Finite Group Databasebeta

← Group #11797884

Character table — Group #11797884

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222222444444444444444466666666888888888888121212121212121212121212121212121212121216161616161624242424242424243636363648487272
order124423346688881212121236661212121224242424242424248888242424246881224242424242424244412121212161616162424484848484848484824242424242422446612121616161661288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-11-11111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111111111111111-11-11-1-1-1-1-1-1-1-111-1-1
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
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-11-11-11111-1-1-1-1-1-111
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
χ911-1-1-111111-1-111-1-1-1-11-11-111-1-11111-1-1-1-1ii−i−iii−i−i-1i−i1ii−i−i11-1-1i−iii−i−iii−i−ii−iiiii−i−i−i−ii−iii−i−i11-1-111-1-111-1-11-1i−i
χ1011-1-1-111111-1-111-1-1-1-11-11-111-1-11111-1-1-1-1ii−i−iii−i−i-1i−i1ii−i−i11-1-1i−iii−i−i−i−iiii−i−i−i−i−iiiiii−iii−i−i1-1-1111-1-1-1-111-11−ii
χ1111-1-1-111111-1-111-1-1-1-11-11-111-1-11111-1-1-1-1ii−i−iii−i−i-1−ii1−i−iii11-1-1i−iii−i−iii−i−ii−iiiii−i−i−i−i−ii−i−iii-1-111-1-11111-1-1-11−ii
χ1211-1-1-111111-1-111-1-1-1-11-11-111-1-11111-1-1-1-1ii−i−iii−i−i-1−ii1−i−iii11-1-1i−iii−i−i−i−iiii−i−i−i−i−iiiii−ii−i−iii-111-1-1-111-1-1111-1i−i
χ1311-1-1-111111-1-111-1-1-1-11-11-111-1-11111-1-1-1-1−i−iii−i−iii-1i−i1ii−i−i11-1-1−ii−i−iiiii−i−i−iiiiii−i−i−i−ii−iii−i−i-111-1-1-111-1-1111-1−ii
χ1411-1-1-111111-1-111-1-1-1-11-11-111-1-11111-1-1-1-1−i−iii−i−iii-1i−i1ii−i−i11-1-1−ii−i−iii−i−iii−ii−i−i−i−iiiiii−iii−i−i-1-111-1-11111-1-1-11i−i
χ1511-1-1-111111-1-111-1-1-1-11-11-111-1-11111-1-1-1-1−i−iii−i−iii-1−ii1−i−iii11-1-1−ii−i−iiiii−i−i−iiiiii−i−i−i−i−ii−i−iii1-1-1111-1-1-1-111-11i−i
χ1611-1-1-111111-1-111-1-1-1-11-11-111-1-11111-1-1-1-1−i−iii−i−iii-1−ii1−i−iii11-1-1−ii−i−iii−i−iii−ii−i−i−i−iiiii−ii−i−iii11-1-111-1-111-1-11-1−ii
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
χ19222222-122-1222222-1-1-12-1-12-1-1-122-1-1-1-1222222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-10000-1-10000000022-1-1-1-12020-1-1-1-100000000
χ20222222-122-1222222-1-1-12-1-12-1-1-122-1-1-1-1222222-1-1-1-1-1-2-2-11111-1-1-1-122-1-1-1-10000-1-100000000-2-21111-20-20111100000000
χ21222222-122-1222222-1-1-12-1-12-1-1-122-1-1-1-122-2-2-2-21111-122-1-1-1-1-1-1-1-1-1-2-211110000110000000022-1-1-1-1-20-20111100000000
χ22222222-122-1222222-1-1-12-1-12-1-1-122-1-1-1-122-2-2-2-21111-1-2-2-11111-1-1-1-1-2-2111100001100000000-2-211112020-1-1-1-100000000
χ23222222-122-1-2-2-2-222-1-1-12-1-12-1-1-1-2-21111-2-22222-1-1-1-1-100-1−i3i3−i3i31111-2-211110000-1-10000000000−i3i3−i3i30000−i3i3−i3i300000000
χ24222222-122-1-2-2-2-222-1-1-12-1-12-1-1-1-2-21111-2-22222-1-1-1-1-100-1i3−i3i3−i31111-2-211110000-1-10000000000i3−i3i3−i30000i3−i3i3−i300000000
χ25222222-122-1-2-2-2-222-1-1-12-1-12-1-1-1-2-21111-2-2-2-2-2-21111-100-1−i3i3−i3i3111122-1-1-1-10000110000000000−i3i3−i3i30000i3−i3i3−i300000000
