Finite Group Databasebeta

← Group #11782891

Character table — Group #11782891

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222244444444444444444444444444444444444444444444444444444444444444443636363636363636484848484848484848484848
order12223344444466666636668888121212121212121212121212121212121212121212121212242424242424242424242424242424242424242424242424242424242424242488888888244466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-1
χ61111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-111
χ71111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111
χ81111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1
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χ1822222-122222222-1-1-12-1-1-1-1-2-2-2-222-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111111111-2-2-2-211111111111100000000-220011-1-10000
χ1922222-122-2-2-2-222-1-1-12-1-1-1-122-2-2-2-211-2-21111111111-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000−i3i3−i3i30000
χ2022222-122-2-2-2-222-1-1-12-1-1-1-122-2-2-2-211-2-21111111111-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000i3−i3i3−i30000
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χ834-44-4-2-20000-44-2222-2211-1-1−222222−2200002-22-23i−3i3i−3i-1-1110000−3i3i−3i3i22−2−222−2−2−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23−2−222−2−222−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ2300000000000000000000
χ844-44-4-2-20000-44-2222-2211-1-1−222222−2200002-22-2−3i3i−3i3i-1-11100003i−3i3i−3i22−2−222−2−22ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2−222−2−222ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ2300000000000000000000
χ854-4-44444-40000-4-4-44-444-4-44000000000000000000004-44-4-444-40000000000000000000000000000000000000000000000000000
χ864-4-4444-440000-4-4-44-444-4-4400000000000000000000-44-444-4-440000000000000000000000000000000000000000000000000000
χ874-4-444-24-40000-4-42-224-222-200000000000000000000-224-42-2-220000000000000000000023−23−232323−2323−23−2323−232300000000000000000000
χ884-4-444-24-40000-4-42-224-222-200000000000000000000-224-42-2-2200000000000000000000−232323−23−2323−232323−2323−2300000000000000000000
χ894-4-444-2-440000-4-42-224-222-2000000000000000000002-2-44-222-2000023−23−232323−2323−23−2323−2323000000000000000000000000000000000000
χ904-4-444-2-440000-4-42-224-222-2000000000000000000002-2-44-222-20000−232323−23−2323−232323−2323−23000000000000000000000000000000000000
χ914-4-44-244-4000022-44-4-2-222-2000000000000000000004-4-222-2-22−2i32i32i3−2i30000−2i32i32i3−2i32i3−2i3−2i32i3000000000000000000000000000000000000
χ924-4-44-244-4000022-44-4-2-222-2000000000000000000004-4-222-2-222i3−2i3−2i32i300002i3−2i3−2i32i3−2i32i32i3−2i3000000000000000000000000000000000000
χ934-4-44-24-44000022-44-4-2-222-200000000000000000000-442-2-222-20000000000000000−2i32i32i3−2i30000−2i32i32i3−2i32i3−2i3−2i32i300000000000000000000
χ944-4-44-24-44000022-44-4-2-222-200000000000000000000-442-2-222-200000000000000002i3−2i3−2i32i300002i3−2i3−2i32i3−2i32i32i3−2i300000000000000000000
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χ964-4-44-2-24-40000222-22-21-1-110000000000003i−3i−3i3i3i−3i−3i3i-22-22-111-12i3−2i3−2i32i30000−i3i3i3−i3i3−i3−i3i3000023−23−2323−33−333−33−300000000000000000000
χ974-4-44-2-24-40000222-22-21-1-11000000000000−3i3i3i−3i−3i3i3i−3i-22-22-111-1−2i32i32i3−2i30000i3−i3−i3i3−i3i3i3−i3000023−23−2323−33−333−33−300000000000000000000
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χ994-4-44-2-2-440000222-22-21-1-110000000000003i−3i−3i3i−3i3i3i−3i2-22-21-1-11000023−23−2323−33−333−33−3−2i32i32i3−2i30000i3−i3−i3i3−i3i3i3−i300000000000000000000
χ1004-4-44-2-2-440000222-22-21-1-110000000000003i−3i−3i3i−3i3i3i−3i2-22-21-1-110000−232323−233−33−3−33−332i3−2i3−2i32i30000−i3i3i3−i3i3−i3−i3i300000000000000000000
χ1014-4-44-2-2-440000222-22-21-1-11000000000000−3i3i3i−3i3i−3i−3i3i2-22-21-1-11000023−23−2323−33−333−33−32i3−2i3−2i32i30000−i3i3i3−i3i3−i3−i3i300000000000000000000
χ1024-4-44-2-2-440000222-22-21-1-11000000000000−3i3i3i−3i3i−3i−3i3i2-22-21-1-110000−232323−233−33−3−33−33−2i32i32i3−2i30000i3−i3−i3i3−i3i3i3−i300000000000000000000

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