Finite Group Databasebeta

← Group #11797885

Character table — Group #11797885

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222222444444444444444466666666888888888888121212121212121212121212121212121212121216161616161624242424242424243636363648487272
order124423346688881212121236661212121224242424242424248888242424242466612121224242424441212121216161616242448484848484848486661212122488242424241616161661288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
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
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ911-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-1-1-111ii−i−iii−i−i1-111-1-1-1111-1-1i−iii−i−i11-1-1i−i1111-1-1-1-1111-1-1-11-1i−iii−i−iii−i−i1-1i−i
χ1011-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-1-1-111ii−i−iii−i−i1-111-1-1-1111-1-1i−iii−i−i-1-111i−i-1-1-1-11111111-1-1-1-11i−iii−i−i−i−iii-11−ii
χ1111-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-1-1-111ii−i−iii−i−i-11-1-1-111111-1-1i−iii−i−i11-1-1i−i1111-1-1-1-1-1-1-1111-11−ii−i−iiiii−i−i-11−ii
χ1211-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-1-1-111ii−i−iii−i−i-11-1-1-111111-1-1i−iii−i−i-1-111i−i-1-1-1-11111-1-1-11111-1−ii−i−iii−i−iii1-1i−i
χ1311-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-1-1-111−i−iii−i−iii1-111-1-1-1111-1-1−ii−i−iii11-1-1−ii1111-1-1-1-1111-1-1-11-1−ii−i−iii−i−iii1-1−ii
χ1411-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-1-1-111−i−iii−i−iii1-111-1-1-1111-1-1−ii−i−iii-1-111−ii-1-1-1-11111111-1-1-1-11−ii−i−iiiii−i−i-11i−i
χ1511-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-1-1-111−i−iii−i−iii-11-1-1-111111-1-1−ii−i−iii11-1-1−ii1111-1-1-1-1-1-1-1111-11i−iii−i−i−i−iii-11i−i
χ1611-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-1-1-111−i−iii−i−iii-11-1-1-111111-1-1−ii−i−iii-1-111−ii-1-1-1-11111-1-1-11111-1i−iii−i−iii−i−i1-1−ii
χ172222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-22222222200002002-2-2-2-2-2-2-2-2-2-2000022000000000000000000000000000000
χ182222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200002002-2-2-2-22222220000-2-2000000000000000000000000000000
χ19222222-122-12222-1-122-1-12-1-1-12-12222-1-1-1-1000000002222-122-1-1-1-1-1000000222200-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000000000-1-100
χ20222222-122-12222-1-122-1-12-1-1-12-12222-1-1-1-1000000002222-122-1-1-1-1-1000000-2-2-2-20011111111-1-1-1-1-1-1-2-200000000001100
χ21222222-122-12222-1-122-1-12-1-1-12-12222-1-1-1-100000000-2-2-2-2-1-2-2-1-1-1-1-1000000222200-1-1-1-1-1-1-1-1111111-2-200000000001100
χ22222222-122-12222-1-122-1-12-1-1-12-12222-1-1-1-100000000-2-2-2-2-1-2-2-1-1-1-1-1000000-2-2-2-20011111111111111220000000000-1-100
χ2322222-122-12222222-1-1-12-1-1-1-1-12-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-10000-1-1000000002-1-12-1-10022-1-1-1-100000000
χ2422222-122-12222222-1-1-12-1-1-1-1-12-1-1-1-122222222-1-1-1-1-2-211-111-1-1-1-1-122-1-1-1-10000-1-100000000-211-21100-2-2111100000000
χ2522222-122-12222222-1-1-12-1-1-1-1-12-1-1-1-12222-2-2-2-2111122-1-1-1-1-1-1-1-1-1-1-2-21111000011000000002-1-12-1-100-2-2111100000000
