444-4-44-422-2-200242-2-2-42-24-40004-4-20200022-2-22-200−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3200001−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i320000−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i3200000
χ324444-4-44-422-2-200-2-42-224-22-440004-420-200022-2-2-2200111111110000-1-111-1-1-1-111-1-100001-11-11-11-1-11-11-11-111-1-111-1-1100000
χ334444-4-44-422-2-200-2-42-224-22-440004-420-200022-2-2-2200−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3200001+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i320000−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i3200000
χ344444-4-44-422-2-200-2-42-224-22-440004-420-200022-2-2-2200−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3200001−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i320000−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i3200000
χ354444-4-44-4-2-222002-4-22-242-2-440004-4-202000-2-2222-200111111110000-1-1-1-111-1-1-1-11100001-1-1-11-1-1-11-1-111-1-11-1111-111100000
χ364444-4-44-4-2-222002-4-22-242-2-440004-4-202000-2-2222-200−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3200001+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i320000−1−i321+i321+i321+i32−1+i321−i321−i321−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i32−1−i321−i32−1+i32−1+i32−1+i3200000
χ374444-4-44-4-2-222002-4-22-242-2-440004-4-202000-2-2222-200−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3200001−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i320000−1+i321−i321−i321−i32−1−i321+i321+i321+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i32−1+i321+i32−1−i32−1−i32−1−i3200000
χ384444-4-44-4-2-22200-24-222-4-224-40004-420-2000-2-222-2200111111110000-1-1-1-111-1-1-1-11100001-1111-111-111-1-111-1-11-1-1-11-1-100000
χ394444-4-44-4-2-22200-24-222-4-224-40004-420-2000-2-222-2200−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3200001+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i320000−1−i321+i32−1−i32−1−i32−1+i321−i32−1+i32−1+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i321+i32−1−i321+i321+i321−i32−1+i321−i321−i3200000
χ404444-4-44-4-2-22200-24-222-4-224-40004-420-2000-2-222-2200−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3200001−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i320000−1+i321−i32−1+i32−1+i32−1−i321+i32−1−i32−1−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i321−i32−1+i321−i321−i321+i32−1−i321+i321+i3200000
χ414444-4-4-4422-2-20042-22-4-2-44-2204-4000-202002-22-2002-2111111110000-1-111-1-1-1-111-1-10000-111-1-111-11-11-11-11-1-11-11-11-1100000
χ424444-4-4-4422-2-20042-22-4-2-44-2204-4000-202002-22-2002-2−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3200001+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i3200001+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i3200000
χ434444-4-4-4422-2-20042-22-4-2-44-2204-4000-202002-22-2002-2−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3200001−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i3200001−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i3200000
χ444444-4-4-4422-2-200-4-2-22424-42-204-400020-2002-22-200-22111111110000-1-111-1-1-1-111-1-10000-11-11-11-11-11-11-11-11-111-1-111-100000
χ454444-4-4-4422-2-200-4-2-22424-42-204-400020-2002-22-200-22−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3200001+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i3200001+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i3200000
χ464444-4-4-4422-2-200-4-2-22424-42-204-400020-2002-22-200-22−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3200001−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i3200001−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i3200000
χ474444-4-4-44-2-222004-22-2-42-442-204-400020-200-22-2200-22111111110000-1-1-1-111-1-1-1-1110000-1111-11111-1-111-1-111-1-1-11-1-1-100000
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Here i is the imaginary unit (i² = −1).