χ26222222-122-1-2-2-2-222-1-1-12-1-12-1-1-1-2-21111-2-2-2-2-2-21111-100-1i3−i3i3−i3111122-1-1-1-10000110000000000i3−i3i3−i30000−i3i3−i3i300000000
χ2722222-122-122222-1-122-1-1-12-12-1-1-1-12222-1-100000000-122-12222-1-1-1-1000000222200-1-1-1-1-1-1-1-1-1-1-1-1-1-1020200000000-1-100
χ2822222-122-122222-1-122-1-1-12-12-1-1-1-12222-1-100000000-122-12222-1-1-1-1000000-2-2-2-20011111111-1-1-1-1-1-10-20-2000000001100
χ2922222-122-122222-1-122-1-1-12-12-1-1-1-12222-1-100000000-1-2-2-1-2-2-2-2-1-1-1-1000000222200-1-1-1-1-1-1-1-11111110-20-2000000001100
χ3022222-122-122222-1-122-1-1-12-12-1-1-1-12222-1-100000000-1-2-2-1-2-2-2-2-1-1-1-1000000-2-2-2-20011111111111111020200000000-1-100
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−2i200-200000000000000−i2i2i2−i2−2i2i−i2−i2i2i2i2i2−i2−i200000000000000−222−20000
χ3622-2-2222-2220000-2-2-2-22222-2-2-2-2000000002i−2i−2i2i2i2i−2i−2i200-200000000000000i2−i2−i2i2−2i2ii2i2−i2−i2−i2−i2i2i2000000000000002−2−220000
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χ3822-2-2222-2220000-2-2-2-22222-2-2-2-200000000−2i2i2i−2i−2i−2i2i2i200-200000000000000i2−i2−i2i22i−2ii2i2−i2−i2−i2−i2i2i200000000000000−222−20000
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χ4022-2-2-22222222-2-2-2-2-2-22-22-222-2-2-2-2-2-22222−2i−2i2i2i−2i−2i2i2i-20020000-2-2222i−2i2i2i−2i−2i0000−2i2i000000000000000000000000000000
χ4122-2-2-22-122-122-2-2-2-211-1-2-112-111-2-211-1-1222i2i−2i−2i−i−iii100-13−3−3311-1-1−2i2iii−i−i0000−ii00000000003−3−330000−i3i3i3−i300000000
χ4222-2-2-22-122-122-2-2-2-211-1-2-112-111-2-211-1-1222i2i−2i−2i−i−iii100-1−333−311-1-1−2i2iii−i−i0000−ii0000000000−333−30000i3−i3−i3i300000000
χ4322-2-2-22-122-122-2-2-2-211-1-2-112-111-2-211-1-122−2i−2i2i2iii−i−i100-13−3−3311-1-12i−2i−i−iii0000i−i00000000003−3−330000i3−i3−i3i300000000
χ4422-2-2-22-122-122-2-2-2-211-1-2-112-111-2-211-1-122−2i−2i2i2iii−i−i100-1−333−311-1-12i−2i−i−iii0000i−i0000000000−333−30000−i3i3i3−i300000000
χ4522-2-2-22-122-1-2-222-2-211-1-2-112-11122-1-111-2-22i2i−2i−2i−i−iii12i−2i-1−i−iii-1-1112i−2i−i−iii0000−ii000000002i−2i−i−iii20-20-1-11100000000
χ4622-2-2-22-122-1-2-222-2-211-1-2-112-11122-1-111-2-22i2i−2i−2i−i−iii1−2i2i-1ii−i−i-1-1112i−2i−i−iii0000−ii00000000−2i2iii−i−i-202011-1-100000000
χ4722-2-2-22-122-1-2-222-2-211-1-2-112-11122-1-111-2-2−2i−2i2i2iii−i−i12i−2i-1−i−iii-1-111−2i2iii−i−i0000i−i000000002i−2i−i−iii-202011-1-100000000
χ4822-2-2-22-122-1-2-222-2-211-1-2-112-11122-1-111-2-2−2i−2i2i2iii−i−i1−2i2i-1ii−i−i-1-111−2i2iii−i−i0000i−i00000000−2i2iii−i−i20-20-1-11100000000
χ4922-2-2-2-122-12-2-22211-2-2-11-1-2-1211-1-122-2-2110000000012i−2i-12i2i−2i−2i-1-1110000002i2i−2i−2i00−i−i−i−iiiii−ii−i−iii020-200000000-1100
χ5022-2-2-2-122-12-2-22211-2-2-11-1-2-1211-1-122-2-2110000000012i−2i-12i2i−2i−2i-1-111000000−2i−2i2i2i00iiii−i−i−i−i−ii−i−iii0-202000000001-100
