Finite Group Databasebeta

← Group #13156468

Character table — Group #13156468

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size11112222222222222244444444444444444488888888888888121212121212121212121212181818181818242424242424242424242424242424242424242424363636363636363636363636363636216
order122233344666666666333666666666121212121212366612121212121212121212444412121212121212122266664121212121212121212121212121212121212121248888121224242424242424244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-11111-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-11111-111-1-1-1-11111-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111
χ511111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-11-1-1111111-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-11
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11
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
χ11222222-12222-122-122-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1022220000-1-1-1-1-1-1-1-1000020000-1-1000000000
χ12222222-12222-122-122-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-122-2-2-1-1-1-11111-2-21111022-2-20000-1-1-1-111110000-2000011000000000
χ13222222-12222-122-122-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-2-2221111-1-1-1-1-2-211110-2-22200001111-1-1-1-10000-2000011000000000
χ14222222-12222-122-122-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111111122-1-1-1-10-2-2-2-2000011111111000020000-1-1000000000
χ15222222-1-2-222-122-122-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-2111111110000−i3−i3i3i3−i3−i3i3i322-1-1-1-1000000000−i3−i3i3i3−i3−i3i3i30000-2000011000000000
χ16222222-1-2-222-122-122-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-2111111110000−i3−i3i3i3i3i3−i3−i3-2-21111000000000−i3−i3i3i3i3i3−i3−i3000020000-1-1000000000
χ17222222-1-2-222-122-122-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-2111111110000i3i3−i3−i3−i3−i3i3i3-2-21111000000000i3i3−i3−i3−i3−i3i3i3000020000-1-1000000000
χ18222222-1-2-222-122-122-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-2111111110000i3i3−i3−i3i3i3−i3−i322-1-1-1-1000000000i3i3−i3−i3i3i3−i3−i30000-2000011000000000
χ1922222-12222-122-122-12-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1002200002222000000200-1-122-1-10000-1-1-1-1-1-1-1-100022000000-1-1-1-10
χ2022222-12222-122-122-12-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1002200002222000000-200-1-1-2-2110000-1-1-1-11111000-2-200000011110
χ2122222-12222-122-122-12-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-100-2-20000-2-2-2-20000002001122-1-100001111-1-1-1-1000-2-200000011110
χ2222222-12222-122-122-12-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-100-2-20000-2-2-2-2000000-20011-2-21100001111111100022000000-1-1-1-10
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χ242222-12222-122-122-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1220022220000000000-2-1-10011-2-2-1-1-1-1000011110-2-20000111100000
χ252222-12222-122-122-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2-2-2-2000000000021100-1-12211110000-1-1-1-10-2-20000111100000
χ262222-12222-122-122-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2-2-2-20000000000-2110011-2-21111000011110220000-1-1-1-100000
χ2722-2-222200222-2-2-2-2-2-2222222-2-2-2-2-2-200000022-2-200000000000000000000002-222-2-200000000000000000000002−22−20022−2−222−2−20
χ2822-2-222200222-2-2-2-2-2-2222222-2-2-2-2-2-200000022-2-200000000000000000000002-222-2-20000000000000000000000−22−2200−2−222−2−2220
