Finite Group Databasebeta

← Group #72221795

Character table — Group #72221795

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size1111224444444444888888888888101010101010101016161616161616161616161616161616202020202525252525252525252525254040404040404040505050505050505050505050505080808080100100100100100100100100100100
order1244242455101020202020551010101020202020202044444444101010101010101020202020202020208888224444444444202020202020202024444444444444404040402444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1iiii−i−i−i−i-1-11111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1-1-1−i−iii−i−i−i−iiiii11-1-1-1-1−i−iii−i−iii
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-111-1-1iiii−i−i−i−i-1-1-1-1-1-11111-1-1ii−i−i−i−i−i−iiiii-1-111-1-1ii−i−i−i−iii
χ61111111111111111111111111111-1-1-1-111111111111111111111-1-111-1-1−i−i−i−iiiii-1-1-1-1-1-11111-1-1−i−iiiiiii−i−i−i−i-1-111-1-1−i−iiiii−i−i
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111
χ9111111-1-11111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ10111111-1-11111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ11111111-1-1111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1iiii−i−i−i−i-1-11111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-11111−i−iii−i−iii
χ12111111-1-1111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1−i−i−i−iiiii-1-11111-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-11111ii−i−iii−i−i
χ13111111-1-111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-11111-1-1ii−i−i−i−i−i−iiiii11-1-111−i−iiiii−i−i
χ14111111-1-111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-11111-1-1−i−iiiiiii−i−i−i−i11-1-111ii−i−i−i−iii
χ15111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ16111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-11111-1-1-1-1
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χ1811-1-1-111-11111-1-1-1-11111-1-111-1-1-1-1ii−i−iii−i−i11-1-11111-1-111-1-1-1-1i−ii−i11-1-111-1-111-1-1ii−i−iii−i−i-11-11-11−i−iii−i−iiii−ii−i1-1-11-11−ii−ii
χ1911-1-1-111-11111-1-1-1-11111-1-111-1-1-1-1ii−i−i−i−iii11-1-11111-1-111-1-1-1-1i−i−ii-1-1ii−i−i−i−iii11ii−i−i−i−iii1-1i−i−ii-1-11111-1-1i−i−ii-11i−i−ii-111-1
χ2011-1-1-111-11111-1-1-1-11111-1-111-1-1-1-1ii−i−i−i−iii11-1-11111-1-111-1-1-1-1i−i−ii-1-1−i−iiiii−i−i11ii−i−i−i−iii1-1−iii−i11-1-1-1-111i−i−ii-11−iii−i1-1-11
χ2111-1-1-111-11111-1-1-1-11111-1-111-1-1-1-1−i−iiiii−i−i11-1-11111-1-111-1-1-1-1−iii−i-1-1ii−i−i−i−iii11−i−iiiii−i−i1-1i−i−ii11-1-1-1-111−iii−i-11i−i−ii1-1-11
χ2211-1-1-111-11111-1-1-1-11111-1-111-1-1-1-1−i−iiiii−i−i11-1-11111-1-111-1-1-1-1−iii−i-1-1−i−iiiii−i−i11−i−iiiii−i−i1-1−iii−i-1-11111-1-1−iii−i-11−iii−i-111-1
χ2311-1-1-111-11111-1-1-1-11111-1-111-1-1-1-1−i−iii−i−iii11-1-11111-1-111-1-1-1-1−ii−ii1111-1-111-1-1-1-1−i−iii−i−iii-111-11-1−i−iii−i−iii−ii−ii1-11-11-1−ii−ii
χ2411-1-1-111-11111-1-1-1-11111-1-111-1-1-1-1−i−iii−i−iii11-1-11111-1-111-1-1-1-1−ii−ii11-1-111-1-111-1-1−i−iii−i−iii-11-11-11ii−i−iii−i−i−ii−ii1-1-11-11i−ii−i
χ2511-1-1-11-111111-1-1-1-11111-1-111-1-1-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-111111111−ii−ii1111-1-111-1-1-1-1ii−i−iii−i−i-111-11-1ii−i−iii−i−i−ii−ii-11-11-11−ii−ii
χ2611-1-1-11-111111-1-1-1-11111-1-111-1-1-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-111111111−ii−ii11-1-111-1-111-1-1ii−i−iii−i−i-11-11-11−i−iii−i−iii−ii−ii-111-11-1i−ii−i
