Finite Group Databasebeta

← Group #72271297

Character table — Group #72271297

Order 12288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122448888121216161616161616161616242424242448484848484848484848484848486464646464646464128128128128128128128128128128128128192192192192192192256256256256256256256256256256256256256256256256256256256256256256256256384384384384384
order122222222222222244444444244442244444444444433666666666666666666444444666666661212121212121212121212121212121248888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111−1−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+i32111111−1−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−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111111−1+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
χ411111111111111-1-1-1-1-1-111-1-111111-1-1111111-1-1-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-1-1-1
χ511111111111111-1-1-1-1-1-111-1-111111-1-1111111-1-1-1-1-1-1−1−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+i32111111−1−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
χ611111111111111-1-1-1-1-1-111-1-111111-1-1111111-1-1-1-1-1-1−1+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−i32111111−1+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
χ711111111-1-1-1-1111-111-1-1-1-11-1111111-111-1-1-1-111-1-11-11111111111-1-1-1-111-1-1-1-11111-1-1111-1111-111-1-111-1-1-1-11-1-1-11-1-111-1-1
χ811111111-1-1-1-1111-111-1-1-1-11-1111111-111-1-1-1-111-1-11-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321111-1-1−1−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
χ911111111-1-1-1-1111-111-1-1-1-11-1111111-111-1-1-1-111-1-11-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321111-1-1−1+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
χ1011111111-1-1-1-111-11-1-111-1-1-1111111-1111-1-1-1-1-1-111-111111111111-1-1-1-111-1-1-1-11111-1-111-1111-11-1-111-1-111-1-1-11-1-1-11-1-1-111
χ1111111111-1-1-1-111-11-1-111-1-1-1111111-1111-1-1-1-1-1-111-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321111-1-1−1−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
χ1211111111-1-1-1-111-11-1-111-1-1-1111111-1111-1-1-1-1-1-111-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321111-1-1−1+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
χ13333333333333333333333333333333333333333333300000000000000000000-1-1-1-1-1-1000000000000000000000000-1-1-1-1-1
χ1433333333333333-3-3-3-3-3-333-3-333333-3-3333333-3-3-3-3-3-300000000000000000000-1-1-1-1-1-1000000000000000000000000-11111
χ1533333333-3-3-3-3333-333-3-3-3-33-3333333-333-3-3-3-333-3-33-300000000000000000000-1-1-1-1110000000000000000000000001-1-111
χ1633333333-3-3-3-333-33-3-333-3-3-3333333-3333-3-3-3-3-3-333-3300000000000000000000-1-1-1-111000000000000000000000000111-1-1
χ17444444-4-444444422-2-2-2-2-4-422-4000022000000-2-2-2-22211111111111111111111000000-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-100000
χ18444444-4-444444422-2-2-2-2-4-422-4000022000000-2-2-2-222−1−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+i320000001+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
χ19444444-4-444444422-2-2-2-2-4-422-4000022000000-2-2-2-222−1+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−i320000001−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
χ20444444-4-4444444-2-22222-4-4-2-2-40000-2-20000002222-2-211111111111111111111000000-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-11100000
χ21444444-4-4444444-2-22222-4-4-2-2-40000-2-20000002222-2-2−1−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+i320000001+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
χ22444444-4-4444444-2-22222-4-4-2-2-40000-2-20000002222-2-2−1+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−i320000001−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
χ23444444-4-4-4-4-4-4442-2-2-222442-2-400002-2000000-2-2222-21111111111-1-1-1-111-1-1-1-1000000-1-1-11-1-1-1111-1-111-1-111-1111-1100000
χ24444444-4-4-4-4-4-4442-2-2-222442-2-400002-2000000-2-2222-2−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i320000001+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
χ25444444-4-4-4-4-4-4442-2-2-222442-2-400002-2000000-2-2222-2−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i320000001−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
