Finite Group Databasebeta

← Group #11792024

Character table — Group #11792024

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size11111111222222222222222222224444444444444444444444444444444444444444444444444444444444442424242424242424242424242424242424242424242424243636363636363636
order1222222233444466666666666666366666668888121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424242424444444441212121212121212121212121212121222448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ92222222222-2-2-2-222222222222222222222220000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000000022-2-20000
χ102222222222-2-2-2-222222222222222222222220000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000-2-2220000
χ11222222222-1222222222-1-1-1-1-12-12-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-12-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002200220000-1-1-1-10000-1-1-1-100000000
χ12222222222-1222222222-1-1-1-1-12-12-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-12-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-2000011110000111100000000
χ13222222222-1222222222-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-2-2-2-2222-1-1-1-1-1-1-1-1-12-1-1-1-2-2-2-2-2-2-2-2111111111111111111111111002200-2-20000-1-1-1-10000111100000000
χ14222222222-1222222222-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-2-2-2-2222-1-1-1-1-1-1-1-1-12-1-1-1-2-2-2-2-2-2-2-211111111111111111111111100-2-20022000011110000-1-1-1-100000000
χ1522222222-122222-1-1-1-1-122222-12-12-1-1-1-1-1-1-1-12222-1-1-1222-1-1-1-1-1-1-12-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122002200-1-1-1-10000-1-1-1-1000000000000
χ1622222222-122222-1-1-1-1-122222-12-12-1-1-1-1-1-1-1-12222-1-1-1222-1-1-1-1-1-1-12-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-200111100001111000000000000
χ1722222222-122222-1-1-1-1-122222-12-12-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1222-1-1-1-1-1-1-12-1-111111111-2-2-2-2-2-2-2-211111111111111112200-2-200-1-1-1-100001111000000000000
χ1822222222-122222-1-1-1-1-122222-12-12-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1222-1-1-1-1-1-1-12-1-111111111-2-2-2-2-2-2-2-21111111111111111-2-200220011110000-1-1-1-1000000000000
χ192222-2-2-2-2220000222-2-2222-2-2-2-2-2-22222-2-2-2-222−2−200000000000000002222−2−2−2−22222−2−2−2−222222222−2−2−2−2−2−2−2−20000000000000000000000002-20022−2−2
χ202222-2-2-2-2220000222-2-2222-2-2-2-2-2-22222-2-2-2-222−2−200000000000000002222−2−2−2−22222−2−2−2−222222222−2−2−2−2−2−2−2−2000000000000000000000000-2200−2−222
χ212222-2-2-2-2220000222-2-2222-2-2-2-2-2-22222-2-2-2-2−2−2220000000000000000−2−2−2−22222−2−2−2−22222−2−2−2−2−2−2−2−2222222220000000000000000000000002-200−2−222
χ222222-2-2-2-2220000222-2-2222-2-2-2-2-2-22222-2-2-2-2−2−2220000000000000000−2−2−2−22222−2−2−2−22222−2−2−2−2−2−2−2−222222222000000000000000000000000-220022−2−2
χ2322-2-22-2-222222-2-22-2-22-22-2-22-2-2-22222-2-22-2-222i−2i2i−2i22-222-22222-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ2422-2-22-2-222222-2-22-2-22-22-2-22-2-2-22222-2-22-2-22−2i2i−2i2i22-222-22222-2-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ2522-2-22-2-2222-2-2222-2-22-22-2-22-2-2-22222-2-22-2-220000-2-22-2-22-2-2-2-22222220000000000000000000000000000000000000000000000000000000000002-22-2
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χ2722-2-22-2-222-122-2-22-2-22-2-111-11-212-1-1-111-111-12i−2i2i−2i22-2-1-11-1-1-1-111-21112i2i−2i−2i2i2i−2i−2i−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii00000000000033−3−30000−i3−i3i3i300000000
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χ3122-2-22-2-22-1222-2-2-111-112-2-22-21-2-12-1-111-111-12i−2i2i−2i-1-1122-2-1-1-1-1111-211−i−iii−i−iii2i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii0000000033−3−30000−i3−i3i3i3000000000000
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χ3422-2-22-2-22-1222-2-2-111-112-2-22-21-2-12-1-111-111-1−2i2i−2i2i-1-1122-2-1-1-1-1111-211ii−i−iii−i−i−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i00000000−3−3330000−i3−i3i3i3000000000000
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χ392-22-2-22-22222-22-2-22-2-22-22-2-2-2-22222-22-2-22-2200002-2-22-2-222-2-2-2-2222200000000000000000000000000000000002-2000000002-22-20000000000000000
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χ412-22-2-22-2222-22-22-22-2-22-22-2-2-2-22222-22-2-22-220000-222-222-2-22222-2-2-2-20000000000000000000000000000000000002-200000000002-22-2000000000000
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χ482-22-2-22-22-12-22-221-111-1-22-2-2-212-12-11-111-11-100001-1-1-22211-1-1-1-11-2113−33−33−33−3000000003−33−33−33−33−33−33−33−30000-2200−33−3300001-11-1000000000000
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χ502-22-2-22-22-12-22-221-111-1-22-2-2-212-12-11-111-11-100001-1-1-22211-1-1-1-11-211−33−33−33−3300000000−33−33−33−33−33−33−33−330000-22003−33−300001-11-1000000000000
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χ522-2-22-2-222222-2-22-2-22-2-2-2-22-222-2222-2-22-2-22200002-222-2222-2-222-2-2-2-200000000000000000000000000000000000000-22000000000000-222-200000000
χ532-2-22-2-22222-222-2-2-22-2-2-2-22-222-2222-2-22-2-2220000-22-2-22-2-2-222-2-22222000000000000000000000000000000002-20000002-2-2200000000000000000000
χ542-2-22-2-22222-222-2-2-22-2-2-2-22-222-2222-2-22-2-2220000-22-2-22-2-2-222-2-2222200000000000000000000000000000000-22000000-222-200000000000000000000
χ552-2-22-2-2222-12-2-22-2-22-2-211-11-1212-1-111-111-1-100002-22-11-1-1-111-1-1-2111000000003−3−333−3−3333−3−3−3−33333−3−3−3−3330000002-200003−3−330000-111-100000000
χ562-2-22-2-2222-12-2-22-2-22-2-211-11-1212-1-111-111-1-100002-22-11-1-1-111-1-1-2111000000003−3−333−3−3333−3−3−3−33333−3−3−3−333000000-220000−333−300001-1-1100000000
χ572-2-22-2-2222-12-2-22-2-22-2-211-11-1212-1-111-111-1-100002-22-11-1-1-111-1-1-211100000000−333−3−333−3−3−33333−3−3−3−33333−3−30000002-20000−333−30000-111-100000000
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χ622-2-22-2-222-12-222-211-111-2-22-22-1-2-12-111-111-1-100001-11-22-211-1-111-12-1-1i3−i3−i3i3i3−i3−i3i300000000i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3-220000001-1-110000−i3i3i3−i3000000000000
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χ694444-4-4-4-44-20000444-4-4-2-2-222-42-42-2-2-2-222222222−22−22000000000000000022222222−22−22−22−22−2−2−2−22222−2−2−2−2−2−2−2−22222222200000000000000000000000000000000
χ704444-4-4-4-44-20000444-4-4-2-2-222-42-42-2-2-2-22222−22−2222220000000000000000−22−22−22−22222222222222−2−2−2−222222222−2−2−2−2−2−2−2−200000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.