Finite Group Databasebeta

← Group #72222861

Character table — Group #72222861

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11222222244444444448888888888888881212121212121212161616161616161616161616161616161618181818181824242424242424242424242424242424242424243232323236484848484848484848484848727272727272
order12233446636668812121212226881212161624242424242444448888666624242424244848484848484848224488224444441212121216161616242424246624248661212121212124848484822881616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-111-1-111111111111111111-1-1-1-1-1-11-11-111-1-111-1-111-1-111-1-11111-11-11-111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-11111111111111111111-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1111111-1-11-11-1-111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-111-1-1111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1111111-1-11-1-1-1-11111-1-1-1-111-1-1-1-1
χ61111111111111111111111-1-111-1-111111111-1-111-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-11111-1-111-1-1-1-11-1111-1-1-1-111-1-11111
χ71111111111111111111111-1-111-1-1111111-1-111-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-1-1-11111-1-1-11-11-1-1-11111-1-1-1-11111
χ81111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111-1-1-1-1111111-1-1-1-1
χ91111111111111111111-1-111111-1-111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1
χ101111111111111111111-1-111111-1-111111111-1-111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-11111-1-1-1-111-11-11-1-1-111-1-11111-1-111
χ111111111111111111111-1-111111-1-1111111-1-111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-11111-1-1-1-111-1-111-1-11-1111-1-111-1-111-1-111
χ121111111111111111111-1-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-111111111-1-111-1-1
χ131111111111111111111-1-11-1-1111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111
χ141111111111111111111-1-11-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-11-11-1-11111-1-111-1-111-1-1-1-1-1-1-1-11-11-1-11111-1-11111-1-1
χ151111111111111111111-1-11-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-111-1-1-1-111-1-111-1-111-1-1-1-1-11-11-111-1-1-1-1111111-1-1
χ161111111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111
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χ1811-1111-11111-1-11-111-1-11-1-1i−i1-1i−i-1-1-1-111i−i−iii−i−ii11-1-1ii−i−i1iiii−i−i−i−i-11-11-1-11-1-11i−i−iii−i−ii1-1-11i−i−ii1-1i−i11-1-11i−i−ii1-1-11-11−ii−ii
χ1911-1111-11111-1-11-111-1-11-1-1i−i1-1i−i-1-1-1-111−iii−i−iii−i11-1-1ii−i−i1iiii−i−i−i−i-11-11-1-1-111-1−iii−i−iii−i-111-1−iii−i1-1i−i1-111-1−iii−i-111-1-11−ii−ii
χ2011-1111-11111-1-11-111-1-11-1-1i−i1-1i−i-1-1-1-111−ii−ii−ii−ii11-1-1ii−i−i1iiii−i−i−i−i1-11-111-1-111−ii−ii−ii−ii-11-11−ii−ii1-1i−i-1-1-111−ii−ii-11-111-1i−ii−i
χ2111-1111-11111-1-11-111-1-11-1-1−ii1-1−ii-1-1-1-111i−ii−ii−ii−i11-1-1−i−iii1−i−i−i−iiiii1-11-111-1-111i−ii−ii−ii−i-11-11i−ii−i1-1−ii-1-1-111i−ii−i-11-111-1−ii−ii