χ2711-1-1-11-111111-1-1-1-11111-1-111-1-1-1-1ii−i−i−i−iii-1-1-1-1-1-1-1-111111111−iii−i-1-1ii−i−i−i−iii11ii−i−i−i−iii1-1i−i−ii-1-11111-1-1−iii−i1-1−iii−i1-1-11
χ2811-1-1-11-111111-1-1-1-11111-1-111-1-1-1-1ii−i−i−i−iii-1-1-1-1-1-1-1-111111111−iii−i-1-1−i−iiiii−i−i11ii−i−i−i−iii1-1−iii−i11-1-1-1-111−iii−i1-1i−i−ii-111-1
χ2911-1-1-11-111111-1-1-1-11111-1-111-1-1-1-1−i−iiiii−i−i-1-1-1-1-1-1-1-111111111i−i−ii-1-1ii−i−i−i−iii11−i−iiiii−i−i1-1i−i−ii11-1-1-1-111i−i−ii1-1−iii−i-111-1
χ3011-1-1-11-111111-1-1-1-11111-1-111-1-1-1-1−i−iiiii−i−i-1-1-1-1-1-1-1-111111111i−i−ii-1-1−i−iiiii−i−i11−i−iiiii−i−i1-1−iii−i-1-11111-1-1i−i−ii1-1i−i−ii1-1-11
χ3111-1-1-11-111111-1-1-1-11111-1-111-1-1-1-1−i−iii−i−iii-1-1-1-1-1-1-1-111111111i−ii−i1111-1-111-1-1-1-1−i−iii−i−iii-111-11-1−i−iii−i−iiii−ii−i-11-11-11i−ii−i
χ3211-1-1-11-111111-1-1-1-11111-1-111-1-1-1-1−i−iii−i−iii-1-1-1-1-1-1-1-111111111i−ii−i11-1-111-1-111-1-1−i−iii−i−iii-11-11-11ii−i−iii−i−ii−ii−i-111-11-1−ii−ii
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χ362222-2-200222222222222-2-2-2-222220000000000-2-2000000-2-200000000-2-2−2i−2i−2i−2i2i2i2i2i-2-200000000222i2i−2i−2i0000000000000000000000
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χ3822-2-22-2002222-2-2-2-2222222-2-2-2-2-2-2000000000022000000-2-20000000022-2-222-2-222-2-2000000002-22-22-20000000000000000000000
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χ442-22i−2i000022-2-22i2i−2i−2i22-2-200002i2i−2i−2i1+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000000000000000-22−2i2i2-22i−2i-22−2i2i1+i−1−i1−i−1+i−1−i1+i−1+i1−i0000001−i−1+i−1−i1+i−1+i1−i1+i−1−i00000000000000
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χ482-22i−2i000022-2-22i2i−2i−2i22-2-200002i2i−2i−2i−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000000000002-2-22−2i2i-22−2i2i2i−2i−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000000000
χ492-2−2i2i000022-2-2−2i−2i2i2i22-2-20000−2i−2i2i2i1−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000000000002-22-2−2i2i2-2−2i2i−2i2i1−i−1+i1+i−1−i1−i−1+i1+i−1−i0000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000000000
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χ522-2−2i2i000022-2-2−2i−2i2i2i22-2-20000−2i−2i2i2i1−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000000000000000-22−2i2i-222i−2i2-22i−2i1−i−1+i1+i−1−i−1+i1−i−1−i1+i000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i00000000000000
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χ61444444-4-44-14-14-14-1-1-1-1-14-14-1-1-1-1-100004444-41-1-11111-41-1-1111100-4-40000000000000000-1-1-1-10000000000000000110000000000
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χ75888888-8-8-2-2-2-2-2-2-2-23-23-2-2-2-2-23-23-200000000223-2-3-322223-2-3-3220000000000000000000000000000000000000000000000000000
χ76888888-8-8-2-2-2-2-2-2-2-2-23-23-2-2-2-2-23-230000000022-2322-3-322-2322-3-30000000000000000000000000000000000000000000000000000
χ778888-8-8008-28-28-28-2-2-2-2-2-82-82-2-2-2-20000000000220000002200000000000000000000000000000000000000000000000000000000
χ788888-8-800-28-28-28-28-2-2-2-22-82-8-2-2-2-20000000000220000002200000000000000000000000000000000000000000000000000000000
χ798888-8-800-2-2-2-2-2-2-2-23-23-222223-23-20000000000-325−525−2500-325−525−250000000000000000000000000000000000000000000000000000
