Finite Group Databasebeta

← Group #13156409

Character table — Group #13156409

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size11112222222222222244444444444444444488888888888888121212121212121212121212181818181818242424242424242424242424242424242424242424363636363636363636363636363636216
order1222333446666666663336666666661212121212123666121212121212121212124444121212121212121222666626666666612121212121212121212121248888121224242424242424244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-111111
χ511111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1111111111-1-111-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1-11111-1-1-1-11
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000000000222222000000000000000000000-20000-2-2000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000000000-2-2-2-2-2-20000000000000000000002000022000000000
χ11222222-12222-12222-1-1-1-12-1-122-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-10000000002222-1-1-1-1-1-1-1-120000-1-1000000000
χ12222222-12222-12222-1-1-1-12-1-122-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-122-2-2-1-1-1-11111-2-2111100000000022-2-2-1-1-1-11111-2000011000000000
χ13222222-12222-12222-1-1-1-12-1-122-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-2-2221111-1-1-1-1-2-21111000000000-2-2221111-1-1-1-1-2000011000000000
χ14222222-12222-12222-1-1-1-12-1-122-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111111122-1-1-1-1000000000-2-2-2-21111111120000-1-1000000000
χ15222222-1-2-222-12222-1-1-1-12-1-122-1-12-1-1-2-211-2-2-1-1-1-1-2-2111111110000−i3−i3i3i3−i3−i3i3i322-1-1-1-10000000000000−i3−i3i3i3−i3−i3i3i3-2000011000000000
χ16222222-1-2-222-12222-1-1-1-12-1-122-1-12-1-1-2-211-2-2-1-1-1-1-2-2111111110000−i3−i3i3i3i3i3−i3−i3-2-211110000000000000−i3−i3i3i3i3i3−i3−i320000-1-1000000000
χ17222222-1-2-222-12222-1-1-1-12-1-122-1-12-1-1-2-211-2-2-1-1-1-1-2-2111111110000i3i3−i3−i3−i3−i3i3i3-2-211110000000000000i3i3−i3−i3−i3−i3i3i320000-1-1000000000
χ18222222-1-2-222-12222-1-1-1-12-1-122-1-12-1-1-2-211-2-2-1-1-1-1-2-2111111110000i3i3−i3−i3i3i3−i3−i322-1-1-1-10000000000000i3i3−i3−i3i3i3−i3−i3-2000011000000000
χ1922222-12222-122-12-1222-1-12-1-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1002200002222000000222-1-1-1-1-1-100-1-10000-1-1-1-100022000000-1-1-1-10
χ2022222-12222-122-12-1222-1-12-1-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1002200002222000000-2-2-211111100-1-10000-1-1-1-1000-2-200000011110
χ2122222-12222-122-12-1222-1-12-1-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-100-2-20000-2-2-2-2000000222-1-1-1-1-1-1001100001111000-2-200000011110
χ2222222-12222-122-12-1222-1-12-1-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-100-2-20000-2-2-2-2000000-2-2-211111100110000111100022000000-1-1-1-10
χ232222-12222-122-12-1222-12-1-12-1-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-12200222200000000002-1-122-1-1-1-1-1-100-1-1-1-100000220000-1-1-1-100000
χ242222-12222-122-12-1222-12-1-12-1-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1220022220000000000-211-2-21111-1-100-1-1-1-100000-2-20000111100000
χ252222-12222-122-12-1222-12-1-12-1-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2-2-2-200000000002-1-122-1-1-1-11100111100000-2-20000111100000
χ262222-12222-122-12-1222-12-1-12-1-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2-2-2-20000000000-211-2-211111100111100000220000-1-1-1-100000
χ2722-2-22222-2-2-2-222-2-22-2222-2-2-2-2222-2-22-22-2-222-2-222-22-22-222-2-22i−2i002i−2i2i−2i00000000000000000002i−2i002i−2i2i−2i00000000000000000000
χ2822-2-22222-2-2-2-222-2-22-2222-2-2-2-2222-2-22-22-2-222-2-222-22-22-222-2-2−2i2i00−2i2i−2i2i0000000000000000000−2i2i00−2i2i−2i2i00000000000000000000
χ2922-2-2222-22-2-2-222-2-22-2222-2-2-2-2222-2-2-22-222-22-2-22-22-22-22-2-222002i−2i00002i−2i2i−2i000000000000000002i−2i00002i−2i2i−2i0000000000000000
χ3022-2-2222-22-2-2-222-2-22-2222-2-2-2-2222-2-2-22-222-22-2-22-22-22-22-2-22200−2i2i0000−2i2i−2i2i00000000000000000−2i2i0000−2i2i−2i2i0000000000000000
