Finite Group Databasebeta

← Group #11797882

Character table — Group #11797882

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222222444444444444444466666666888888888888121212121212121212121212121212121212121216161616161624242424242424243636363648487272
order1244233466888812121212366612121212242424242424242488882424242468812242424242424242444121212121616161624244848484848484848242424242424246688121216161616242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-11-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111111111111111-1-1-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ911-1-1-11111111-1-1-1-1-1-11-11-111-1-111-1-1-1-111ii−i−iii−i−i-1i−i1ii−i−i11-1-1i−iii−i−i11-1-1i−i1111-1-1-1-1i−iii−i−i1-111i−i-1-1ii−i−ii−i1-1
χ1011-1-1-11111111-1-1-1-1-1-11-11-111-1-111-1-1-1-111ii−i−iii−i−i-1i−i1ii−i−i11-1-1i−iii−i−i-1-111i−i-1-1-1-11111i−iii−i−i1-111−ii-1-1−i−iii−ii-11
χ1111-1-1-11111111-1-1-1-1-1-11-11-111-1-111-1-1-1-111ii−i−iii−i−i-1−ii1−i−iii11-1-1i−iii−i−i11-1-1i−i1111-1-1-1-1−ii−i−iii-11-1-1−ii11ii−i−i−ii-11
χ1211-1-1-11111111-1-1-1-1-1-11-11-111-1-111-1-1-1-111ii−i−iii−i−i-1−ii1−i−iii11-1-1i−iii−i−i-1-111i−i-1-1-1-11111−ii−i−iii-11-1-1i−i11−i−iiii−i1-1
χ1311-1-1-11111111-1-1-1-1-1-11-11-111-1-111-1-1-1-111−i−iii−i−iii-1i−i1ii−i−i11-1-1−ii−i−iii11-1-1−ii1111-1-1-1-1i−iii−i−i-11-1-1i−i11−i−iiii−i-11
χ1411-1-1-11111111-1-1-1-1-1-11-11-111-1-111-1-1-1-111−i−iii−i−iii-1i−i1ii−i−i11-1-1−ii−i−iii-1-111−ii-1-1-1-11111i−iii−i−i-11-1-1−ii11ii−i−i−ii1-1
χ1511-1-1-11111111-1-1-1-1-1-11-11-111-1-111-1-1-1-111−i−iii−i−iii-1−ii1−i−iii11-1-1−ii−i−iii11-1-1−ii1111-1-1-1-1−ii−i−iii1-111−ii-1-1−i−iii−ii1-1
χ1611-1-1-11111111-1-1-1-1-1-11-11-111-1-111-1-1-1-111−i−iii−i−iii-1−ii1−i−iii11-1-1−ii−i−iii-1-111−ii-1-1-1-11111−ii−i−iii1-111i−i-1-1ii−i−ii−i-11
χ172222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-22222222220020000-2-2-2-2-2-2-2-2-2-2000022000000000000000000000000000000
χ182222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-220020000-2-2-2-22222220000-2-2000000000000000000000000000000
χ19222222-122-12222-1-122-12-1-12-1-1-1-1-122-1-1222222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-10000-1-10000000022-1-1-1-122-1-100-1-100000000
χ20222222-122-12222-1-122-12-1-12-1-1-1-1-122-1-1222222-1-1-1-1-1-2-2-11111-1-1-1-122-1-1-1-10000-1-100000000-2-21111-2-211001100000000
χ21222222-122-12222-1-122-12-1-12-1-1-1-1-122-1-122-2-2-2-21111-122-1-1-1-1-1-1-1-1-1-2-211110000110000000022-1-1-1-1-2-211001100000000
χ22222222-122-12222-1-122-12-1-12-1-1-1-1-122-1-122-2-2-2-21111-1-2-2-11111-1-1-1-1-2-2111100001100000000-2-2111122-1-100-1-100000000
χ23222222-122-1-2-2-2-2-1-122-12-1-12-1-1-111-2-211-2-22222-1-1-1-1-100-1−i3i3−i3i31111-2-211110000-1-10000000000−i3i3−i3i300−i3i300−i3i300000000