χ808888-8-800-2-2-2-2-2-2-2-23-23-222223-23-20000000000-32−55−252500-32−55−25250000000000000000000000000000000000000000000000000000
χ818888-8-800-2-2-2-2-2-2-2-2-23-232222-23-2300000000002-325−25−55002-325−25−550000000000000000000000000000000000000000000000000000
χ828888-8-800-2-2-2-2-2-2-2-2-23-232222-23-2300000000002-3−25255−5002-3−25255−50000000000000000000000000000000000000000000000000000
χ8388-8-88-8008-28-2-82-82-2-2-2-28-2-8222220000000000-2-20000002200000000000000000000000000000000000000000000000000000000
χ8488-8-88-800-28-282-82-8-2-2-2-2-282-822220000000000-2-20000002200000000000000000000000000000000000000000000000000000000
χ8588-8-88-800-2-2-2-222223-23-2-2-222-32-3200000000003-25−525−2500-32−55−25250000000000000000000000000000000000000000000000000000
χ8688-8-88-800-2-2-2-222223-23-2-2-222-32-3200000000003-2−55−252500-325−525−250000000000000000000000000000000000000000000000000000
χ8788-8-88-800-2-2-2-22222-23-23-2-2222-32-30000000000-2325−25−55002-3−25255−50000000000000000000000000000000000000000000000000000
χ8888-8-88-800-2-2-2-22222-23-23-2-2222-32-30000000000-23−25255−5002-325−25−550000000000000000000000000000000000000000000000000000
χ8988-8-8-888-8-2-2-2-222223-23-222-2-2-32-3200000000-2-2-3233-2-2223-2-3-3220000000000000000000000000000000000000000000000000000
χ9088-8-8-888-8-2-2-2-22222-23-2322-2-22-32-300000000-2-22-3-2-23322-2322-3-30000000000000000000000000000000000000000000000000000
χ9188-8-8-88-88-2-2-2-222223-23-222-2-2-32-320000000022-32-3-322-2-23-233-2-20000000000000000000000000000000000000000000000000000
χ9288-8-8-88-88-2-2-2-22222-23-2322-2-22-32-300000000222-322-3-3-2-2-23-2-2330000000000000000000000000000000000000000000000000000
χ938-88i−8i00008-2-828i−2i−8i2i-2-2220000−2i−2i2i2i00004+4i−4−4i4−4i−4+4i000000000000000000000000000000000000−1−i1+i−1+i1−i0000000000000000000000000000
χ948-88i−8i00008-2-828i−2i−8i2i-2-2220000−2i−2i2i2i0000−4−4i4+4i−4+4i4−4i0000000000000000000000000000000000001+i−1−i1−i−1+i0000000000000000000000000000
χ958-88i−8i0000-282-8−2i8i2i−8i-2-2220000−2i−2i2i2i4+4i−4−4i4−4i−4+4i000000000000000000000000000000000000−1−i1+i−1+i1−i00000000000000000000000000000000
χ968-88i−8i0000-282-8−2i8i2i−8i-2-2220000−2i−2i2i2i−4−4i4+4i−4+4i4−4i0000000000000000000000000000000000001+i−1−i1−i−1+i00000000000000000000000000000000
χ978-8−8i8i00008-2-82−8i2i8i−2i-2-22200002i2i−2i−2i00004−4i−4+4i4+4i−4−4i000000000000000000000000000000000000−1+i1−i−1−i1+i0000000000000000000000000000
χ988-8−8i8i00008-2-82−8i2i8i−2i-2-22200002i2i−2i−2i0000−4+4i4−4i−4−4i4+4i0000000000000000000000000000000000001−i−1+i1+i−1−i0000000000000000000000000000
χ998-8−8i8i0000-282-82i−8i−2i8i-2-22200002i2i−2i−2i4−4i−4+4i4+4i−4−4i000000000000000000000000000000000000−1+i1−i−1−i1+i00000000000000000000000000000000
χ1008-8−8i8i0000-282-82i−8i−2i8i-2-22200002i2i−2i−2i−4+4i4−4i−4−4i4+4i0000000000000000000000000000000000001−i−1+i1+i−1−i00000000000000000000000000000000
χ10116-1616i−16i0000-4-444−4i−4i4i4i6-4-6400006i−4i−6i4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ10216-1616i−16i0000-4-444−4i−4i4i4i-464-60000−4i6i4i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ10316-16−16i16i0000-4-4444i4i−4i−4i6-4-640000−6i4i6i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ10416-16−16i16i0000-4-4444i4i−4i−4i-464-600004i−6i−4i6i0000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).