Finite Group Databasebeta

← Group #13155264

Character table — Group #13155264

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size11222222222222222444444444444444444444444888888888881212121212121212121212121212121212121212121212121212121212121212121212121818243636363636484848487272144144216
order123334666881212242424243336661212121212122424242424242424242424243612121224242424242416161616484848484848484848484848484848484848484848484848484848484848484824468122424121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111-11-1-1
χ4111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111
χ51111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-1-1-1-1-11111-11-11-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-11111-1
χ9222222222-2-222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2-20000000000000000000000000000000000002202-22-2-2000000000
χ10222222222-2-222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2-2000000000000000000000000000000000000-2-20-22-222000000000
χ1122222-222200-2-20000222222-2-2-2-2-2-200000000000022-2-2-20000002−22−222−2−222−2−2222222−2−2−2−2−2−2222222−2−2−2−2−2−22-2020-200000000000
χ1222222-222200-2-20000222222-2-2-2-2-2-200000000000022-2-2-20000002−2−2222−2−2−2−222222222−2−2−2−2−2−2−2−2−2−2−2−2222222-220-20200000000000
χ1322222-222200-2-20000222222-2-2-2-2-2-200000000000022-2-2-2000000−222−2−2−22222−2−2−2−2−2−2−2−2222222222222−2−2−2−2−2−2-220-20200000000000
χ1422222-222200-2-20000222222-2-2-2-2-2-200000000000022-2-2-2000000−22−22−2−222−2−222−2−2−2−2−2−2222222−2−2−2−2−2−22222222-2020-200000000000
χ152222-12-12222-1-1-1-1-1-12-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1220-12-1-1-1000000000
χ162222-12-12222-1-1-1-1-1-12-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-122-2-2-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-201-2111000000000
χ172222-12-12222-1-1-1-1-1-12-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-1-2-2221111-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-201-2111000000000
χ182222-12-12222-1-1-1-1-1-12-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-1-2-2-2-211111111-2-21111-2-21111-2-21111-2-21111220-12-1-1-1000000000
χ192222-12-122-2-2-1-111112-1-1-1-1222-1-1-1-1-2-2-2-211111111-1-12-1-1-2-2111100003−33−33−33−30033−3−30033−3−30033−3−30033−3−3220-1-2-111000000000
χ202222-12-122-2-2-1-111112-1-1-1-1222-1-1-1-1-2-2-2-211111111-1-12-1-1-2-2111100003−33−3−33−330033−3−30033−3−300−3−33300−3−333-2-20121-1-1000000000
χ212222-12-122-2-2-1-111112-1-1-1-1222-1-1-1-1-2-2-2-211111111-1-12-1-1-2-211110000−33−333−33−300−3−33300−3−3330033−3−30033−3−3-2-20121-1-1000000000
χ222222-12-122-2-2-1-111112-1-1-1-1222-1-1-1-1-2-2-2-211111111-1-12-1-1-2-211110000−33−33−33−3300−3−33300−3−33300−3−33300−3−333220-1-2-111000000000
χ232222-1-2-122001133−3−32-1-1-1-12-2-2111100003333−3−3−3−3-1-1-2110033−3−32−22−2ζ10−ζ14ζ26−ζ46−ζ10+ζ14−ζ26+ζ46ζ10−ζ14ζ26−ζ46−ζ10+ζ14−ζ26+ζ4622ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ4622ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ462-20-1013−3000000000
χ242222-1-2-122001133−3−32-1-1-1-12-2-2111100003333−3−3−3−3-1-1-2110033−3−32−2−22ζ10−ζ14ζ26−ζ46−ζ10+ζ14−ζ26+ζ46−ζ10+ζ14−ζ26+ζ46ζ10−ζ14ζ26−ζ4622ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ4622ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46-22010-1−33000000000
χ252222-1-2-122001133−3−32-1-1-1-12-2-2111100003333−3−3−3−3-1-1-2110033−3−3−222−2−ζ10+ζ14−ζ26+ζ46ζ10−ζ14ζ26−ζ46ζ10−ζ14ζ26−ζ46−ζ10+ζ14−ζ26+ζ46−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ4622ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ4622ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46-22010-1−33000000000
χ262222-1-2-122001133−3−32-1-1-1-12-2-2111100003333−3−3−3−3-1-1-2110033−3−3−22−22−ζ10+ζ14−ζ26+ζ46ζ10−ζ14ζ26−ζ46−ζ10+ζ14−ζ26+ζ46ζ10−ζ14ζ26−ζ46−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ4622ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ4622ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ462-20-1013−3000000000
χ272222-1-2-1220011−3−3332-1-1-1-12-2-211110000−3−3−3−33333-1-1-21100−3−3332−22−2ζ26−ζ46ζ10−ζ14−ζ26+ζ46−ζ10+ζ14ζ26−ζ46ζ10−ζ14−ζ26+ζ46−ζ10+ζ1422ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−2−2−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ1422ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−2−2−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ142-20-101−33000000000
