Finite Group Databasebeta

← Group #13138721

Character table — Group #13138721

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222222222222226666666612121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order12442346668888121212122424242424242424336612121212366666121212121212242424242424242424242424242424241616161616161616484848484848484848484848484848482244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511-1-1-111-1-11-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ611-1-1-111-1-11-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711-1-1-111-1-11-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ811-1-1-111-1-11-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222-12-122-1-1-12-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000020200-1-100-1-1
χ10222222222222222222222222222-12-122-1-1-12-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000000000000-20-200110011
χ1122222222222222222222222222-12-12-1-122-1-12-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-10000000000000000000000002020-1-100-1-100
χ1222222222222222222222222222-12-12-1-122-1-12-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000-20-2011001100
χ132222222222-2-2-2-22222-2-2-2-2-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ142222222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-122-1-1-12-1-1-1-1-1-12-1-1-1-2-2111111-2-2111111000000000000000000000000000000−i3i300−i3i3
χ152222222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-122-1-1-12-1-1-1-1-1-12-1-1-1-2-2111111-2-2111111000000000000000000000000000000i3−i300i3−i3
χ162222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-12-1-122-1-12-1-1-1-1-1-12-1-111-2-2111111-2-211110000000000000000000000000000−i3i300−i3i300
χ172222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-12-1-122-1-12-1-1-1-1-1-12-1-111-2-2111111-2-211110000000000000000000000000000i3−i300i3−i300
χ182222-22-2-2-22000022-2-200000000222222222-2-2-2-2222-2-2-2-2000000000000000022−2−222−2−22222−2−2−2−22222−2−2−2−2000000000000
χ192222-22-2-2-22000022-2-200000000222222222-2-2-2-2222-2-2-2-20000000000000000−2−222−2−222−2−2−2−22222−2−2−2−22222000000000000
χ2022-2-222-22220000-2-2-2-2000000002222-2-2-2-2222222-2-2-2-2-2-2000000000000000022−2−2−2−2222222−2−2−2−2−2−2−2−22222000000000000
χ2122-2-222-22220000-2-2-2-2000000002222-2-2-2-2222222-2-2-2-2-2-20000000000000000−2−22222−2−2−2−2−2−222222222−2−2−2−2000000000000
χ2222-2-2-222-2-2222-2-2-2-2222222-2-2-2-22222-2-2-2-22-2-2-2-22-2-22222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ2322-2-2-222-2-2222-2-2-2-2222222-2-2-2-22-12-1-2-211-1-2111-1112-1-1-1-2-211111122-1-1-1-1-1-1000000000000000000000000000000−i3i300i3−i3
χ2422-2-2-222-2-2222-2-2-2-2222222-2-2-2-22-12-1-2-211-1-2111-1112-1-1-1-2-211111122-1-1-1-1-1-1000000000000000000000000000000i3−i300−i3i3
χ2522-2-2-222-2-2222-2-2-2-2222222-2-2-2-2-12-1211-2-2-11-211-111-12-1-111-2-21111-1-122-1-1-1-10000000000000000000000000000−i3i300i3−i300
χ2622-2-2-222-2-2222-2-2-2-2222222-2-2-2-2-12-1211-2-2-11-211-111-12-1-111-2-21111-1-122-1-1-1-10000000000000000000000000000i3−i300−i3i300
χ2722-2-2-222-2-22-2-222-2-222-2-2-2-222222-12-1-2-211-1-2111-1112-1-1-122-1-1-1-1-1-1-2-2111111000000000000000000000000020-200-1-10011
χ2822-2-2-222-2-22-2-222-2-222-2-2-2-222222-12-1-2-211-1-2111-1112-1-1-122-1-1-1-1-1-1-2-21111110000000000000000000000000-202001100-1-1
χ2922-2-2-222-2-22-2-222-2-222-2-2-2-22222-12-1211-2-2-11-211-111-12-1-1-1-122-1-1-1-111-2-2111100000000000000000000000020-20-1-1001100
χ3022-2-2-222-2-22-2-222-2-222-2-2-2-22222-12-1211-2-2-11-211-111-12-1-1-1-122-1-1-1-111-2-21111000000000000000000000000-20201100-1-100
χ312-22i−2i02000-2−i2i22−22i−2i00−i2−i2i2i222−2−222-2-22i−2i2i−2i20000-22i−2i00002−22−222−2−2−i2i2−i2i2−i2−i2i2i2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47000000000000
χ322-22i−2i02000-2−i2i22−22i−2i00−i2−i2i2i222−2−222-2-22i−2i2i−2i20000-22i−2i00002−22−222−2−2−i2i2−i2i2−i2−i2i2i2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47000000000000
χ332-22i−2i02000-2i2−i2−222i−2i00i2i2−i2−i2−2−22222-2-22i−2i2i−2i20000-22i−2i0000−22−22−2−222i2−i2i2−i2i2i2−i2−i2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43000000000000
