Finite Group Databasebeta

← Group #72266627

Character table — Group #72266627

Order 12288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size11111111444444446666242424242424242496969696969696969696969696969696192192192192192192192192192192192192256256256256256256256256256256256256256256256256256256256256256256256256256256256256256256256256
order1222222222222222222244444444444444444444444488888888888833666666666666666666666666666666
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ311111111111111111111111111111111111111111111111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ422222222-2-2-2-2-2-2-2-222222222-2-2-2-2222200000000-2-2-2-2000000000000-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1
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χ622222222-2-2-2-2-2-2-2-222222222-2-2-2-2222200000000-2-2-2-20000000000001−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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+i32
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χ7616-1616-1616-1616-16-888-88-8-880000000000000000000000000000000000000000−1+i32−1−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32
χ77242424242424242400000000-8-8-8-8000000004-44-400000000000000000000000000000000000000000000000000000000
χ78242424242424242400000000-8-8-8-800000000-44-4400000000000000000000000000000000000000000000000000000000
χ79242424-24-2424-24-2400000000-8-888000000000000000000004i−4i4i−4i00000000000000000000000000000000000000000000
χ80242424-24-2424-24-2400000000-8-88800000000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000
χ812424-2424-24-2424-2412-1212-1212-1212-120000000000000000-22-22-22-22000000000000000000000000000000000000000000000000
χ822424-24-2424-24-2424-1212-121212-1212-120000000000000000-22-222-22-2000000000000000000000000000000000000000000000000
χ8324-242424-24-24-2424-121212-12-121212-120000000000000000-222-2-222-2000000000000000000000000000000000000000000000000
χ8424-2424-2424-2424-2412-12-1212-121212-120000000000000000-222-22-2-22000000000000000000000000000000000000000000000000
χ8524-24-24242424-24-2400000000-88-88000000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ8624-24-24242424-24-2400000000-88-8800000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ8724-24-24-24-2424242400000000-888-8000000004-4-4400000000000000000000000000000000000000000000000000000000
χ8824-24-24-24-2424242400000000-888-800000000-444-400000000000000000000000000000000000000000000000000000000

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