χ5122-2-2-2-122-12-2-22211-2-2-11-1-2-1211-1-122-2-211000000001−2i2i-1−2i−2i2i2i-1-1110000002i2i−2i−2i00−i−i−i−iiiiii−iii−i−i0-202000000001-100
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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
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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
χ584444-44-2-44-2000044-2-2-2-4-22-42-2-2000000004-44-4-2-2-2-2200200000000000000000022000000000000000000000000000000
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χ844-4−4i4i04-20-42−2i22i2−2222−4i4i2i−2i-2020002i−2i−22222−2i2−i2−2i22i20000−2ζ10+2ζ262ζ10−2ζ262ζ14−2ζ46−2ζ14+2ζ46000000002−2i2−i200ζ8−ζ28−ζ40+ζ44−ζ8+ζ28+ζ40−ζ44ζ8+ζ28−ζ40−ζ44−ζ8−ζ28+ζ40+ζ44000000000000000000000000000000000000
χ854-4−4i4i04-20-422i2−2i222−22−4i4i2i−2i-2020002i−2i22−22−22−i2i22i2−2i200002ζ10−2ζ26−2ζ10+2ζ26−2ζ14+2ζ462ζ14−2ζ4600000000−22−i2i200ζ8−ζ28−ζ40+ζ44−ζ8+ζ28+ζ40−ζ44ζ8+ζ28−ζ40−ζ44−ζ8−ζ28+ζ40+ζ44000000000000000000000000000000000000
χ864-4−4i4i04-20-422i2−2i222−22−4i4i2i−2i-2020002i−2i22−22−22−i2i22i2−2i20000−2ζ10+2ζ262ζ10−2ζ262ζ14−2ζ46−2ζ14+2ζ4600000000−22−i2i200−ζ8+ζ28+ζ40−ζ44ζ8−ζ28−ζ40+ζ44−ζ8−ζ28+ζ40+ζ44ζ8+ζ28−ζ40−ζ44000000000000000000000000000000000000
χ874-4−4i4i0-2402-4−2i22i2−22222i−2i−4i4i-2020002i−2i2−2−2222−2i22i2i2−i200000000000000002−2i2−i2000000000000ζ13−ζ29−ζ31+ζ47−ζ13+ζ29+ζ31−ζ47ζ11−ζ25+ζ41−ζ43−ζ11+ζ25−ζ41+ζ43ζ11+ζ25−ζ41−ζ43−ζ11−ζ25+ζ41+ζ43−ζ13+ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ470000000000000000000000
χ884-4−4i4i0-2402-4−2i22i2−22222i−2i−4i4i-2020002i−2i2−2−2222−2i22i2i2−i200000000000000002−2i2−i2000000000000−ζ13+ζ29+ζ31−ζ47ζ13−ζ29−ζ31+ζ47−ζ11+ζ25−ζ41+ζ43ζ11−ζ25+ζ41−ζ43−ζ11−ζ25+ζ41+ζ43ζ11+ζ25−ζ41−ζ43ζ13−ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ470000000000000000000000
χ894-4−4i4i0-2402-42i2−2i222−222i−2i−4i4i-2020002i−2i−2222−222i2−2i2−i2i20000000000000000−22−i2i2000000000000ζ11−ζ25+ζ41−ζ43−ζ11+ζ25−ζ41+ζ43−ζ13+ζ29+ζ31−ζ47ζ13−ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ47ζ11+ζ25−ζ41−ζ43−ζ11−ζ25+ζ41+ζ430000000000000000000000
χ904-4−4i4i0-2402-42i2−2i222−222i−2i−4i4i-2020002i−2i−2222−222i2−2i2−i2i20000000000000000−22−i2i2000000000000−ζ11+ζ25−ζ41+ζ43ζ11−ζ25+ζ41−ζ43ζ13−ζ29−ζ31+ζ47−ζ13+ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ47−ζ11−ζ25+ζ41+ζ43ζ11+ζ25−ζ41−ζ430000000000000000000000
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−8i0-4-4044−4i24i242−42−4i4i−4i4i20-20002i−2i−2222−22222i2−2i22i2−2i200000000000000002−2−i2i2000000000000000000000000000000000000000000
χ948-88i−8i0-4-40444i2−4i2−4242−4i4i−4i4i20-20002i−2i22−2222−22−2i22i2−2i22i20000000000000000−22i2−i2000000000000000000000000000000000000000000
χ958-8−8i8i0-4-4044−4i24i2−42424i−4i4i−4i20-2000−2i2i22−2222−222i2−2i22i2−2i20000000000000000−22−i2i2000000000000000000000000000000000000000000
χ968-8−8i8i0-4-40444i2−4i242−424i−4i4i−4i20-2000−2i2i−2222−2222−2i22i2−2i22i200000000000000002−2i2−i2000000000000000000000000000000000000000000

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