χ2211-1111-11111-1-11-111-1-11-1-1−ii1-1−ii-1-1-1-111i−i−iii−i−ii11-1-1−i−iii1−i−i−i−iiiii-11-11-1-1-111-1i−i−iii−i−ii-111-1i−i−ii1-1−ii1-111-1i−i−ii-111-1-11i−ii−i
χ2311-1111-11111-1-11-111-1-11-1-1−ii1-1−ii-1-1-1-111−iii−i−iii−i11-1-1−i−iii1−i−i−i−iiiii-11-11-1-11-1-11−iii−i−iii−i1-1-11−iii−i1-1−ii11-1-11−iii−i1-1-11-11i−ii−i
χ2411-1111-11111-1-11-111-1-11-1-1−ii1-1−ii-1-1-1-111−ii−ii−ii−ii11-1-1−i−iii1−i−i−i−iiiii1-11-11111-1-1−ii−ii−ii−ii1-11-1−ii−ii1-1−ii-111-1-1−ii−ii1-11-11-1−ii−ii
χ2511-1111-11111-1-11-111-1-1-11-1i−i1-1−ii-1-1-1-111i−ii−ii−ii−i-1-111ii−i−i1−i−i−i−iiiii1-11-11111-1-1−ii−iii−ii−i-11-11i−ii−i-11i−i-111-1-1−ii−ii-11-11-11i−i−ii
χ2611-1111-11111-1-11-111-1-1-11-1i−i1-1−ii-1-1-1-111i−i−iii−i−ii-1-111ii−i−i1−i−i−i−iiiii-11-11-1-11-1-11−iii−ii−i−ii-111-1i−i−ii-11i−i11-1-11−iii−i-111-11-1−iii−i
χ2711-1111-11111-1-11-111-1-1-11-1i−i1-1−ii-1-1-1-111−iii−i−iii−i-1-111ii−i−i1−i−i−i−iiiii-11-11-1-1-111-1i−i−ii−iii−i1-1-11−iii−i-11i−i1-111-1i−i−ii1-1-111-1−iii−i
χ2811-1111-11111-1-11-111-1-1-11-1i−i1-1−ii-1-1-1-111−ii−ii−ii−ii-1-111ii−i−i1−i−i−i−iiiii1-11-111-1-111i−ii−i−ii−ii1-11-1−ii−ii-11i−i-1-1-111i−ii−i1-11-1-11i−i−ii
χ2911-1111-11111-1-11-111-1-1-11-1−ii1-1i−i-1-1-1-111i−ii−ii−ii−i-1-111−i−iii1iiii−i−i−i−i1-11-111-1-111−ii−iii−ii−i1-11-1i−ii−i-11−ii-1-1-111−ii−ii1-11-1-11−iii−i
χ3011-1111-11111-1-11-111-1-1-11-1−ii1-1i−i-1-1-1-111i−i−iii−i−ii-1-111−i−iii1iiii−i−i−i−i-11-11-1-1-111-1−iii−ii−i−ii1-1-11i−i−ii-11−ii1-111-1−iii−i1-1-111-1i−i−ii
χ3111-1111-11111-1-11-111-1-1-11-1−ii1-1i−i-1-1-1-111−iii−i−iii−i-1-111−i−iii1iiii−i−i−i−i-11-11-1-11-1-11i−i−ii−iii−i-111-1−iii−i-11−ii11-1-11i−i−ii-111-11-1i−i−ii
χ3211-1111-11111-1-11-111-1-1-11-1−ii1-1i−i-1-1-1-111−ii−ii−ii−ii-1-111−i−iii1iiii−i−i−i−i1-11-11111-1-1i−ii−i−ii−ii-11-11−ii−ii-11−ii-111-1-1i−ii−i-11-11-11−iii−i
χ332222222222222-2-22222002002200-2-2-2-2-2-22222-2-2-2-200000000-2000000002222-2-20000000022220000-2-2-2-20000-2000000000000000000
χ342222222222222-2-22222002002200-2-2-2-2-2-222-2-2-2-22200000000-200000000-2-2-2-2220000000022-2-20000-2-22200002000000000000000000
χ352222222222222-2-22222002002200-2-2-2-2-2-2-2-22222-2-200000000-200000000-2-2-2-22200000000-2-222000022-2-200002000000000000000000
χ362222222222222-2-22222002002200-2-2-2-2-2-2-2-2-2-2222200000000-2000000002222-2-200000000-2-2-2-2000022220000-2000000000000000000
χ372222-1222-1-1-12-1222-12-122-122-1-1222-1-1-12-1002200222-12-12-12-1-12-1-1-12-1-1-10000000202002200-1-1002200-1-1-1-1-1-100-10-100-1-100-1-1000000
χ382222-1222-1-1-12-1222-12-122-122-1-1222-1-1-12-100-2-200-2-22-12-12-12-1-12-1-1-12-1-1-10000000-20-200-2-2001100-2-20011-1-1-1-10010100110011000000
χ392222-1222-1-1-12-1222-12-122-1-2-2-1-1-2-22-1-1-12-1002200222-12-1-21-21-1-2111-21110000000-20-2002200-1-100-2-200-1-1-1-1110010100-1-10011000000
χ402222-1222-1-1-12-1222-12-122-1-2-2-1-1-2-22-1-1-12-100-2-200-2-22-12-1-21-21-1-2111-2111000000020200-2-2001100220011-1-11100-10-1001100-1-1000000
χ412222-1222-1-1-12-1222-12-1-2-2-122-1-1-2-22-1-1-12-100220022-21-212-12-1-1-2111-2111000000020200-2-200-1-100-2-200-1-111-1-100-10-100110011000000