χ26444444-4-4-4-4-4-444-2222-2-244-22-40000-2200000022-2-2-221111111111-1-1-1-111-1-1-1-1000000-1-11-1-1-11-1-1-111-1-111111-1111-100000
χ27444444-4-4-4-4-4-444-2222-2-244-22-40000-2200000022-2-2-22−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i320000001+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
χ28444444-4-4-4-4-4-444-2222-2-244-22-40000-2200000022-2-2-22−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i320000001−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
χ294444-4-44-422-2-200242-24-42-2-2-40004-4-200022-2-22-2002011111111-1-111-1-1-1-111-1-10000001-1-111-1-111-11-11-11-11-11-11-11-100000
χ304444-4-44-422-2-200242-24-42-2-2-40004-4-200022-2-22-20020−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32000000−1−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
χ314444-4-44-422-2-200242-24-42-2-2-40004-4-200022-2-22-20020−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32000000−1+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
χ324444-4-44-422-2-200-2-4-22-442-2240004-4200022-2-2-2200-2011111111-1-111-1-1-1-111-1-10000001-11-11-11-1-11-11-11-111-1-111-1-1100000
χ334444-4-44-422-2-200-2-4-22-442-2240004-4200022-2-2-2200-20−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32000000−1−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
χ344444-4-44-422-2-200-2-4-22-442-2240004-4200022-2-2-2200-20−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32000000−1+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
χ354444-4-44-4-2-222002-42-2-44-22-240004-4-2000-2-2222-2002011111111-1-1-1-111-1-1-1-1110000001-1-1-11-1-1-11-1-111-1-11-1111-111100000
χ364444-4-44-4-2-222002-42-2-44-22-240004-4-2000-2-2222-20020−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32000000−1−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
χ374444-4-44-4-2-222002-42-2-44-22-240004-4-2000-2-2222-20020−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32000000−1+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
χ384444-4-44-4-2-22200-24-224-4-222-40004-42000-2-222-2200-2011111111-1-1-1-111-1-1-1-1110000001-1111-111-111-1-111-1-11-1-1-11-1-100000
χ394444-4-44-4-2-22200-24-224-4-222-40004-42000-2-222-2200-20−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32000000−1−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
χ404444-4-44-4-2-22200-24-224-4-222-40004-42000-2-222-2200-20−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32000000−1+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
χ414444-4-4-4422-2-20042-44-22-22-4-204-4000-2002-22-2002-20211111111-1-111-1-1-1-111-1-1000000-111-1-111-11-11-11-11-1-11-11-11-1100000
χ424444-4-4-4422-2-20042-44-22-22-4-204-4000-2002-22-2002-202−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i320000001+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
χ434444-4-4-4422-2-20042-44-22-22-4-204-4000-2002-22-2002-202−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i320000001−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
χ444444-4-4-4422-2-200-4-24-42-2-224204-40002002-22-200-220-211111111-1-111-1-1-1-111-1-1000000-11-11-11-11-11-11-11-11-111-1-111-100000
χ454444-4-4-4422-2-200-4-24-42-2-224204-40002002-22-200-220-2−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i320000001+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
χ464444-4-4-4422-2-200-4-24-42-2-224204-40002002-22-200-220-2−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i320000001−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
χ474444-4-4-44-2-222004-2-442-22-2-4204-4000200-22-2200-220-211111111-1-1-1-111-1-1-1-111000000-1111-11111-1-111-1-111-1-1-11-1-1-100000
χ484444-4-4-44-2-222004-2-442-22-2-4204-4000200-22-2200-220-2−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i320000001+i32−1−i32−1−i32−1−i321−i32−1+i32−1+i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i321+i32−1+i321−i321−i321−i3200000
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χ9832-3232-320000000000000000000000000000000000000002−2i32+2i32−2i3−2+2i32+2i3−2−2i3−2+2i3−2−2i300000000000000000000000000000000000000000000000

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