Finite Group Databasebeta

← Group #72253909

Character table — Group #72253909

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222244444444444444444488888888888816161616161616161616161616161616161616161616161616161616161616161616161624242424242424242424242448484848484848484848
order122222344446662222224444446612121212666666121212121212224466668888888812121212242424242424242424242424242424242222444444442244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-111-1-1-1-1
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11111
χ91111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11-11-11-111-1-1
χ101111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-11-11-11-1-111
χ111111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-11-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-11-11-1111-1-1
χ121111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-11-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-11-11-11-1-1-111
χ131111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-11-11-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-111-1-11-1-111
χ141111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-11-11-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1111-1-111-111-1-1
χ151111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-11-11-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1111-1-111-1-1-111
χ161111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-11-11-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-111-1-1111-1-1
χ172222222222222222-2-2-2-22-2-22-2-222222222-2-2-2-22-2-2-22-200000000000000000000000000000000000000000000222200-2-2000000
χ182222222222222222-2-2-2-22-2-22-2-222222222-2-2-2-22-2-2-22-200000000000000000000000000000000000000000000-2-2-2-20022000000
χ1922222222222222-2-222-2-2-22-2-22-2222222-2-222-2-2-22-2-2-220000000000000000000000000000000000000000000000002200-2-20000
χ2022222222222222-2-222-2-2-22-2-22-2222222-2-222-2-2-22-2-2-22000000000000000000000000000000000000000000000000-2-200220000
χ2122222222222222-2-2-2-222-2-22-2-22222222-2-2-2-222-2-222-2-222-2-2222200000000-2-2-2-200000000000000000000000000000000000000
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χ282222222-2-2-2-2222-2-222222-2-22-2-222-2-2-2-2-2-222222-2-2-22-200000000000000000000000000000000000000000000-2-222002-2000000
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χ31222222-12222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111110000000000000000000000
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χ41222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2222222-1-11111111111-1-1-1-1-1-12-22-2-1-11122-2-222-2-2-1-111-1-1-1-11111-1-1-1-111110000000000000000000000
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χ462-2-22-22222-2-2-2-222-22-22-2222-2-2-2-2222-2-22-22-22-2222-2-2-200000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ472-2-22-22222-2-2-2-222-2-22-222-2-2-222-2222-2-22-2-22-222-2-22-220000000000000000000000000000000000002-22-22-22-200000000000000
χ482-2-22-22222-2-2-2-222-2-22-222-2-2-222-2222-2-22-2-22-222-2-22-22000000000000000000000000000000000000-22-22-22-2200000000000000
χ492-2-22-22222-2-2-2-22-222-2-22-22-22-22-2222-2-2-222-2-22-22-222-20000000000000000000000000000000000000000000000000000002-22-2
χ502-2-22-22222-2-2-2-22-222-2-22-22-22-22-2222-2-2-222-2-22-22-222-2000000000000000000000000000000000000000000000000000000-22-22
