Finite Group Databasebeta

← Group #13156536

Character table — Group #13156536

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363654545454727272727272
order12223334466666666633366666666612121212121212121212888836661212121212121212242424242424242424242424242424244444441212121212121212121212121212121212121212888824661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111
χ51111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2000000000000000022-2-200000000000000000022-2-20000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-20000000000000000-2-222000000000000000000-2-2220000000000
χ11222222-1222-12-12-12222-1-12-1-1-12-1-12-122-12-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000020-1-1002200-1-1-1-100000000000020-1-100
χ12222222-1222-12-12-12222-1-12-1-1-12-1-12-122-12-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-201100-2-2001111000000000000-201100
χ13222222-1222-12-12-12222-1-12-1-1-12-1-12-122-12-1-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111111111000020-1-1002200-1-1-1-1000000000000-201100
χ14222222-1222-12-12-12222-1-12-1-1-12-1-12-122-12-1-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-21111111111110000-201100-2-200111100000000000020-1-100
χ1522222-122222-1222-1-12-12-1-122-1-12-1-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ1622222-122222-1222-1-12-12-1-122-1-12-1-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-2-2-2-2-2-2111111111111-1-1-1-10000000000
χ1722222-122222-1222-1-12-12-1-122-1-12-1-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-22-222-2-2-1-111-1-1-1-1111111110000000000
χ1822222-122222-1222-1-12-12-1-122-1-12-1-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2-22-2-22211-1-11111-1-1-1-111110000000000
χ1922222-12-2-222-1222-1-12-12-1-122-1-12-1-1-111-2-2-2-2-2-2-2-20000-1-1-1-111111111000000000000000022-2-2000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3-1-1110000000000
χ2022222-12-2-222-1222-1-12-12-1-122-1-12-1-1-111-2-2-2-2-2-2-2-20000-1-1-1-111111111000000000000000022-2-2000000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3-1-1110000000000
χ2122222-12-2-222-1222-1-12-12-1-122-1-12-1-1-111-2-2-2-2-2-2-2-20000-1-1-1-1111111110000000000000000-2-222000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i311-1-10000000000
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χ242222-12222-1222-1222-1-1-12-1-1-12-1-12-12222-1-1-12-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000-2001100-2-200001111000000000-20011
χ252222-12222-1222-1222-1-1-12-1-1-12-1-12-12222-1-1-12-1-1-1-2-2-2-2-1-1-1-1-1-122-1-1-1-11111-2-2-2-21111111100000200-1-100220000-1-1-1-1000000000-20011
χ262222-12222-1222-1222-1-1-12-1-1-12-1-12-12222-1-1-12-1-1-1-2-2-2-2-1-1-1-1-1-122-1-1-1-11111-2-2-2-21111111100000-2001100-2-200001111000000000200-1-1
χ2722-2-2222002-2-2-2-222-2-222222-2-2-2-2-2-22000000000022−2−222-2-20000000022−2−222−2−22222−2−2−2−2002i−2i000000000000000000002i−2i−i2−i2i2i2000000
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χ2922-2-2222002-2-2-2-222-2-222222-2-2-2-2-2-220000000000−2−22222-2-200000000−2−222−2−222−2−2−2−22222002i−2i000000000000000000002i−2ii2i2−i2−i2000000
χ3022-2-2222002-2-2-2-222-2-222222-2-2-2-2-2-220000000000−2−22222-2-200000000−2−222−2−222−2−2−2−2222200−2i2i00000000000000000000−2i2i−i2−i2i2i2000000
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χ412-2-2222-1-22-212-1-21-2-222-1-1-21112-1-1-21-22-12-1-11-211−2i2i2i−2i-111-1-221-111-1-1−2i2i2i−2ii−i−iiii−i−i−i−iii0000003−30000003−33−300000000000000i3−i300
χ422-2-2222-1-22-212-1-21-2-222-1-1-21112-1-1-21-22-12-1-11-211−2i2i2i−2i-111-1-221-111-1-1−2i2i2i−2ii−i−iiii−i−i−i−iii000000−33000000−33−3300000000000000−i3i300
χ432-2-22-122-221-2221-2-2-2-1-1-12111-2-1-121-2-222-1-1-1-21112i−2i−2i2i-111-11-1-2211-1-1−iii−i2i−2i−2i2i−i−iiiii−i−i000000003−3000000003−33−3000000000000−i3i3
χ442-2-22-122-221-2221-2-2-2-1-1-12111-2-1-121-2-222-1-1-1-21112i−2i−2i2i-111-11-1-2211-1-1−iii−i2i−2i−2i2i−i−iiiii−i−i00000000−3300000000−33−33000000000000i3−i3
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χ47444444-2-4-44-24-24-24444-2-24-2-2-24-2-24-2-4-42-4222-4220000-2-2-2-2-4-42222220000000000000000000000000000000000000000000000000000
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χ1038-88-88-4-400-8-444844-4-8-4-4244-4244-2-4-2000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4800484-8-4-84-442-4-4-24-4-4-24424000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
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χ1078-8-88-4-4-48-844-4-44444-4222-2-2-2-2222-2-2-4444-2-2-4-4220000-111-12-22-2-1-1110000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-8844-4-44444-4222-2-2-2-2222-2-24-4-4-42244-2-20000-111-1-22-2211-1-10000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.