χ422222-1222-1-1-12-1222-12-1-2-2-122-1-1-2-22-1-1-12-100-2-200-2-2-21-212-12-1-1-2111-21110000000-20-2002200110022001111-1-10010100-1-100-1-1000000
χ432222-1222-1-1-12-1222-12-1-2-2-1-2-2-1-1222-1-1-12-100220022-21-21-21-21-12-1-1-12-1-1-10000000-20-200-2-200-1-1002200-1-1111100101001100-1-1000000
χ442222-1222-1-1-12-1222-12-1-2-2-1-2-2-1-1222-1-1-12-100-2-200-2-2-21-21-21-21-12-1-1-12-1-1-100000002020022001100-2-20011111100-10-100-1-10011000000
χ45222-1222-12-1-1-1222-12-1222-122-1-122-12-1-1-1222002200-12-12-12-12-1-12-1-1-12-1-100000020202200-1-1002200-1-100-1-1-1-10-10-10-1-100-1-100000000
χ46222-1222-12-1-1-1222-12-1222-122-1-122-12-1-1-12-2-200-2-200-12-12-12-12-1-12-1-1-12-1-1000000-20-20-2-2001100-2-2001100-1-1-1-10101011001100000000
χ47222-1222-12-1-1-1222-12-1222-1-2-2-1-1-2-2-12-1-1-1222002200-12-121-21-2-11-2111-211000000-20-202200-1-100-2-200-1-100-1-11101010-1-1001100000000
χ48222-1222-12-1-1-1222-12-1222-1-2-2-1-1-2-2-12-1-1-12-2-200-2-200-12-121-21-2-11-2111-2110000002020-2-200110022001100-1-1110-10-101100-1-100000000
χ49222-1222-12-1-1-1222-12-12-2-2-122-1-1-2-2-12-1-1-12220022001-21-2-12-12-11-2111-2110000002020-2-200-1-100-2-200-1-10011-1-10-10-1011001100000000
χ50222-1222-12-1-1-1222-12-12-2-2-122-1-1-2-2-12-1-1-12-2-200-2-2001-21-2-12-12-11-2111-211000000-20-20220011002200110011-1-101010-1-100-1-100000000
χ51222-1222-12-1-1-1222-12-12-2-2-1-2-2-1-122-12-1-1-12220022001-21-21-21-2-1-12-1-1-12-1-1000000-20-20-2-200-1-1002200-1-1001111010101100-1-100000000
χ52222-1222-12-1-1-1222-12-12-2-2-1-2-2-1-122-12-1-1-12-2-200-2-2001-21-21-21-2-1-12-1-1-12-1-1000000202022001100-2-200110011110-10-10-1-1001100000000
χ5322-2222-22222-2-2-2222-2-200-2002-2002222-2-22i−2i2i−2i−2i2i−2i2i00000000-2000000002-22-2-2-2000000002i−2i2i−2i0000−2i2i−2i2i00002000000000000000000
χ5422-2222-22222-2-2-2222-2-200-2002-2002222-2-22i−2i−2i2i−2i2i2i−2i00000000-200000000-22-2222000000002i−2i−2i2i0000−2i2i2i−2i0000-2000000000000000000
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χ6822-2-122-2-12-1-11-22-2-121-22-21−2i2i-11−2i2i1-211-12−2i2i00−2i2i00-121-2i−2i−i2i-1i−2iii−i2i−i−i00000020-20−2i2i00i−i002-200i−i00-11i−i0-1010i−i00-1100000000
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χ79444-2-244-2-211-2-244-2-2-2-2441441144-2-211-2-200000000-2-2-2-2-2-2-2-21-2-211-2-2110000000000000000000000000011110000000000000000000
χ80444-2-244-2-211-2-244-2-2-2-2441-4-411-4-4-2-211-2-200000000-2-2-2-22222122-1-122-1-10000000000000000000000000011-1-10000000000000000000
χ81444-2-244-2-211-2-244-2-2-2-2-4-414411-4-4-2-211-2-2000000002222-2-2-2-2122-1-122-1-100000000000000000000000000-1-1110000000000000000000
χ82444-2-244-2-211-2-244-2-2-2-2-4-41-4-41144-2-211-2-200000000222222221-2-211-2-21100000000000000000000000000-1-1-1-10000000000000000000
χ8344-444-444444-4-400-4-44400-400-440000000000000000000000000000000004-4-44000000000000000000000000000000000000000000000
χ8444-444-444444-4-400-4-44400-400-44000000000000000000000000000000000-444-4000000000000000000000000000000000000000000000