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χ3222-2-222-12-2-2-2122-2-2-11-1-1211-2-2-1-12112-2-11-22-111-12-2-11-11-1-1112i−2i00−ii−ii−333−300i3i3−i3−i30000000002i−2i00−ii−ii−333−300000i3−i3000000000
χ3322-2-222-12-2-2-2122-2-2-11-1-1211-2-2-1-12112-2-11-22-111-12-2-11-11-1-111−2i2i00i−ii−i3−3−3300i3i3−i3−i3000000000−2i2i00i−ii−i3−3−3300000i3−i3000000000
χ3422-2-222-12-2-2-2122-2-2-11-1-1211-2-2-1-12112-2-11-22-111-12-2-11-11-1-111−2i2i00i−ii−i−333−300−i3−i3i3i3000000000−2i2i00i−ii−i−333−300000−i3i3000000000
χ3522-2-222-1-22-2-2122-2-2-11-1-1211-2-2-1-1211-221-12-2-111-1-221-11-111-1-1002i−2i3−3−33−ii−ii00−i3−i3i3i3000000000002i−2i3−3−33−ii−ii00000i3−i3000000000
χ3622-2-222-1-22-2-2122-2-2-11-1-1211-2-2-1-1211-221-12-2-111-1-221-11-111-1-1002i−2i−333−3−ii−ii00i3i3−i3−i3000000000002i−2i−333−3−ii−ii00000−i3i3000000000
χ3722-2-222-1-22-2-2122-2-2-11-1-1211-2-2-1-1211-221-12-2-111-1-221-11-111-1-100−2i2i3−3−33i−ii−i00i3i3−i3−i300000000000−2i2i3−3−33i−ii−i00000−i3i3000000000
χ3822-2-222-1-22-2-2122-2-2-11-1-1211-2-2-1-1211-221-12-2-111-1-221-11-111-1-100−2i2i−333−3i−ii−i00−i3−i3i3i300000000000−2i2i−333−3i−ii−i00000i3−i3000000000
χ3922-2-22-12-22-21-22-1-212-22-1-1-21112-1-1-21-2-1-2221-111-11-1-221-111-1-1002i−2i00002i−2i2i−2i000000000−i3i3−i3−i3i3i300−ii0000−ii−ii0000000000033−3−30
χ4022-2-22-12-22-21-22-1-212-22-1-1-21112-1-1-21-2-1-2221-111-11-1-221-111-1-1002i−2i00002i−2i2i−2i000000000i3−i3i3i3−i3−i300−ii0000−ii−ii00000000000−3−3330
χ4122-2-22-12-22-21-22-1-212-22-1-1-21112-1-1-21-2-1-2221-111-11-1-221-111-1-100−2i2i0000−2i2i−2i2i000000000−i3i3−i3−i3i3i300i−i0000i−ii−i00000000000−3−3330
χ4222-2-22-12-22-21-22-1-212-22-1-1-21112-1-1-21-2-1-2221-111-11-1-221-111-1-100−2i2i0000−2i2i−2i2i000000000i3−i3i3i3−i3−i300i−i0000i−ii−i0000000000033−3−30
χ4322-2-2-1222-21-2-2-121-22-2-12-11-211-12-11-2-1-22-212-111-1-11-112-2-1-1112i−2i002i−2i2i−2i00000000000−i3i300−i3i3−i3i3−ii00−ii−ii0000000000033−3−300000
χ4422-2-2-1222-21-2-2-121-22-2-12-11-211-12-11-2-1-22-212-111-1-11-112-2-1-1112i−2i002i−2i2i−2i00000000000i3−i300i3−i3i3−i3−ii00−ii−ii00000000000−3−33300000
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χ472-2-2222200222-2-2-2-2-2-2222222-2-2-2-2-2-200000022-2-200000000000000000000002-22-22-20000000000000000000000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20
χ482-2-2222200222-2-2-2-2-2-2222222-2-2-2-2-2-200000022-2-200000000000000000000002-22-22-20000000000000000000000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20
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χ5244444-2-2444-2-24-24-2-2-2-21-2-21-2-2-21-2-214-2-2-24-21111-2-2-2-211111100440000-2-2-2-200000000000000000-2-2000011110000000000000000
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χ9488-8-8-4-4-48-8444-4-444-44222-2-2-2-2222-2-2-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-4-88444-4-444-44222-2-2-2-2222-2-24-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000000000
χ968-88-88-4-400-844-848-44-4-42-44-24-44-24-420000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-48-4004-844-8-484-42-4-4-244-4-2442-40000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-480044-844-4-4-88-4-4244-2244-2-4-40000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-40044444-4-44-4222-2-2-22-2-2-222000000-11-1100000033−3333−330000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-40044444-4-44-4222-2-2-22-2-2-222000000-11-11000000−3333−33330000000000000000000000000000000000000000000000000000000
χ1018-8-888-4-4008-4-4-84-8444-42-4-42-444-244-200000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1028-8-88-48-400-48-44-84-8442-4-42-4-44-244-2400000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-4800-4-484444-8-8-4-42-4-42-244-24400000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-400-4-4-4444444222222-2-2-2-2-2-2000000-1-11100000033−33−33330000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-400-4-4-4444444222222-2-2-2-2-2-2000000-1-111000000−333333−330000000000000000000000000000000000000000000000000000000

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