χ2622222-122-12222222-1-1-12-1-1-1-1-12-1-1-1-12222-2-2-2-21111-2-211-111-1-1-1-1-1-2-2111100001100000000-211-2110022-1-1-1-100000000
χ2722222-122-12-2-2-2-222-1-1-12-1-1-1-1-121111-2-2-2-22222-1-1-1-100−i3i3-1−i3i3-11111-2-211110000-1-1000000000−i3i30−i3i30000−i3i3−i3i300000000
χ2822222-122-12-2-2-2-222-1-1-12-1-1-1-1-121111-2-2-2-22222-1-1-1-100i3−i3-1i3−i3-11111-2-211110000-1-1000000000i3−i30i3−i30000i3−i3i3−i300000000
χ2922222-122-12-2-2-2-222-1-1-12-1-1-1-1-121111-2-2-2-2-2-2-2-2111100−i3i3-1−i3i3-1111122-1-1-1-1000011000000000−i3i30−i3i30000i3−i3i3−i300000000
χ3022222-122-12-2-2-2-222-1-1-12-1-1-1-1-121111-2-2-2-2-2-2-2-2111100i3−i3-1i3−i3-1111122-1-1-1-1000011000000000i3−i30i3−i30000−i3i3−i3i300000000
χ312222-222-222000022222-2-2222-2-2000000002-22-222220000-200-200000000002−22−2-2-222−2−222−2−2000000000000002−22−20000
χ322222-222-222000022222-2-2222-2-2000000002-22-222220000-200-20000000000−22−22-2-2−2−222−2−22200000000000000−22−220000
χ332222-222-222000022222-2-2222-2-200000000-22-22-2-2-2-20000-200-200000000002−22−22222−2−222−2−200000000000000−22−220000
χ342222-222-222000022222-2-2222-2-200000000-22-22-2-2-2-20000-200-20000000000−22−2222−2−222−2−222000000000000002−22−20000
χ3522-2-2222-2220000-2-2-2-22222-2-2-2-2000000002i−2i−2i2i2i2i−2i−2i0000200-200000000002−2−22−2i2i22−2−2−2−22200000000000000i2−i2−i2i20000
χ3622-2-2222-2220000-2-2-2-22222-2-2-2-2000000002i−2i−2i2i2i2i−2i−2i0000200-20000000000−222−2−2i2i−2−22222−2−200000000000000−i2i2i2−i20000
χ3722-2-2222-2220000-2-2-2-22222-2-2-2-200000000−2i2i2i−2i−2i−2i2i2i0000200-200000000002−2−222i−2i22−2−2−2−22200000000000000−i2i2i2−i20000
χ3822-2-2222-2220000-2-2-2-22222-2-2-2-200000000−2i2i2i−2i−2i−2i2i2i0000200-20000000000−222−22i−2i−2−22222−2−200000000000000i2−i2−i2i20000
χ3922-2-2-222222-2-222-2-2-2-22-2-22-2-222-2-22222-2-22i2i−2i−2i2i2i−2i−2i0000-2002-2-222−2i2i−2i−2i2i2i00002i−2i000000000000000000000000000000
χ4022-2-2-222222-2-222-2-2-2-22-2-22-2-222-2-22222-2-2−2i−2i2i2i−2i−2i2i2i0000-2002-2-2222i−2i2i2i−2i−2i0000−2i2i000000000000000000000000000000
χ4122-2-2-22-122-122-2-211-2-2-11-2-1112-122-2-211-1-1000000002-2221-2-2-1-1-11100000022-2-200-1-1-1-11111-1-1-11112-20000000000-1100
χ4222-2-2-22-122-122-2-211-2-2-11-2-1112-122-2-211-1-1000000002-2221-2-2-1-1-111000000-2-222001111-1-1-1-1-1-1-1111-2200000000001-100
χ4322-2-2-22-122-122-2-211-2-2-11-2-1112-122-2-211-1-100000000-22-2-2122-1-1-11100000022-2-200-1-1-1-11111111-1-1-1-2200000000001-100
χ4422-2-2-22-122-122-2-211-2-2-11-2-1112-122-2-211-1-100000000-22-2-2122-1-1-111000000-2-222001111-1-1-1-1111-1-1-12-20000000000-1100
χ4522-2-2-2-122-1222-2-2-2-211-1-21-111-12-1-111-2-2222i2i−2i−2i−i−iii2-2-1-1111-1-1-1112i−2i−i−iii0000−ii000000002-1-1-211002i−2i−i−iii00000000
χ4622-2-2-2-122-1222-2-2-2-211-1-21-111-12-1-111-2-2222i2i−2i−2i−i−iii-22111-1-1-1-1-1112i−2i−i−iii0000−ii00000000-2112-1-100−2i2iii−i−i00000000
χ4722-2-2-2-122-1222-2-2-2-211-1-21-111-12-1-111-2-222−2i−2i2i2iii−i−i2-2-1-1111-1-1-111−2i2iii−i−i0000i−i000000002-1-1-21100−2i2iii−i−i00000000
χ4822-2-2-2-122-1222-2-2-2-211-1-21-111-12-1-111-2-222−2i−2i2i2iii−i−i-22111-1-1-1-1-111−2i2iii−i−i0000i−i00000000-2112-1-1002i−2i−i−iii00000000