χ512-2-22-22222-2-2-2-22-22-222-2-2-2222-2-2222-2-2-22-222-2-2-22-2220000000000002-22-20000000000002-22-22-22-20000000000000000000000
χ522-2-22-22222-2-2-2-22-22-222-2-2-2222-2-2222-2-2-22-222-2-2-22-222000000000000-22-22000000000000-22-22-22-220000000000000000000000
χ532-2-22-222-2-222-2-222-22-2-22-2-2222-2-22-2-2222-22-2-22-2-22-2220000000000002-2-220000000000002-22-2-22-220000000000000000000000
χ542-2-22-222-2-222-2-222-22-2-22-2-2222-2-22-2-2222-22-2-22-2-22-222000000000000-222-2000000000000-22-222-22-20000000000000000000000
χ552-2-22-222-2-222-2-222-2-222-2-22-22-22-22-2-2222-2-222-2-22-222-20000000000000000000000000000000000000000000000000000002-2-22
χ562-2-22-222-2-222-2-222-2-222-2-22-22-22-22-2-2222-2-222-2-22-222-2000000000000000000000000000000000000000000000000000000-222-2
χ572-2-22-222-2-222-2-22-222-22-22-2-2-222-22-2-222-222-22-22-2-22-220000000000000000000000000000000000002-2-222-2-2200000000000000
χ582-2-22-222-2-222-2-22-222-22-22-2-2-222-22-2-222-222-22-22-2-22-22000000000000000000000000000000000000-222-2-222-200000000000000
χ592-2-22-222-2-222-2-22-22-22-22222-2-2-2-22-2-222-22-22-22222-2-2-2000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ602-2-22-222-2-222-2-22-22-22-22222-2-2-2-22-2-222-22-22-22222-2-2-200000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ612-2-22-22-122-2-211-12-22-22-2222-2-2-21-1-1-111-11-11-11-1-1-11110000−i3i3−i3i32i−2i2i−2i0000−i3i3−i3i3−ii−ii−ii−ii3−3−333−3−330000000000000000000000
χ622-2-22-22-122-2-211-12-22-22-2222-2-2-21-1-1-111-11-11-11-1-1-11110000−i3i3−i3i3−2i2i−2i2i0000−i3i3−i3i3i−ii−ii−ii−i−333−3−333−30000000000000000000000
χ632-2-22-22-122-2-211-12-22-22-2222-2-2-21-1-1-111-11-11-11-1-1-11110000i3−i3i3−i32i−2i2i−2i0000i3−i3i3−i3−ii−ii−ii−ii−333−3−333−30000000000000000000000
χ642-2-22-22-122-2-211-12-22-22-2222-2-2-21-1-1-111-11-11-11-1-1-11110000i3−i3i3−i3−2i2i−2i2i0000i3−i3i3−i3i−ii−ii−ii−i3−3−333−3−330000000000000000000000
χ652-2-22-22-122-2-211-1-22-222-2-2-2222-21-1-1-1111-11-1-1111-11-1-10000−i3i3−i3i300002-22-2i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3-11-11-11-110000000000000000000000
χ662-2-22-22-122-2-211-1-22-222-2-2-2222-21-1-1-1111-11-1-1111-11-1-10000−i3i3−i3i30000-22-22i3−i3i3−i3i3−i3−i3i3i3−i3−i3i31-11-11-11-10000000000000000000000
χ672-2-22-22-122-2-211-1-22-222-2-2-2222-21-1-1-1111-11-1-1111-11-1-10000i3−i3i3−i300002-22-2−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3-11-11-11-110000000000000000000000
χ682-2-22-22-122-2-211-1-22-222-2-2-2222-21-1-1-1111-11-1-1111-11-1-10000i3−i3i3−i30000-22-22−i3i3−i3i3−i3i3i3−i3−i3i3i3−i31-11-11-11-10000000000000000000000
χ692-2-22-22-1-2-22211-12-22-2-22-2-2222-21-111-1-1-11-111-111-11-1-10000−i3i3i3−i300002-2-22i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3-11-111-11-10000000000000000000000
χ702-2-22-22-1-2-22211-12-22-2-22-2-2222-21-111-1-1-11-111-111-11-1-10000−i3i3i3−i30000-222-2i3−i3−i3i3i3−i3−i3i3−i3i3i3−i31-11-1-11-110000000000000000000000
χ712-2-22-22-1-2-22211-12-22-2-22-2-2222-21-111-1-1-11-111-111-11-1-10000i3−i3−i3i300002-2-22−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3-11-111-11-10000000000000000000000
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χ732-2-22-22-1-2-22211-1-22-22-22222-2-2-21-111-1-11-11-11-1-1-1-11110000−i3i3i3−i32i−2i−2i2i0000−i3i3i3−i3−ii−iii−ii−i3−3−33−333−30000000000000000000000
