Finite Group Databasebeta

← Group #13171658

Character table — Group #13171658

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11222222233334444444444446666666666668888888888899121212121212121212121212121212121212121616161618181818181818242424242424242424242424363636363636363636364854547272108
order1233346664444333466612121212122288121212121212121236121212121212121212222246666666612121212242424241212121246688886666666612122424224121212242424241288664
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-111111111111111111111111-1111111111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-11111-1-11111111111111111-1-111-1-1-1-1111-1-1-11111-1-1-1-111111111-11-1-11111111-1-111-1-1-1-1-1-111-1-1-11-1-11111-111-1-1-1
χ41111111111111111-11111-1-11111-1-11111111111-1-111-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-11-1-1111-1-1-1-1-1-111-1-1-1-111-1-111-11-1-1-1-1-1-11-1-1111
χ511111111111-1-11111111111111-11111-1-111-1-111111111111-1-11-1111-1-111-1-111-1-111111111-1-1-111-1-11-11-111-1-111111-1-1-1-1-111-1-11-1-11-1-1
χ611111111111-1-11111111111111-1-1-111-1-111-1-111111111111-1-11-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1111-11-111-1-1-1-1-1-1-11-1-1-1-1-1-111-111-111
χ711111111111-1-1111-11111-1-1111-11111-1-111-1-111-1-111-1-1-1-11-1-1-11-111-1-1-1-11111-1-11111-11-1-1-1-1-111-1-1-111-1-1-111-1-111-111-11111-1-1-1-1-1-111
χ811111111111-1-1111-11111-1-1111-1-1-111-1-111-1-111-1-111-1-1-1-11-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1-1-1-1-1-1-111-111-1-1-11111-1-11-11-111-1-1111111-1-1
χ9111111111-1-111111111111111-1111-1-111-1-11111111111111-1-1-111-1-111-1-111-1-11111111111-1-1-1-1-111-11-11-1-1111111-11-1-1-1-1-1-1111-1-1-11-1
χ10111111111-1-111111111111111-11-1-1-1-111-1-11111111111111-1-1-11-1-1-111-1-111-1-111-1-1-1-11111-1-1-111-1-1-11-11-1-111-1-1-1-11-1-1-1-1-111-1-1-1111-11
χ11111111111-1-111111-11111-1-111-1111-1-111-1-11111-1-111-1-1-1-11-1-11-1-1-1-11111-1-1-1-1111111-11-1-1-1-1-1-1-1111-1-1111-1-1-1-1111-11-111-1-111-1-1-11-11
χ12111111111-1-111111-11111-1-111-11-1-1-1-111-1-11111-1-111-1-1-1-11-1-11-11-1-11111-1-1-1-111-1-1-1-1-11-1-1-1-1-111-1-11-1-1111-1-111-1-1-111-11111-1-1111-11-1
χ13111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-11
χ14111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1
χ15111111111-1-1-1-1111-11111-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-1-1-1-1-11111-1-1-1-11111-11-1-1111-1-1-1-111-1-11111-1-11111-11-1-1-1-1-1-1-11111-1
χ16111111111-1-1-1-1111-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1111111111-1-1111111-1-1-1-1-11-1-111111-1-1-1-11
χ1722222-222222222220222-200-2-2-2-200222222222200-2-20000-222000-2-2-2-20000222200000-200-222000000-2-200000000000-2000000000000