χ4922-2-2-2-122-12-2-222-2-211-1-21-111-1211-1-122-2-22i2i−2i−2i−i−iii00−i3i31i3−i3-111-1-1−2i2iii−i−i0000−ii000000000−i3i30i3−i300003−3−3300000000
χ5022-2-2-2-122-12-2-222-2-211-1-21-111-1211-1-122-2-22i2i−2i−2i−i−iii00i3−i31−i3i3-111-1-1−2i2iii−i−i0000−ii000000000i3−i30−i3i30000−333−300000000
χ5122-2-2-2-122-12-2-222-2-211-1-21-111-1211-1-122-2-2−2i−2i2i2iii−i−i00−i3i31i3−i3-111-1-12i−2i−i−iii0000i−i000000000−i3i30i3−i30000−333−300000000
χ5222-2-2-2-122-12-2-222-2-211-1-21-111-1211-1-122-2-2−2i−2i2i2iii−i−i00i3−i31−i3i3-111-1-12i−2i−i−iii0000i−i000000000i3−i30−i3i300003−3−3300000000
χ53444444-244-2-4-4-4-4-2-244-2-24-2-2-24-2-4-4-4-42222000000000000-200-22222000000000000000000000000000000000000000000
χ5444444-2-24-2-24444-2-2-2-21-2-2111-2-2-2-2-2-2-2-2-2-20000000044-2-21-2-21111100000000000000000000-211-2110000000000000000
χ5544444-2-24-2-24444-2-2-2-21-2-2111-2-2-2-2-2-2-2-2-2-200000000-4-42212211111000000000000000000002-1-12-1-10000000000000000
χ5644444-2-24-2-2-4-4-4-4-2-2-2-21-2-2111-2-2222222220000000000−2i32i31−2i32i31-1-1-1-1000000000000000000000i3−i30i3−i30000000000000000
χ5744444-2-24-2-2-4-4-4-4-2-2-2-21-2-2111-2-22222222200000000002i3−2i312i3−2i31-1-1-1-1000000000000000000000−i3i30−i3i30000000000000000
χ584444-44-2-44-20000-2-244-22-4-2-2-2-42000000000000000000002002000000000022−2222−2200−2−222−2−2220000000000000000000000
χ594444-44-2-44-20000-2-244-22-4-2-2-2-420000000000000000000020020000000000−2222−22220022−2−222−2−20000000000000000000000
χ604444-4-24-4-24000044-2-2-2-42-2-2-22-4000000004-44-4-2-2-2-2000020020000000000000022000000000000000000000000000000
χ614444-4-24-4-24000044-2-2-2-42-2-2-22-400000000-44-4422220000200200000000000000-2-2000000000000000000000000000000
χ6244-4-444-2-44-2000022-4-4-2-24-222-4200000000000000000000-2002000000000022−22−222200−2−22222−2−20000000000000000000000
χ6344-4-444-2-44-2000022-4-4-2-24-222-4200000000000000000000-20020000000000−222222−220022−2−2−2−2220000000000000000000000
χ6444-4-44-24-4-240000-4-422-24-2-2222-4000000004i−4i−4i4i−2i−2i2i2i0000-2002000000000000002i−2i000000000000000000000000000000
χ6544-4-44-24-4-240000-4-422-24-2-2222-400000000−4i4i4i−4i2i2i−2i−2i0000-200200000000000000−2i2i000000000000000000000000000000
χ6644-4-4-44-244-2-4-44422-4-4-22-4-2224-2-4-444-2-222000000000000200-222-2-2000000000000000000000000000000000000000000
χ6744-4-4-4-2-24-2-244-4-422221221-1-1-2-2-2-22222-2-2000000004-4-2-2-122111-1-100000000000000000000-2112-1-10000000000000000
χ6844-4-4-4-2-24-2-244-4-422221221-1-1-2-2-2-22222-2-200000000-4422-1-2-2111-1-1000000000000000000002-1-1-2110000000000000000
χ6944-4-4-4-2-24-2-2-4-44422221221-1-1-2-222-2-2-2-2220000000000−2i32i3-12i3−2i31-1-111000000000000000000000i3−i30−i3i30000000000000000
χ7044-4-4-4-2-24-2-2-4-44422221221-1-1-2-222-2-2-2-22200000000002i3−2i3-1−2i32i31-1-111000000000000000000000−i3i30i3−i30000000000000000
χ714-44i−4i0440-4-422−22−2i22i24i−4i4i−4i400-44i−4i0022−22−2i22i2−2i22i222−22000000000000000022−22−2i22i2000000000000000000000000000000000000000000
χ724-44i−4i0440-4-4−22222i2−2i24i−4i4i−4i400-44i−4i00−22222i2−2i22i2−2i2−22220000000000000000−22222i2−2i2000000000000000000000000000000000000000000