χ24222222-122-1-2-2-2-2-1-122-12-1-12-1-1-111-2-211-2-22222-1-1-1-1-100-1i3−i3i3−i31111-2-211110000-1-10000000000i3−i3i3−i300i3−i300i3−i300000000
χ25222222-122-1-2-2-2-2-1-122-12-1-12-1-1-111-2-211-2-2-2-2-2-21111-100-1−i3i3−i3i3111122-1-1-1-10000110000000000−i3i3−i3i300i3−i300i3−i300000000
χ26222222-122-1-2-2-2-2-1-122-12-1-12-1-1-111-2-211-2-2-2-2-2-21111-100-1i3−i3i3−i3111122-1-1-1-10000110000000000i3−i3i3−i300−i3i300−i3i300000000
χ2722222-122-12222222-1-1-1-1-12-12-1-122-1-122-1-100000000-122-12222-1-1-1-1000000222200-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022000000-1-100
χ2822222-122-12222222-1-1-1-1-12-12-1-122-1-122-1-100000000-122-12222-1-1-1-1000000-2-2-2-20011111111-1-1-1-1-1-10000-2-20000001100
χ2922222-122-12222222-1-1-1-1-12-12-1-122-1-122-1-100000000-1-2-2-1-2-2-2-2-1-1-1-1000000222200-1-1-1-1-1-1-1-11111110000-2-20000001100
χ3022222-122-12222222-1-1-1-1-12-12-1-122-1-122-1-100000000-1-2-2-1-2-2-2-2-1-1-1-1000000-2-2-2-20011111111111111000022000000-1-100
χ312222-222-222000022222-22-2-2-222000000002-22-22222-200-2000000000000002−22−2-2-222−2−222−2−2000000000000002−22−20000
χ322222-222-222000022222-22-2-2-222000000002-22-22222-200-200000000000000−22−22-2-2−2−222−2−22200000000000000−22−220000
χ332222-222-222000022222-22-2-2-22200000000-22-22-2-2-2-2-200-2000000000000002−22−22222−2−222−2−200000000000000−22−220000
χ342222-222-222000022222-22-2-2-22200000000-22-22-2-2-2-2-200-200000000000000−22−2222−2−222−2−222000000000000002−22−20000
χ3522-2-2222-2220000-2-2-2-22222-2-2-2-2000000002i−2i−2i2i2i2i−2i−2i200-2000000000000002−2−22−2i2i22−2−2−2−22200000000000000i2−i2−i2i20000
χ3622-2-2222-2220000-2-2-2-22222-2-2-2-2000000002i−2i−2i2i2i2i−2i−2i200-200000000000000−222−2−2i2i−2−22222−2−200000000000000−i2i2i2−i20000
χ3722-2-2222-2220000-2-2-2-22222-2-2-2-200000000−2i2i2i−2i−2i−2i2i2i200-2000000000000002−2−222i−2i22−2−2−2−22200000000000000−i2i2i2−i20000
χ3822-2-2222-2220000-2-2-2-22222-2-2-2-200000000−2i2i2i−2i−2i−2i2i2i200-200000000000000−222−22i−2i−2−22222−2−200000000000000i2−i2−i2i20000
χ3922-2-2-222222-2-222-2-2-2-22-22-222-2-2-2-22222-2-22i2i−2i−2i2i2i−2i−2i-20020000-2-222−2i2i−2i−2i2i2i00002i−2i000000000000000000000000000000
χ4022-2-2-222222-2-222-2-2-2-22-22-222-2-2-2-22222-2-2−2i−2i2i2i−2i−2i2i2i-20020000-2-2222i−2i2i2i−2i−2i0000−2i2i000000000000000000000000000000
χ4122-2-2-22-122-122-2-211-2-2-1-2-112-111-1-1-2-211222i2i−2i−2i−i−iii12i−2i-1−i−iii-1-1112i−2i−i−iii0000−ii000000002i−2i−i−iii2-2-1-1001100000000
χ4222-2-2-22-122-122-2-211-2-2-1-2-112-111-1-1-2-211222i2i−2i−2i−i−iii1−2i2i-1ii−i−i-1-1112i−2i−i−iii0000−ii00000000−2i2iii−i−i-221100-1-100000000
χ4322-2-2-22-122-122-2-211-2-2-1-2-112-111-1-1-2-21122−2i−2i2i2iii−i−i12i−2i-1−i−iii-1-111−2i2iii−i−i0000i−i000000002i−2i−i−iii-221100-1-100000000