χ742-2-22-22-1-2-22211-1-22-22-22222-2-2-21-111-1-11-11-11-1-1-1-11110000−i3i3i3−i3−2i2i2i−2i0000−i3i3i3−i3i−ii−i−ii−ii−333−33−3−330000000000000000000000
χ752-2-22-22-1-2-22211-1-22-22-22222-2-2-21-111-1-11-11-11-1-1-1-11110000i3−i3−i3i32i−2i−2i2i0000i3−i3−i3i3−ii−iii−ii−i−333−33−3−330000000000000000000000
χ762-2-22-22-1-2-22211-1-22-22-22222-2-2-21-111-1-11-11-11-1-1-1-11110000i3−i3−i3i3−2i2i2i−2i0000i3−i3−i3i3i−ii−i−ii−ii3−3−33−333−30000000000000000000000
χ77444444-24444-2-2-244-4-4-4-44-4-44-4-4-2-2-2-2-2-2-2-22222-2222-220000000000000000000000000000000000000000000000000000000000
χ78444444-24444-2-2-2-4-444-4-4-44-4-44-4-2-2-2-2-2-222-2-2222-2222-20000000000000000000000000000000000000000000000000000000000
χ79444444-2-4-4-4-4-2-2-244-4-444-44-4-44-4-2-22222-2-222-2-22-2222-20000000000000000000000000000000000000000000000000000000000
χ80444444-2-4-4-4-4-2-2-2-4-444444-4-44-4-4-2-2222222-2-2-2-2-2222-220000000000000000000000000000000000000000000000000000000000
χ814444-4-444-44-4444000000000000-4-44-44-40000000000000000000000000000000000000000000000002222-2-2-2-200000000000000
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χ844444-4-44-44-44444000000000000-4-4-44-44000000000000000000000000000000000000000000000000-2-22222-2-200000000000000
χ854-4-444-444-4-44-4-440000000000004-44-4-440000000000000000000000000000000000000000000000002-22-2-22-2200000000000000
χ864-4-444-444-4-44-4-440000000000004-44-4-44000000000000000000000000000000000000000000000000-22-222-22-200000000000000
χ874-4-444-44-444-4-4-440000000000004-4-444-40000000000000000000000000000000000000000000000002-2-22-222-200000000000000
χ884-4-444-44-444-4-4-440000000000004-4-444-4000000000000000000000000000000000000000000000000-222-22-2-2200000000000000
χ894-4-44-44-244-4-422-24-4-44-444-4-4-4442-2-2-222-222-22-2-222-22-20000000000000000000000000000000000000000000000000000000000
χ904-4-44-44-244-4-422-2-444-4-44-44-44-442-2-2-2222-2-222-22-22-2-220000000000000000000000000000000000000000000000000000000000
χ914-4-44-44-2-4-44422-24-4-444-4-44-44-442-222-2-2-222-2-222-22-2-220000000000000000000000000000000000000000000000000000000000
χ924-4-44-44-2-4-44422-2-444-44-44-4-4-4442-222-2-22-2-22-22-222-22-20000000000000000000000000000000000000000000000000000000000
χ938888-8-8-48-88-8-4-4-400000000000044-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ948888-8-8-4-88-88-4-4-4000000000000444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-800800008-8-800000000000000000000000000000000000000000000000000000000000000000000000000004-40000000000
χ9688-8-800800008-8-80000000000000000000000000000000000000000000000000000000000000000000000000000-440000000000
χ978-88-80080000-88-8000000000000000000000000000000000000000000000000000000000000000000000000004-4000000000000
χ988-88-80080000-88-800000000000000000000000000000000000000000000000000000000000000000000000000-44000000000000
χ998-8-888-8-48-8-8844-4000000000000-44-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-888-8-4-888-844-4000000000000-444-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ1011616-16-1600-80000-8880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10216-1616-1600-800008-880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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