χ282222-1-2-1220011−3−3332-1-1-1-12-2-211110000−3−3−3−33333-1-1-21100−3−3332−2−22ζ26−ζ46ζ10−ζ14−ζ26+ζ46−ζ10+ζ14−ζ26+ζ46−ζ10+ζ14ζ26−ζ46ζ10−ζ1422ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−2−2−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14−2−2−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ1422ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14-22010-13−3000000000
χ292222-1-2-1220011−3−3332-1-1-1-12-2-211110000−3−3−3−33333-1-1-21100−3−333−222−2−ζ26+ζ46−ζ10+ζ14ζ26−ζ46ζ10−ζ14ζ26−ζ46ζ10−ζ14−ζ26+ζ46−ζ10+ζ14−2−2−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ1422ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ1422ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−2−2−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14-22010-13−3000000000
χ302222-1-2-1220011−3−3332-1-1-1-12-2-211110000−3−3−3−33333-1-1-21100−3−333−22−22−ζ26+ζ46−ζ10+ζ14ζ26−ζ46ζ10−ζ14−ζ26+ζ46−ζ10+ζ14ζ26−ζ46ζ10−ζ14−2−2−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ1422ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−2−2−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ1422ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ142-20-101−33000000000
χ31222-12222-122222222-12-12-1-12-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-1002000002-1-1-1020-10
χ32222-12222-122222222-12-12-1-12-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100-200000-21110-2010
χ33222-12222-122222222-12-12-1-12-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-2000000000000111111111111002000002-1-1-10-2010
χ34222-12222-122222222-12-12-1-12-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-200000000000011111111111100-200000-2111020-10
χ3522-12222-1222222222-1-12-12-1-12-1-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000200000-12-1-120-100
χ3622-12222-1222222222-1-12-12-1-12-1-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2000001-211-20100
χ3722-12222-1222222222-1-12-12-1-12-1-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2000011111111111100000000000000200000-12-1-1-20100
χ3822-12222-1222222222-1-12-12-1-12-1-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2000011111111111100000000000000-2000001-21120-100
χ39444-24444-2-4-444-4-4-4-4-24-24-2-24-244-2-2-4-422-4-422-4-422-2-2-2-2-222222200000000000000000000000000000000000000000000000000000
χ40444-24-444-200-4-40000-24-24-2-2-42-4-422000000000000-2-22220000000022−2200002222−22−22000000000000−2−2−2−2−2−222222200000000000000000
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χ42444-2-24-24-244-2-2-2-2-2-2-2-21-21-24-2-2-21144-2-2-2-211-2-21111-211-2-2111100440000-2-2-2-2000000000000-2-21111-2-2111100000000000000000
χ43444-2-24-24-244-2-2-2-2-2-2-2-21-21-24-2-2-21144-2-2-2-211-2-21111-211-2-2111100-4-40000222200000000000022-1-1-1-122-1-1-1-100000000000000000
χ44444-2-24-24-2-4-4-2-22222-2-21-21-24-2-2-211-4-42222-1-122-1-111-21122-1-1-1-10000000023−2323−2300000000000000−3−33300−3−33300000000000000000
χ45444-2-24-24-2-4-4-2-22222-2-21-21-24-2-2-211-4-42222-1-122-1-111-21122-1-1-1-100000000−2323−23230000000000000033−3−30033−3−300000000000000000
χ46444-2-2-4-24-200222323−23−23-2-21-21-2-4222-1-100002323−3−3−23−2333112-1-100−3−3330022−2200002ζ10−2ζ142ζ26−2ζ46−2ζ10+2ζ14−2ζ26+2ζ46000000000000−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ4622ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ4600000000000000000
χ47444-2-2-4-24-200222323−23−23-2-21-21-2-4222-1-100002323−3−3−23−2333112-1-100−3−33300−22220000−2ζ10+2ζ14−2ζ26+2ζ462ζ10−2ζ142ζ26−2ζ4600000000000022ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ4600000000000000000
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χ5344-24-24-2-2444-2-2-2-2-2-2-21-21-2-2-2411-2-2-2-24411-2-211-2-211-211-2-211114400-2-2-2-20000-2-21111-2-2111100000000000000000000000000000
χ5444-24-24-2-2444-2-2-2-2-2-2-21-21-2-2-2411-2-2-2-24411-2-211-2-211-211-2-21111-4-4002222000022-1-1-1-122-1-1-1-100000000000000000000000000000
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χ6344-2-2444-2-2-4-444-4-4-4-41-2-2-2-21-2-2-2-2-2-222222222222211111-1-1-1-1-1-100000000000000000000000000000000000000000000003-300000
χ6444-2-2444-2-2-4-444-4-4-4-41-2-2-2-21-2-2-2-2-2-222222222222211111-1-1-1-1-1-10000000000000000000000000000000000000000000000-3300000
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χ694-444-202-4-4−222223−23−2ζ10+2ζ142ζ10−2ζ14−2ζ26+2ζ462ζ26−2ζ464-2-222-40023−2323−23−2222−2222−2ζ10+2ζ142ζ10−2ζ14−2ζ10+2ζ142ζ10−2ζ14−2ζ26+2ζ462ζ26−2ζ46−2ζ26+2ζ462ζ26−2ζ46-22023−23−2222−2ζ10+2ζ142ζ10−2ζ14−2ζ26+2ζ462ζ26−2ζ4600000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1).