χ4422-2-2-22-122-122-2-211-2-2-1-2-112-111-1-1-2-21122−2i−2i2i2iii−i−i1−2i2i-1ii−i−i-1-111−2i2iii−i−i0000i−i00000000−2i2iii−i−i2-2-1-1001100000000
χ4522-2-2-22-122-1-2-22211-2-2-1-2-112-1111122-1-1-2-22i2i−2i−2i−i−iii100-13−3−3311-1-1−2i2iii−i−i0000−ii00000000003−3−3300−i3i300i3−i300000000
χ4622-2-2-22-122-1-2-22211-2-2-1-2-112-1111122-1-1-2-22i2i−2i−2i−i−iii100-1−333−311-1-1−2i2iii−i−i0000−ii0000000000−333−300i3−i300−i3i300000000
χ4722-2-2-22-122-1-2-22211-2-2-1-2-112-1111122-1-1-2-2−2i−2i2i2iii−i−i100-13−3−3311-1-12i−2i−i−iii0000i−i00000000003−3−3300i3−i300−i3i300000000
χ4822-2-2-22-122-1-2-22211-2-2-1-2-112-1111122-1-1-2-2−2i−2i2i2iii−i−i100-1−333−311-1-12i−2i−i−iii0000i−i0000000000−333−300−i3i300i3−i300000000
χ4922-2-2-2-122-1222-2-2-2-211-11-1-2-12112211-2-2-1-10000000012i−2i-12i2i−2i−2i-1-11100000022-2-200-1-1-1-11111−ii−i−iii00002i−2i000000−ii00
χ5022-2-2-2-122-1222-2-2-2-211-11-1-2-12112211-2-2-1-10000000012i−2i-12i2i−2i−2i-1-111000000-2-222001111-1-1-1-1−ii−i−iii0000−2i2i000000i−i00
χ5122-2-2-2-122-1222-2-2-2-211-11-1-2-12112211-2-2-1-1000000001−2i2i-1−2i−2i2i2i-1-11100000022-2-200-1-1-1-11111i−iii−i−i0000−2i2i000000i−i00
χ5222-2-2-2-122-1222-2-2-2-211-11-1-2-12112211-2-2-1-1000000001−2i2i-1−2i−2i2i2i-1-111000000-2-222001111-1-1-1-1i−iii−i−i00002i−2i000000−ii00
χ5344444-244-24-4-4-4-444-2-2-2-2-24-24-2-2-4-422-4-42200000000-200-200002222000000000000000000000000000000000000000000
χ5444444-2-24-2-24444-2-2-2-21-21-2-2-211-2-2-2-2-2-2-2-2000000001441-2-2-2-2111100000000000000000000-2-211110000000000000000
χ5544444-2-24-2-24444-2-2-2-21-21-2-2-211-2-2-2-2-2-2-2-2000000001-4-41222211110000000000000000000022-1-1-1-10000000000000000
χ5644444-2-24-2-2-4-4-4-4-2-2-2-21-21-2-2-21122222222000000001001−2i32i3−2i32i3-1-1-1-10000000000000000000000i3−i3i3−i30000000000000000
χ5744444-2-24-2-2-4-4-4-4-2-2-2-21-21-2-2-211222222220000000010012i3−2i32i3−2i3-1-1-1-10000000000000000000000−i3i3−i3i30000000000000000
χ584444-44-2-44-20000-2-244-2-4-22-42-2-2000000004-44-4-2-2-2-2200200000000000000000022000000000000000000000000000000
χ594444-44-2-44-20000-2-244-2-4-22-42-2-200000000-44-4422222002000000000000000000-2-2000000000000000000000000000000
χ604444-4-24-4-24000044-2-2-22-2-42-4-2-2000000000000000020020000000000000022−2222−2200−2−222−2−2220000000000000000000000
χ614444-4-24-4-24000044-2-2-22-2-42-4-2-20000000000000000200200000000000000−2222−22220022−2−222−2−20000000000000000000000
χ6244-4-444-2-44-2000022-4-4-24-2-2-4222000000004i−4i−4i4i−2i−2i2i2i-20020000000000000000002i−2i000000000000000000000000000000
χ6344-4-444-2-44-2000022-4-4-24-2-2-422200000000−4i4i4i−4i2i2i−2i−2i-2002000000000000000000−2i2i000000000000000000000000000000
χ6444-4-44-24-4-240000-4-422-2-2-242-4220000000000000000-20020000000000000022−22−222200−2−22222−2−20000000000000000000000
