Finite Group Databasebeta

← Group #13150645

Character table — Group #13150645

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111222222446666666666661212121212121212121218181818181818181818181836363636363636363636363611112222224466666666666612121212121212121212181818181818181818181818363636363636363636363636
order124423461212612336666121212121212366661212121212888824242424242424242244666612121212224426461212612666666121212121212666661212121212888824242424242424242244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-1-11111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-1-11111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1
χ611-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111
χ711-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-11111-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-111
χ811-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-11111-111-1-1-11111-1-111-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-11111-111-1-1-11111-1-1
χ92222222222222-1222-122-1-122-1-1-1-1-1-1-1-1-1-1000000000000020200-1-100-1-12222222222222-1222-122-1-122-1-1-1-1-1-1-1-1-1-1000000000000020200-1-100-1-1
χ102222222222222-1222-122-1-122-1-1-1-1-1-1-1-1-1-10000000000000-20-2001100112222222222222-1222-122-1-122-1-1-1-1-1-1-1-1-1-10000000000000-20-200110011
χ11222222222222-12-1-1-12-1-122-1-1-12-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1000000000000222222222222-12-1-1-12-1-122-1-1-12-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ12222222222222-12-1-1-12-1-122-1-1-12-1-1-12-1-1-1-1-2-2-2-211111111000000000000222222222222-12-1-1-12-1-122-1-1-12-1-1-12-1-1-1-1-2-2-2-211111111000000000000
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χ152222-22-2222-2-22-1-2-22-122-1-1-2-2-1111-1111-1-1000000000000000000i3−i300i3−i32222-22-2222-2-22-1-2-22-122-1-1-2-2-1111-1111-1-1000000000000000000i3−i300i3−i3
χ162222-22-2222-2-2-1211-12-1-12211-1-211-1-211-1-1000033−3−333−3−30000000000002222-22-2222-2-2-1211-12-1-12211-1-211-1-211-1-1000033−3−333−3−3000000000000
χ172222-22-2222-2-2-1211-12-1-12211-1-211-1-211-1-10000−3−333−3−3330000000000002222-22-2222-2-2-1211-12-1-12211-1-211-1-211-1-10000−3−333−3−333000000000000
χ1822-2-222-22-2-22-2222222-2-2-2-2-2-222222-2-2-2-2-200000000000000000000000022-2-222-22-2-22-2222222-2-2-2-2-2-222222-2-2-2-2-2000000000000000000000000
χ1922-2-222-22-2-22-22-1222-1-2-211-2-2-1-1-1-1-111111000000000000000000−i3i300i3−i322-2-222-22-2-22-22-1222-1-2-211-2-2-1-1-1-1-111111000000000000000000−i3i300i3−i3
χ2022-2-222-22-2-22-22-1222-1-2-211-2-2-1-1-1-1-111111000000000000000000i3−i300−i3i322-2-222-22-2-22-22-1222-1-2-211-2-2-1-1-1-1-111111000000000000000000i3−i300−i3i3
χ2122-2-222-22-2-22-2-12-1-1-1211-2-211-12-1-1-1-21111000033−3−3−3−33300000000000022-2-222-22-2-22-2-12-1-1-1211-2-211-12-1-1-1-21111000033−3−3−3−333000000000000
χ2222-2-222-22-2-22-2-12-1-1-1211-2-211-12-1-1-1-211110000−3−33333−3−300000000000022-2-222-22-2-22-2-12-1-1-1211-2-211-12-1-1-1-211110000−3−33333−3−3000000000000
χ2322-2-2-2222-2-2-222-1-2-22-1-2-21122-1111-1-1-1-111000000000000020-200-1-1001122-2-2-2222-2-2-222-1-2-22-1-2-21122-1111-1-1-1-111000000000000020-200-1-10011
χ2422-2-2-2222-2-2-222-1-2-22-1-2-21122-1111-1-1-1-1110000000000000-202001100-1-122-2-2-2222-2-2-222-1-2-22-1-2-21122-1111-1-1-1-1110000000000000-202001100-1-1
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χ2622-2-2-2222-2-2-22-1211-1211-2-2-1-1-1-211-12-1-111-2-2221111-1-1-1-100000000000022-2-2-2222-2-2-22-1211-1211-2-2-1-1-1-211-12-1-111-2-2221111-1-1-1-1000000000000
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χ282-22i−2i020-22i−2i002200-2-22i−2i2i−2i002000-20002i−2i−22i2−i2−22−22i2−i2i2−i20000000000002-22i−2i020-22i−2i002200-2-22i−2i2i−2i002000-20002i−2i−22i2−i2−22−22i2−i2i2−i2000000000000