χ1822222-222222-2-22220222-200-2-2-220022-2-222-2-22200-2-20000-2-2-2000-2-222000022-2-200000-2002-2-2000000-22000000000002000000000000
χ1922222-2222-2-2222220222-200-2-22-200-2-222-2-2222200-2-20000-2-2-200022-2-20000-2-22200000-2002-2-20000002-2000000000002000000000000
χ2022222-2222-2-2-2-22220222-200-2-22200-2-2-2-2-2-2-2-22200-2-20000-22200022220000-2-2-2-200000-200-2220000002200000000000-2000000000000
χ212222-1222-122222-1-12-1-12-1-1-12222002222-1-1-1-1-1-122-1-1-1-1-1-12222202-12-1-1-1-1-1-1-1-1-100002-1-1-12-1-1000022-1-1-1-1-1-10000002-1-1-10000000000
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χ232222-1222-122-2-22-1-12-1-12-1-1-1222-20022-2-2-1-111-1-122-1-1-1-1-1-12-2-22-202-1-21-1-111-1-11100002-1-1-1-21100002-2-11-1-111000000-21110000000000
χ242222-1222-122-2-22-1-1-2-1-12-111222-20022-2-2-1-111-1-1-2-2-1-111112-2-2-2202-1-2111-1-1-1-1110000-2-111-2110000-22-1111-1-100000021-1-10000000000
χ252222-1222-1-2-2222-1-12-1-12-1-1-122-2200-2-22211-1-1-1-122-1-1-1-1-1-12-2-2-220-212-111-1-111-1-100002-1-1-1-2110000-221-111-1-1000000-21110000000000
χ262222-1222-1-2-2222-1-1-2-1-12-11122-2200-2-22211-1-1-1-1-2-2-1-111112-2-22-20-212-1-1-11111-1-10000-2-111-21100002-21-1-1-11100000021-1-10000000000
χ272222-1222-1-2-2-2-22-1-12-1-12-1-1-122-2-200-2-2-2-21111-1-122-1-1-1-1-1-1222-2-20-21-211111111100002-1-1-12-1-10000-2-21111110000002-1-1-10000000000
χ282222-1222-1-2-2-2-22-1-1-2-1-12-11122-2-200-2-2-2-21111-1-1-2-2-1-11111222220-21-21-1-1-1-111110000-2-1112-1-100002211-1-1-1-1000000-2-1110000000000
χ292222-1-222-122222-1-10-1-121−i3i3-2-2-2-2002222-1-1-1-1-1-10011−i3−i3i3i3-222000-21-21−i3i3−i3i3-1-1-1-1000001−i3i3-2-1-100000011−i3i3−i3i300000001−i3i30000000000
χ302222-1-222-122222-1-10-1-121i3−i3-2-2-2-2002222-1-1-1-1-1-10011i3i3−i3−i3-222000-21-21i3−i3i3−i3-1-1-1-1000001i3−i3-2-1-100000011i3−i3i3−i300000001i3−i30000000000
χ312222-1-222-122-2-22-1-10-1-121−i3i3-2-2-220022-2-2-1-111-1-10011−i3−i3i3i3-2-2-2000-212-1−i3i3i3−i3-1-111000001−i3i32110000001-1−i3i3i3−i30000000-1i3−i30000000000
χ322222-1-222-122-2-22-1-10-1-121i3−i3-2-2-220022-2-2-1-111-1-10011i3i3−i3−i3-2-2-2000-212-1i3−i3−i3i3-1-111000001i3−i32110000001-1i3−i3−i3i30000000-1−i3i30000000000
χ332222-1-222-1-2-2222-1-10-1-121−i3i3-2-22-200-2-22211-1-1-1-10011−i3−i3i3i3-2-2-20002-1-21i3−i3−i3i311-1-1000001−i3i3211000000-11i3−i3−i3i30000000-1i3−i30000000000
χ342222-1-222-1-2-2222-1-10-1-121i3−i3-2-22-200-2-22211-1-1-1-10011i3i3−i3−i3-2-2-20002-1-21−i3i3i3−i311-1-1000001i3−i3211000000-11−i3i3i3−i30000000-1−i3i30000000000
χ352222-1-222-1-2-2-2-22-1-10-1-121−i3i3-2-22200-2-2-2-21111-1-10011−i3−i3i3i3-2220002-12-1i3−i3i3−i31111000001−i3i3-2-1-1000000-1-1i3−i3i3−i300000001−i3i30000000000
χ362222-1-222-1-2-2-2-22-1-10-1-121i3−i3-2-22200-2-2-2-21111-1-10011i3i3−i3−i3-2220002-12-1−i3i3−i3i31111000001i3−i3-2-1-1000000-1-1−i3i3−i3i300000001i3−i30000000000