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χ6644-4-4-4-244-24-4-444-4-422-22-2-4-2422-4-4-2-2442200000000200-2000022-2-2000000000000000000000000000000000000000000
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χ6844-4-4-4-2-24-2-244-4-422221212-2-2-1-1-2-22222-2-200000000-1−4i4i12i2i−2i−2i11-1-1000000000000000000002i−2i−i−iii0000000000000000
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χ824-4−4i4i0440-4-4−2222−2i22i2−4i4i−4i4i40-4000−4i4i−2222−2i22i2−2i22i2−22220000000000000000−2222−2i22i2000000000000000000000000000000000000000000
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χ854-4−4i4i04-20-42−2222−2i22i22i−2i−4i4i-2020002i−2i2−2−2i22i2i2−i2−222200002ζ10−2ζ26−2ζ10+2ζ26−2ζ14+2ζ462ζ14−2ζ46000000002−2i2−i200−ζ8+ζ28+ζ40−ζ44ζ8−ζ28−ζ40+ζ44−ζ8−ζ28+ζ40+ζ44ζ8+ζ28−ζ40−ζ44000000000000000000000000000000000000
χ864-4−4i4i04-20-42−2222−2i22i22i−2i−4i4i-2020002i−2i2−2−2i22i2i2−i2−22220000−2ζ10+2ζ262ζ10−2ζ262ζ14−2ζ46−2ζ14+2ζ46000000002−2i2−i200ζ8−ζ28−ζ40+ζ44−ζ8+ζ28+ζ40−ζ44ζ8+ζ28−ζ40−ζ44−ζ8−ζ28+ζ40+ζ44000000000000000000000000000000000000
χ874-4−4i4i0-2402-422−222i2−2i2−4i4i2i−2i-2020002i−2i22−22−i2i22i2−2i2−220000000000000000−22−i2i2000000000000−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+ζ430000000000000000000000
χ884-4−4i4i0-2402-422−222i2−2i2−4i4i2i−2i-2020002i−2i22−22−i2i22i2−2i2−220000000000000000−22−i2i2000000000000ζ11−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−ζ430000000000000000000000
χ894-4−4i4i0-2402-4−2222−2i22i2−4i4i2i−2i-2020002i−2i−2222i2−i2−2i22i22−200000000000000002−2i2−i2000000000000−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+ζ470000000000000000000000
χ904-4−4i4i0-2402-4−2222−2i22i2−4i4i2i−2i-2020002i−2i−2222i2−i2−2i22i22−200000000000000002−2i2−i2000000000000ζ25+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−ζ470000000000000000000000
χ918888-8-4-4-8-4-40000-4-4-4-4242444220000000000000000-200-200000000000000000000000000000000000000000000000000
χ9288-8-88-4-4-8-4-4000044442-42-444-2-20000000000000000200-200000000000000000000000000000000000000000000000000
χ938-88i−8i0-4-404442−42−4i24i2−4i4i−4i4i20-20002i−2i−22222i2−2i22i2−2i2−222200000000000000002−2−i2i2000000000000000000000000000000000000000000
χ948-88i−8i0-4-4044−42424i2−4i2−4i4i−4i4i20-20002i−2i22−22−2i22i2−2i22i222−220000000000000000−22i2−i2000000000000000000000000000000000000000000
χ958-8−8i8i0-4-404442−424i2−4i24i−4i4i−4i20-2000−2i2i−2222−2i22i2−2i22i2−222200000000000000002−2i2−i2000000000000000000000000000000000000000000
χ968-8−8i8i0-4-4044−4242−4i24i24i−4i4i−4i20-2000−2i2i22−222i2−2i22i2−2i222−220000000000000000−22−i2i2000000000000000000000000000000000000000000

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