χ292-22i−2i020-22i−2i00-12−i3i31-2−ii2i−2i3−3-10−i3i3103−3−ii2−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000002-22i−2i020-22i−2i00-12−i3i31-2−ii2i−2i3−3-10−i3i3103−3−ii2−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ302-22i−2i020-22i−2i00-12−i3i31-2−ii2i−2i3−3-10−i3i3103−3−ii−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000002-22i−2i020-22i−2i00-12−i3i31-2−ii2i−2i3−3-10−i3i3103−3−ii−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ312-22i−2i020-22i−2i00-12i3−i31-2−ii2i−2i−33-10i3−i310−33−ii2−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000002-22i−2i020-22i−2i00-12i3−i31-2−ii2i−2i−33-10i3−i310−33−ii2−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
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χ332-2−2i2i020-2−2i2i002200-2-2−2i2i−2i2i002000-2000−2i2i2−2i2−i22−22−2i2−i2i2−i20000000000002-2−2i2i020-2−2i2i002200-2-2−2i2i−2i2i002000-2000−2i2i2−2i2−i22−22−2i2−i2i2−i2000000000000
χ342-2−2i2i020-2−2i2i002200-2-2−2i2i−2i2i002000-2000−2i2i−22−i2i2−22−22−i2i2−i2i20000000000002-2−2i2i020-2−2i2i002200-2-2−2i2i−2i2i002000-2000−2i2i−22−i2i2−22−22−i2i2−i2i2000000000000
χ352-2−2i2i020-2−2i2i00-12−i3i31-2i−i−2i2i−33-10−i3i310−33i−i2−2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000002-2−2i2i020-2−2i2i00-12−i3i31-2i−i−2i2i−33-10−i3i310−33i−i2−2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ362-2−2i2i020-2−2i2i00-12−i3i31-2i−i−2i2i−33-10−i3i310−33i−i−22−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000002-2−2i2i020-2−2i2i00-12−i3i31-2i−i−2i2i−33-10−i3i310−33i−i−22−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ372-2−2i2i020-2−2i2i00-12i3−i31-2i−i−2i2i3−3-10i3−i3103−3i−i2−2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000002-2−2i2i020-2−2i2i00-12i3−i31-2i−i−2i2i3−3-10i3−i3103−3i−i2−2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ382-2−2i2i020-2−2i2i00-12i3−i31-2i−i−2i2i3−3-10i3−i3103−3i−i−22−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000002-2−2i2i020-2−2i2i00-12i3−i31-2i−i−2i2i3−3-10i3−i3103−3i−i−22−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ39444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2111-21111000000000000000000000000444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2111-21111000000000000000000000000
χ404444-44-4444-4-4-2-222-2-2-2-2-2-22212-1-112-1-1110000000000000000000000004444-44-4444-4-4-2-222-2-2-2-2-2-22212-1-112-1-111000000000000000000000000
χ4144-4-444-44-4-44-4-2-2-2-2-2-22222221-21112-1-1-1-100000000000000000000000044-4-444-44-4-44-4-2-2-2-2-2-22222221-21112-1-1-1-1000000000000000000000000
χ4244-4-4-4444-4-4-44-2-222-2-22222-2-212-1-11-211-1-100000000000000000000000044-4-4-4444-4-4-44-2-222-2-22222-2-212-1-11-211-1-1000000000000000000000000
χ434-44i−4i040-44i−4i004-200-424i−4i−2i2i00-20002000−2i2i0000000000000000000000004-44i−4i040-44i−4i004-200-424i−4i−2i2i00-20002000−2i2i000000000000000000000000
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χ601111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-11-1-111-1-111
χ621111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-111-1-111-1-1
χ6311-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-1-11111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1111-1-1-1111-1-1-111-1-11111-1-1-1111-1-1-1-111-1-111-1-1-1-11111-1-111-1-1-1-11111
χ6411-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1111-1-1-1111-1-1-111-1-11111-1-1-1111-1-1-1-111-1-111-1-1-1-1111111-1-11111-1-1-1-1
χ6511-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-111-1-1111-1-1-1111-1-1-111-1-11111-1-1-1111-1-1-1-11111-1-11111-1-1-1-1-111-1-1-11111-1-1
χ6611-1-1-1111-1-1-1111-1-111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-11111-111-1-1-11111-1-1-1-1111-1-1-1111-1-1-111-1-11111-1-1-1111-1-1-1-11111-1-11111-1-1-1-11-1-1111-1-1-1-111
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χ69222222222222-12-1-1-12-1-122-1-1-12-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1000000000000-2-2-2-2-2-2-2-2-2-2-2-21-2111-211-2-2111-2111-21111-2-2-2-211111111000000000000
