Finite Group Databasebeta

← Group #11772228

Character table — Group #11772228

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222444444444444444488888888181818181818181818181818181818181818181818181818242424242424242424242424242424242424242424242424
order122244444444336666661212121212121212121212121212121288888888161616161616161616161616161616168888888824242424242424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i
χ61111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii
χ71111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii
χ81111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ911-1-1i−ii−ii−i1-11111-1-1-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-11111-1-1-1-1iiii−i−i−i−iζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26
χ1011-1-1i−ii−ii−i1-11111-1-1-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-11111-1-1-1-1iiii−i−i−i−i−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26
χ1111-1-1i−ii−ii−i1-11111-1-1-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-1-1-1-1-11111−i−i−i−iiiiiζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26
χ1211-1-1i−ii−ii−i1-11111-1-1-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-1-1-1-1-11111−i−i−i−iiiii−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26
χ1311-1-1−ii−ii−ii1-11111-1-1-1-1−i−iii−i−iii11-1-1−i−iii−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46
χ1411-1-1−ii−ii−ii1-11111-1-1-1-1−i−iii−i−iii11-1-1−i−iii−i−iii11-1-11111-1-1-1-1−i−i−i−iiiiiζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46
χ1511-1-1−ii−ii−ii1-11111-1-1-1-1−i−iii−i−iii11-1-1−i−iii−i−iii11-1-1-1-1-1-11111iiii−i−i−i−i−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46
χ1611-1-1−ii−ii−ii1-11111-1-1-1-1−i−iii−i−iii11-1-1−i−iii−i−iii11-1-1-1-1-1-11111iiii−i−i−i−iζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46
χ17222222222222222222222222222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
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χ212222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000−2−222−2−22222−2−222−2−2000000000000000000000000
χ222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
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χ2422-2-22i−2i2i−2i−2i2i-222222-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-222−2i−2i2i2i0000000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ2522-2-22i−2i2i−2i−2i2i-222222-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-222−2i−2i2i2i00000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ2622-2-2−2i2i−2i2i2i−2i-222222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2222i2i−2i−2i0000000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ2722-2-2−2i2i−2i2i2i−2i-222222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2222i2i−2i−2i00000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ2822-2-2−2i2i−2i2i−2i2i2-22222-2-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i−2i2i2i2i2i−2i−2i-2-2220000000000000000000000000000000000000000
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χ312-22-222-2-2000022-2-222-2-22222-2-2-2-200000000−22−22−22−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47000000000000000000000000
χ322-22-222-2-2000022-2-222-2-22222-2-2-2-200000000−22−22−22−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47000000000000000000000000
χ332-22-2-2-222000022-2-222-2-2-2-2-2-22222000000002−22−2−22−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47000000000000000000000000
χ342-22-2-2-222000022-2-222-2-2-2-2-2-22222000000002−22−2−22−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47000000000000000000000000
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χ6144-4-44i−4i4i−4i4i−4i4-41-21-2-12-12i−2i−i2ii−2i−i2i1-2-12i−2i−i2i00000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ2600000000−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26
χ6244-4-44i−4i4i−4i4i−4i4-41-21-2-12-12i−2i−i2ii−2i−i2i1-2-12i−2i−i2i0000000000000000000000000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ2600000000ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26
χ6344-4-44i−4i4i−4i4i−4i4-4-21-212-12-1−2ii2i−i−2ii2i−i-212-1−2ii2i−i0000000000000000000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ2600000000
χ6444-4-44i−4i4i−4i4i−4i4-4-21-212-12-1−2ii2i−i−2ii2i−i-212-1−2ii2i−i000000000000000000000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ2600000000
χ6544-4-44i−4i4i−4i−4i4i-441-21-2-12-12i−2i−i2ii−2i−i2i-121-2−i2ii−2i0000000000000000000000000000000000000000−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ46−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ26
χ6644-4-44i−4i4i−4i−4i4i-441-21-2-12-12i−2i−i2ii−2i−i2i-121-2−i2ii−2i0000000000000000000000000000000000000000ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ46ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ26
χ6744-4-44i−4i4i−4i−4i4i-44-21-212-12-1−2ii2i−i−2ii2i−i2-1-212i−i−2ii00000000000000000000000000000000−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ46−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ2600000000
χ6844-4-44i−4i4i−4i−4i4i-44-21-212-12-1−2ii2i−i−2ii2i−i2-1-212i−i−2ii00000000000000000000000000000000ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ46ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ2600000000
χ6944-4-4−4i4i−4i4i4i−4i-441-21-2-12-12−i2ii−2i−i2ii−2i-121-2i−2i−i2i0000000000000000000000000000000000000000ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ26ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ46
χ7044-4-4−4i4i−4i4i4i−4i-441-21-2-12-12−i2ii−2i−i2ii−2i-121-2i−2i−i2i0000000000000000000000000000000000000000−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ26−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ46
χ7144-4-4−4i4i−4i4i4i−4i-44-21-212-12-12i−i−2ii2i−i−2ii2-1-21−2ii2i−i00000000000000000000000000000000ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ26ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ4600000000
χ7244-4-4−4i4i−4i4i4i−4i-44-21-212-12-12i−i−2ii2i−i−2ii2-1-21−2ii2i−i00000000000000000000000000000000−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ26−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ4600000000
χ7344-4-4−4i4i−4i4i−4i4i4-41-21-2-12-12−i2ii−2i−i2ii−2i1-2-12−i2ii−2i0000000000000000000000000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ4600000000ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46
χ7444-4-4−4i4i−4i4i−4i4i4-41-21-2-12-12−i2ii−2i−i2ii−2i1-2-12−i2ii−2i00000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ4600000000−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46
χ7544-4-4−4i4i−4i4i−4i4i4-4-21-212-12-12i−i−2ii2i−i−2ii-212-12i−i−2ii000000000000000000000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ460000ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ4600000000
χ7644-4-4−4i4i−4i4i−4i4i4-4-21-212-12-12i−i−2ii2i−i−2ii-212-12i−i−2ii0000000000000000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ460000−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ4600000000
χ778-88-888-8-800002-4-242-4-242-42-4-24-2400000000000000000000000000000000000000000000000000000000
χ788-88-888-8-80000-424-2-424-2-42-424-24-200000000000000000000000000000000000000000000000000000000
χ798-88-8-8-88800002-4-242-4-24-24-242-42-400000000000000000000000000000000000000000000000000000000
χ808-88-8-8-8880000-424-2-424-24-24-2-42-4200000000000000000000000000000000000000000000000000000000
χ818-8-888i−8i−8i8i00002-4-24-242-42i−4i−2i4i−2i4i2i−4i00000000000000000000000000000000000000000000000000000000
χ828-8-888i−8i−8i8i0000-424-24-2-42−4i2i4i−2i4i−2i−4i2i00000000000000000000000000000000000000000000000000000000
χ838-8-88−8i8i8i−8i00002-4-24-242-4−2i4i2i−4i2i−4i−2i4i00000000000000000000000000000000000000000000000000000000
χ848-8-88−8i8i8i−8i0000-424-24-2-424i−2i−4i2i−4i2i4i−2i00000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.