χ342-22i−2i02000-2i2−i2−222i−2i00i2i2−i2−i2−2−22222-2-22i−2i2i−2i20000-22i−2i0000−22−22−2−222i2−i2i2−i2i2i2−i2−i2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43000000000000
χ352-2−2i2i02000-2−i2i2−22−2i2i00−i2−i2i2i2−2−22222-2-2−2i2i−2i2i20000-2−2i2i0000−22−22−2−222−i2i2−i2i2−i2−i2i2i2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43000000000000
χ362-2−2i2i02000-2−i2i2−22−2i2i00−i2−i2i2i2−2−22222-2-2−2i2i−2i2i20000-2−2i2i0000−22−22−2−222−i2i2−i2i2−i2−i2i2i2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43000000000000
χ372-2−2i2i02000-2i2−i22−2−2i2i00i2i2−i2−i222−2−222-2-2−2i2i−2i2i20000-2−2i2i00002−22−222−2−2i2−i2i2−i2i2i2−i2−i2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47000000000000
χ382-2−2i2i02000-2i2−i22−2−2i2i00i2i2−i2−i222−2−222-2-2−2i2i−2i2i20000-2−2i2i00002−22−222−2−2i2−i2i2−i2i2i2−i2−i2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47000000000000
χ3944444444444444444444444444-2-2-2-2-2-2-2-21-2-211111-2-211-2-2-2-21111-2-2-2-21111000000000000000000000000000000000000
χ404444444444-4-4-4-44444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-21-2-211111-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ414444-44-4-4-44000044-4-4000000004-24-244-2-2-2-4222-2-2-2-42220000000000000000000000000000000000000000000000000000
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χ434444-44-4-4-44000044-4-400000000-2-2-2-2-2-2-2-2122-1-111122-1-100003i−3i3i−3i00003i−3i3i−3i000000000000000000000000000000000000
χ444444-44-4-4-44000044-4-400000000-2-2-2-2-2-2-2-2122-1-111122-1-10000−3i3i−3i3i0000−3i3i−3i3i000000000000000000000000000000000000
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χ4844-4-444-44440000-4-4-4-400000000-2-2-2-222221-2-2111-1-122-1-10000−3i3i−3i3i00003i−3i3i−3i000000000000000000000000000000000000
χ4944-4-4-444-4-4444-4-4-4-4444444-4-4-4-4-2-2-2-22222122-1-11-1-1-2-2112222-1-1-1-1-2-2-2-21111000000000000000000000000000000000000
χ5044-4-4-444-4-44-4-444-4-444-4-4-4-44444-2-2-2-22222122-1-11-1-1-2-211-2-2-2-211112222-1-1-1-1000000000000000000000000000000000000
χ514-44i−4i04000-4−2i22i222−224i−4i00−2i2−2i22i22i22222−22−224-2-424i−4i−2i2i-200002−2i2i000022−22−22−2−222−2i22i2i2−i2i2i2−i2−i2000000000000000000000000000000000000
χ524-44i−4i04000-4−2i22i222−224i−4i00−2i2−2i22i22i22222−22−22-242-4−2i2i4i−4i-200002−2i2i0000−2222−22−2−222i2−i2−2i22i2i2i2−i2−i2000000000000000000000000000000000000
χ534-44i−4i04000-4−2i22i222−224i−4i00−2i2−2i22i22i22222−22−22-2-222−2i2i−2i2i1003-3-1i−i003i−3i−22−22−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ46i2−i2i2−i2ζ10−2ζ14+ζ26−2ζ46−2ζ10+ζ14−2ζ26+ζ46−ζ10+2ζ14−ζ26+2ζ462ζ10−ζ14+2ζ26−ζ46000000000000000000000000000000000000
χ544-44i−4i04000-4−2i22i222−224i−4i00−2i2−2i22i22i22222−22−22-2-222−2i2i−2i2i100-33-1i−i00−3i3i−22−22ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46i2−i2i2−i2−2ζ10+ζ14−2ζ26+ζ46ζ10−2ζ14+ζ26−2ζ462ζ10−ζ14+2ζ26−ζ46−ζ10+2ζ14−ζ26+2ζ46000000000000000000000000000000000000
χ554-44i−4i04000-42i2−2i2−22224i−4i002i22i2−2i2−2i2−22−2222224-2-424i−4i−2i2i-200002−2i2i0000−22222−222−2−22i2−2i2−i2i2−i2−i2i2i2000000000000000000000000000000000000
χ564-44i−4i04000-42i2−2i2−22224i−4i002i22i2−2i2−2i2−22−222222-242-4−2i2i4i−4i-200002−2i2i00002−2−222222−2−2−i2i22i2−2i2−i2−i2i2i2000000000000000000000000000000000000
χ574-44i−4i04000-42i2−2i2−22224i−4i002i22i2−2i2−2i2−22−222222-2-222−2i2i−2i2i1003-3-1i−i003i−3i2−22−22ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ46−i2i2−i2i2−ζ10+2ζ14−ζ26+2ζ462ζ10−ζ14+2ζ26−ζ46ζ10−2ζ14+ζ26−2ζ46−2ζ10+ζ14−2ζ26+ζ46000000000000000000000000000000000000
χ584-44i−4i04000-42i2−2i2−22224i−4i002i22i2−2i2−2i2−22−222222-2-222−2i2i−2i2i100-33-1i−i00−3i3i2−22−2−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46−i2i2−i2i22ζ10−ζ14+2ζ26−ζ46−ζ10+2ζ14−ζ26+2ζ46−2ζ10+ζ14−2ζ26+ζ46ζ10−2ζ14+ζ26−2ζ46000000000000000000000000000000000000
χ594-4−4i4i04000-4−2i22i2−2222−4i4i00−2i2−2i22i22i2−22−2222224-2-42−4i4i2i−2i-2000022i−2i0000−22222−222−2−2−2i22i2i2−i2i2i2−i2−i2000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.