χ8544-44-24-44-2-2-2-42-444-2-4200200-22004-2-2-2-42004i−4i00−4i4i000000002000000000000000000000000−2i2i0000002i−2i00000000000000000000000
χ8644-44-24-44-2-2-2-42-444-2-4200200-22004-2-2-2-4200−4i4i004i−4i0000000020000000000000000000000002i−2i000000−2i2i00000000000000000000000
χ8744-4-244-4-24-2-22-4-44-242-400200-2200-24-2-22-44i−4i00−4i4i000000000020000000000000000000000−2i2i0000002i−2i0000000000000000000000000
χ8844-4-244-4-24-2-22-4-44-242-400200-2200-24-2-22-4−4i4i004i−4i0000000000200000000000000000000002i−2i000000−2i2i0000000000000000000000000
χ8944-4-2-24-4-2-211224-4-2-2224-4-14i−4i1-14i−4i22-1-1-2-200000000-2-222−2i−2i2i2i1−2i−2iii2i2i−i−i000000000000000000000000001-1i−i0000000000000000000
χ9044-4-2-24-4-2-211224-4-2-2224-4-1−4i4i1-1−4i4i22-1-1-2-200000000-2-2222i2i−2i−2i12i2i−i−i−2i−2iii000000000000000000000000001-1−ii0000000000000000000
χ9144-4-2-24-4-2-211224-4-2-222-44-14i−4i1-1−4i4i22-1-1-2-20000000022-2-2−2i−2i2i2i12i2i−i−i−2i−2iii00000000000000000000000000-11i−i0000000000000000000
χ9244-4-2-24-4-2-211224-4-2-222-44-1−4i4i1-14i−4i22-1-1-2-20000000022-2-22i2i−2i−2i1−2i−2iii2i2i−i−i00000000000000000000000000-11−ii0000000000000000000
χ938888-4-8-88-4-4-48-400-84-8400-400440000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ94888-48-8-8-48-4-4-48004-84-800-400440000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ95888-4-488-4-422-4-4-8-8-4-4-4-400200220044-2-2440000000000000000-2000000000000000000000000000000000000000000000000000000000
χ96888-4-4-8-8-4-422-4-400444400200-2-20000000000000000000000000003i2−3i2003i2−3i20000000000000000000000000000000000000000000000000
χ97888-4-4-8-8-4-422-4-400444400200-2-2000000000000000000000000000−3i23i200−3i23i20000000000000000000000000000000000000000000000000
χ9888-88-4-888-4-4-4-8400-848-4004004-40000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-48-88-48-4-44-8004-8-48004004-40000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-4-48-8-4-42244-88-4-44400-2002-200-4-422440000000000000000-2000000000000000000000000000000000000000000000000000000000
χ10188-8-4-4-88-4-422440044-4-400-200-2200000000000000000000000000032−3200−32320000000000000000000000000000000000000000000000000
χ10288-8-4-4-88-4-422440044-4-400-200-22000000000000000000000000000−32320032−320000000000000000000000000000000000000000000000000
χ1038-808800-8-88-8000000000000000000000000000000000000000000000000000042−420000000000000000000000000000000000000000000
χ1048-808800-8-88-80000000000000000000000000000000000000000000000000000−42420000000000000000000000000000000000000000000
χ10516-16016-800-168-880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10616-160-816008-16-880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10716-160-8-800884-4000000000000000000062−620000000000000000000000000000000000000000000000000000000000000000000000000000
χ10816-160-8-800884-40000000000000000000−62620000000000000000000000000000000000000000000000000000000000000000000000000000

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