χ70222222222222-12-1-1-12-1-122-1-1-12-1-1-12-1-1-1-1-2-2-2-211111111000000000000-2-2-2-2-2-2-2-2-2-2-2-21-2111-211-2-2111-2111-211112222-1-1-1-1-1-1-1-1000000000000
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χ872-22i−2i020-22i−2i00-12−i3i31-2−ii2i−2i3−3-10−i3i3103−3−ii2−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000-22−2i2i0-202−2i2i001-2i3−i3-12i−i−2i2i−3310i3−i3-10−33i−i−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
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χ912-2−2i2i020-2−2i2i002200-2-2−2i2i−2i2i002000-2000−2i2i2−2i2−i22−22−2i2−i2i2−i2000000000000-222i−2i0-2022i−2i00-2-200222i−2i2i−2i00-200020002i−2i−22−i2i2−22−22−i2i2−i2i2000000000000
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χ932-2−2i2i020-2−2i2i00-12−i3i31-2i−i−2i2i−33-10−i3i310−33i−i2−2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000-222i−2i0-2022i−2i001-2i3−i3-12−ii2i−2i3−310i3−i3-103−3−ii−22−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ942-2−2i2i020-2−2i2i00-12−i3i31-2i−i−2i2i−33-10−i3i310−33i−i−22−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000-222i−2i0-2022i−2i001-2i3−i3-12−ii2i−2i3−310i3−i3-103−3−ii2−2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ952-2−2i2i020-2−2i2i00-12i3−i31-2i−i−2i2i3−3-10i3−i3103−3i−i2−2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000-222i−2i0-2022i−2i001-2−i3i3-12−ii2i−2i−3310−i3i3-10−33−ii−22−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ962-2−2i2i020-2−2i2i00-12i3−i31-2i−i−2i2i3−3-10i3−i3103−3i−i−22−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000-222i−2i0-2022i−2i001-2−i3i3-12−ii2i−2i−3310−i3i3-10−33−ii2−2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
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χ984444-44-4444-4-4-2-222-2-2-2-2-2-22212-1-112-1-111000000000000000000000000-4-4-4-44-44-4-4-44422-2-2222222-2-2-1-211-1-211-1-1000000000000000000000000
χ9944-4-444-44-4-44-4-2-2-2-2-2-22222221-21112-1-1-1-1000000000000000000000000-4-444-4-44-444-44222222-2-2-2-2-2-2-12-1-1-1-21111000000000000000000000000
χ10044-4-4-4444-4-4-44-2-222-2-22222-2-212-1-11-211-1-1000000000000000000000000-4-4444-4-4-4444-422-2-222-2-2-2-222-1-211-12-1-111000000000000000000000000
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χ10766666-36-3-3-3-3-300000000000000000000000000000000002020-1-100-1-100-6-6-6-6-63-6333330000000000000000000000000000000000-20-2011001100
χ10866666-36-3-3-3-3-30000000000000000000000000000000000-20-2011001100-6-6-6-6-63-63333300000000000000000000000000000000002020-1-100-1-100
χ1096666-6-3-6-3-3-33300000000000000000000000000000000000000−i3i300−i3i300-6-6-6-6636333-3-300000000000000000000000000000000000000i3−i300i3−i300
χ1106666-6-3-6-3-3-33300000000000000000000000000000000000000i3−i300i3−i300-6-6-6-6636333-3-300000000000000000000000000000000000000−i3i300−i3i300
χ11166-6-66-3-6-333-3300000000000000000000000000000000000000−i3i300i3−i300-6-666-6363-3-33-300000000000000000000000000000000000000i3−i300−i3i300
χ11266-6-66-3-6-333-3300000000000000000000000000000000000000i3−i300−i3i300-6-666-6363-3-33-300000000000000000000000000000000000000−i3i300i3−i300
χ11366-6-6-6-36-3333-3000000000000000000000000000000000020-20-1-1001100-6-66663-63-3-3-330000000000000000000000000000000000-20201100-1-100
χ11466-6-6-6-36-3333-30000000000000000000000000000000000-20201100-1-100-6-66663-63-3-3-33000000000000000000000000000000000020-20-1-1001100
χ11512-1212i−12i0-606−6i6i000000000000000000000000000000000000000000000000-1212−12i12i060-66i−6i000000000000000000000000000000000000000000000000
χ11612-12−12i12i0-6066i−6i000000000000000000000000000000000000000000000000-121212i−12i060-6−6i6i000000000000000000000000000000000000000000000000

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