χ2922-2-222200222-2-2-2-2-2-2222222-2-2-2-2-2-200000022-2-20000000000000000000000-22-2-22200000000000000000000002−2−220022−2−2−2−2220
χ3022-2-222200222-2-2-2-2-2-2222222-2-2-2-2-2-200000022-2-20000000000000000000000-22-2-2220000000000000000000000−222−200−2−22222−2−20
χ312-2-222222-2-2-2-2222-2-2-2222-2-2-2222-2-2-22-22-2-222-2-222-22-22-222-2-2002i−2i00002i−2i2i−2i0000000002i−2i000000002i−2i2i−2i00000000000000000000
χ322-2-222222-2-2-2-2222-2-2-2222-2-2-2222-2-2-22-22-2-222-2-222-22-22-222-2-200−2i2i0000−2i2i−2i2i000000000−2i2i00000000−2i2i−2i2i00000000000000000000
χ332-2-22222-22-2-2-2222-2-2-2222-2-2-2222-2-2-2-22-222-22-2-22-22-22-22-2-2222i−2i002i−2i2i−2i000000000002i−2i0000002i−2i2i−2i000000000000000000000000
χ342-2-22222-22-2-2-2222-2-2-2222-2-2-2222-2-2-2-22-222-22-2-22-22-22-22-2-222−2i2i00−2i2i−2i2i00000000000−2i2i000000−2i2i−2i2i000000000000000000000000
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χ372-2-2222-12-2-2-2122-1-2-212-1-1-2112-1-1-2112-2-11-22-111-12-2-11-11-1-11100−2i2i3−3−33i−ii−i00i3−i3i3−i3000−2i2i00003−3−33i−ii−i000000000i3−i3000000000
χ382-2-2222-12-2-2-2122-1-2-212-1-1-2112-1-1-2112-2-11-22-111-12-2-11-11-1-11100−2i2i−333−3i−ii−i00−i3i3−i3i3000−2i2i0000−333−3i−ii−i000000000−i3i3000000000
χ392-2-2222-1-22-2-2122-1-2-212-1-1-2112-1-1-211-221-12-2-111-1-221-11-111-1-12i−2i00−ii−ii3−3−3300−i3i3−i3i302i−2i000000−ii−ii3−3−33000000000i3−i3000000000
χ402-2-2222-1-22-2-2122-1-2-212-1-1-2112-1-1-211-221-12-2-111-1-221-11-111-1-12i−2i00−ii−ii−333−300i3−i3i3−i302i−2i000000−ii−ii−333−3000000000−i3i3000000000
χ412-2-2222-1-22-2-2122-1-2-212-1-1-2112-1-1-211-221-12-2-111-1-221-11-111-1-1−2i2i00i−ii−i3−3−3300i3−i3i3−i30−2i2i000000i−ii−i3−3−33000000000−i3i3000000000
χ422-2-2222-1-22-2-2122-1-2-212-1-1-2112-1-1-211-221-12-2-111-1-221-11-111-1-1−2i2i00i−ii−i−333−300−i3i3−i3i30−2i2i000000i−ii−i−333−3000000000i3−i3000000000
χ432-2-222-122-2-21-22-12-21-2-12-11-21-12-11-21212-2-2-1-111-1-112-2-11-1-111002i−2i00002i−2i2i−2i000000000−ii003−30000−ii−ii33−3−300000000000−i3i3−i3i30
χ442-2-222-122-2-21-22-12-21-2-12-11-21-12-11-21212-2-2-1-111-1-112-2-11-1-111002i−2i00002i−2i2i−2i000000000−ii00−330000−ii−ii−3−33300000000000i3−i3i3−i30
χ452-2-222-122-2-21-22-12-21-2-12-11-21-12-11-21212-2-2-1-111-1-112-2-11-1-11100−2i2i0000−2i2i−2i2i000000000i−i003−30000i−ii−i33−3−300000000000i3−i3i3−i30
χ462-2-222-122-2-21-22-12-21-2-12-11-21-12-11-21212-2-2-1-111-1-112-2-11-1-11100−2i2i0000−2i2i−2i2i000000000i−i00−330000i−ii−i−3−33300000000000−i3i3−i3i30
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χ9888-8-8-4-4-400-4-4-4444444222222-2-2-2-2-2-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000000
χ998-88-88-4-400-844-8448-4-4-4-4244-244-2-4-420000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-48-4004-844-84-48-4-42-44-244-24-42-40000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-480044-844-8-4-482-4-4-244-2442-4-40000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-400444444-4-4-4222-2-2-2-2-2-2222000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400444444-4-4-4222-2-2-2-2-2-2222000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-48-8444-4-4-4444222-2-2-2222-2-2-2-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4-88444-4-4-4444222-2-2-2222-2-2-24-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000000000

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