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χ784-44i−4i0-2402-422−22−2i22i24i−4i−2i2i-2002−2i2i00−22i2−i2−2i22i222−2200002ζ14−2ζ46−2ζ14+2ζ46−2ζ10+2ζ262ζ10−2ζ2600000000−22i2−i200ζ8+ζ28−ζ40−ζ44−ζ8−ζ28+ζ40+ζ44ζ8−ζ28−ζ40+ζ44−ζ8+ζ28+ζ40−ζ44000000000000000000000000000000000000
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χ804-44i−4i0-2402-4−22222i2−2i24i−4i−2i2i-2002−2i2i002−2−i2i22i2−2i2−222200002ζ14−2ζ46−2ζ14+2ζ46−2ζ10+2ζ262ζ10−2ζ26000000002−2−i2i200−ζ8−ζ28+ζ40+ζ44ζ8+ζ28−ζ40−ζ44−ζ8+ζ28+ζ40−ζ44ζ8−ζ28−ζ40+ζ44000000000000000000000000000000000000
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χ824-4−4i4i0440-4-4−2222−2i22i2−4i4i−4i4i400-4−4i4i00−2222−2i22i2−2i22i2−22220000000000000000−2222−2i22i2000000000000000000000000000000000000000000
χ834-4−4i4i04-20-4222−222i2−2i22i−2i−4i4i-20022i−2i0022−222i2−2i2−i2i2−220000000000000000−22−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
χ844-4−4i4i04-20-4222−222i2−2i22i−2i−4i4i-20022i−2i0022−222i2−2i2−i2i2−220000000000000000−22−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
χ854-4−4i4i04-20-42−2222−2i22i22i−2i−4i4i-20022i−2i00−2222−2i22i2i2−i22−200000000000000002−2i2−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
χ864-4−4i4i04-20-42−2222−2i22i22i−2i−4i4i-20022i−2i00−2222−2i22i2i2−i22−200000000000000002−2i2−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
χ874-4−4i4i0-2402-422−222i2−2i2−4i4i2i−2i-20022i−2i00−22−i2i22i2−2i222−2200002ζ10−2ζ26−2ζ10+2ζ26−2ζ14+2ζ462ζ14−2ζ4600000000−22−i2i200ζ8−ζ28−ζ40+ζ44−ζ8+ζ28+ζ40−ζ44ζ8+ζ28−ζ40−ζ44−ζ8−ζ28+ζ40+ζ44000000000000000000000000000000000000
χ884-4−4i4i0-2402-422−222i2−2i2−4i4i2i−2i-20022i−2i00−22−i2i22i2−2i222−220000−2ζ10+2ζ262ζ10−2ζ262ζ14−2ζ46−2ζ14+2ζ4600000000−22−i2i200−ζ8+ζ28+ζ40−ζ44ζ8−ζ28−ζ40+ζ44−ζ8−ζ28+ζ40+ζ44ζ8+ζ28−ζ40−ζ44000000000000000000000000000000000000
χ894-4−4i4i0-2402-4−2222−2i22i2−4i4i2i−2i-20022i−2i002−2i2−i2−2i22i2−222200002ζ10−2ζ26−2ζ10+2ζ26−2ζ14+2ζ462ζ14−2ζ46000000002−2i2−i200−ζ8+ζ28+ζ40−ζ44ζ8−ζ28−ζ40+ζ44−ζ8−ζ28+ζ40+ζ44ζ8+ζ28−ζ40−ζ44000000000000000000000000000000000000
χ904-4−4i4i0-2402-4−2222−2i22i2−4i4i2i−2i-20022i−2i002−2i2−i2−2i22i2−22220000−2ζ10+2ζ262ζ10−2ζ262ζ14−2ζ46−2ζ14+2ζ46000000002−2i2−i200ζ8−ζ28−ζ40+ζ44−ζ8+ζ28+ζ40−ζ44ζ8+ζ28−ζ40−ζ44−ζ8−ζ28+ζ40+ζ44000000000000000000000000000000000000
χ918888-8-4-4-8-4-40000-4-4-4-42442224400000000000000000000-200-20000000000000000000000000000000000000000000000
χ9288-8-88-4-4-8-4-4000044442-4-42-2-24400000000000000000000200-20000000000000000000000000000000000000000000000
χ938-88i−8i0-4-404442−42−4i24i2−4i4i−4i4i200-22i−2i00−22222i2−2i22i2−2i2−222200000000000000002−2−i2i2000000000000000000000000000000000000000000
χ948-88i−8i0-4-4044−42424i2−4i2−4i4i−4i4i200-22i−2i0022−22−2i22i2−2i22i222−220000000000000000−22i2−i2000000000000000000000000000000000000000000
χ958-8−8i8i0-4-404442−424i2−4i24i−4i4i−4i200-2−2i2i00−2222−2i22i2−2i22i2−222200000000000000002−2i2−i2000000000000000000000000000000000000000000
χ968-8−8i8i0-4-4044−4242−4i24i24i−4i4i−4i200-2−2i2i0022−222i2−2i22i2−2i222−220000000000000000−22−i2i2000000000000000000000000000000000000000000

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