Finite Group Databasebeta

← Group #13170582

Character table — Group #13170582

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
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order122333446666612123336666666661212121212121212121212883666612121212121212244482424242424242424242424242424242466661212121212121212121212122224882244666122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1111111111111111111111-1-11-1-1111-1-1-1-11-1-11-1-1-1-1-1-11-1-11-1-1
χ31111111111111111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-111-111-1-1-11111-111-1-1-1-1-1-1-1-111-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ511111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ611111111111111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1111-1-1-1-1-111-1-1-11111-111-1-1-1
χ711111111111111111111111111111111111111-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-111111-1-11-1-111111-1-11-1-1
χ811111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111
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χ874-404-2-200−2i32i32-42−2323-21-200−2i32i3i3−i3-122003−3−232300−3i3i0−2i22i210i3−i3-1000−3i3i3−300000i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000000000000000000000
χ884-404-2-200−2i32i32-42−2323-21-200−2i32i3i3−i3-122003−3−232300−3i3i02i2−2i210i3−i3-1000−3i3i3−300000−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000000000000000000000
χ894-404-2-2002i3−2i32-4223−23-21-2002i3−2i3−i3i3-12200−3323−2300−3i3i0−2i22i210−i3i3-1000−3i3i−3300000i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000000000000000000000
χ904-404-2-2002i3−2i32-4223−23-21-2002i3−2i3−i3i3-12200−3323−2300−3i3i02i2−2i210−i3i3-1000−3i3i−3300000−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000000000000000000000
χ914-404-2-2002i3−2i32-42−2323-21-2002i3−2i3−i3i3-122003−3−2323003i−3i0−2i22i210−i3i3-10003i−3i3−300000i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000000000000000000000
χ924-404-2-2002i3−2i32-42−2323-21-2002i3−2i3−i3i3-122003−3−2323003i−3i02i2−2i210−i3i3-10003i−3i3−300000−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000000000000000000000
χ93888-4-4-488-4-4-4-4-4-4-4222-4-42222222-4-42222-4-422-400-12-1-1-1222-1-1-1-100000000000000000000000000000000000000000000000000000
χ94888-4-4-4-8-8-4-4-4-4-444222-4-4222222244-2-2-2-244-2-2400-12-1-1-1-2-2-2111100000000000000000000000000000000000000000000000000000
χ9588-8-4-4-48-844-4-4-4-4-422244-2-2-2-2222-4-4222244-2-2400-1-211-1-2-2211-1-100000000000000000000000000000000000000000000000000000
χ9688-8-4-4-4-8844-4-4-44422244-2-2-2-222244-2-2-2-2-4-422-400-1-211-122-2-1-11100000000000000000000000000000000000000000000000000000
χ978-80-4880000-84-800-48-4000000-8440000000000000-40004000000000000000000000000000000000000000000000000000000000000
χ988-80-48-400−4i34i344-8002-4-4002i3−2i3−4i34i344-20000000000000202i3−2i3-2000000000000000000000000000000000000000000000000000000000000
χ998-80-48-4004i3−4i344-8002-4-400−2i32i34i3−4i344-2000000000000020−2i32i3-2000000000000000000000000000000000000000000000000000000000000
χ1008-80-4-480000-84443−43-4-420000004-240043−43−232300000002000-200000−232300000000000000000000000000000000000000000000000000000
χ1018-80-4-480000-844−4343-4-420000004-2400−434323−2300000002000-20000023−2300000000000000000000000000000000000000000000000000000
χ1028-80-4-4-400−4i34i344443−43222002i3−2i32i3−2i3-2-2-200−2323−2323006i−6i000-10−i3i31000−3i3i3−300000000000000000000000000000000000000000000000000000
χ1038-80-4-4-400−4i34i3444−4343222002i3−2i32i3−2i3-2-2-20023−2323−2300−6i6i000-10−i3i310003i−3i−3300000000000000000000000000000000000000000000000000000
χ1048-80-4-4-4004i3−4i344443−4322200−2i32i3−2i32i3-2-2-200−2323−232300−6i6i000-10i3−i310003i−3i3−300000000000000000000000000000000000000000000000000000
χ1058-80-4-4-4004i3−4i3444−434322200−2i32i3−2i32i3-2-2-20023−2323−23006i−6i000-10i3−i31000−3i3i−3300000000000000000000000000000000000000000000000000000

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