χ37222-1222-120022-12-122-1-12222-1022200-1-10022-1-12-12-12-12-1-10002200-12002200-1-122-1-1-1-1-1-100000220-10-100-1-12-1-1-102000000-1-1-1000-10
χ38222-1222-120022-12-122-1-12222-102-2-200-1-10022-1-12-12-12-12-1-10002-200-12002200-1-1-2-211-1-1-1-100000-2-20-10-100-1-1-21110-200000011100010
χ39222-1222-120022-12-1-22-1-12-2-22-1022200-1-10022-1-1-212-1-21-21-1000-2-200-1200-2-200-1-122-1-11-1110000022010-10011-21-1-10-2000000-1-1100010
χ40222-1222-120022-12-1-22-1-12-2-22-102-2-200-1-10022-1-1-212-1-21-21-1000-2200-1200-2-200-1-1-2-2111-11100000-2-2010-100112-1110200000011-1000-10
χ41222-1222-1200-2-2-12-122-1-12222-10-222001100-2-2-1-12-12-12-12-1-1000-22001-200-2-2001122-1-1-1-1-1-100000-2-2010100112-1-1-10-200000011-100010
χ42222-1222-1200-2-2-12-122-1-12222-10-2-2-2001100-2-2-1-12-12-12-12-1-1000-2-2001-200-2-20011-2-211-1-1-1-1000002201010011-211102000000-1-11000-10
χ43222-1222-1200-2-2-12-1-22-1-12-2-22-10-222001100-2-2-1-1-212-1-21-21-10002-2001-20022001122-1-11-11100000-2-20-10100-1-1-21-1-102000000111000-10
χ44222-1222-1200-2-2-12-1-22-1-12-2-22-10-2-2-2001100-2-2-1-1-212-1-21-21-100022001-200220011-2-2111-11100000220-10100-1-12-1110-2000000-1-1-100010
χ4522-1222-1222200-1-122-12-1222-122022-1-1002200-1-1-12-12-12-12-100202-12002200-1-100-1-122-1-1-1-10002200-10-10-1-100-12-1-1200000-1-100-100-100
χ4622-1222-1222200-1-122-12-1222-1220-2-2-1-1002200-1-1-12-12-12-12-10020-2-12002200-1-10011-2-2-1-1-1-1000-2-200-10-10-1-1001-211-2000001100100100
χ4722-1222-1222200-1-12-2-12-12-2-2-122022-1-1002200-1-11-2-121-21-2-100-20-2-1200-2-200-1-100-1-1221-111000220010-1011001-2-1-1-200000-1-100100100
χ4822-1222-1222200-1-12-2-12-12-2-2-1220-2-2-1-1002200-1-11-2-121-21-2-100-202-1200-2-200-1-10011-2-21-111000-2-20010-101100-12112000001100-100-100
χ4922-1222-122-2-200-1-122-12-1222-12-20221100-2-200-1-1-12-12-12-12-100-2021-200-2-2001100-1-122-1-1-1-1000-2-20010101100-12-1-1-2000001100-100100
χ5022-1222-122-2-200-1-122-12-1222-12-20-2-21100-2-200-1-1-12-12-12-12-100-20-21-200-2-200110011-2-2-1-1-1-10002200101011001-211200000-1-100100-100
χ5122-1222-122-2-200-1-12-2-12-12-2-2-12-20221100-2-200-1-11-2-121-21-2-10020-21-20022001100-1-1221-111000-2-200-1010-1-1001-2-1-12000001100100-100
χ5222-1222-122-2-200-1-12-2-12-12-2-2-12-20-2-21100-2-200-1-11-2-121-21-2-1002021-2002200110011-2-21-1110002200-1010-1-100-1211-200000-1-100-100100
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χ8044-24-2-4-24-2-4-400-21-201-2-222i3−2i32-44000220022001100-12−i32i3i3−2i3200000-2-200−2i32i300-1-10000000-1−i3i300000000010i3−i30000000000000000000000
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χ864-444-20-4-424i−4i−4i4i4-2-2022-40000000004i−4i−4i4i−2i2i2i−2i-22000000000-4400000000000−2i2i2i−2i0000000002-200000000000000000000000000000000
χ874-444-20-4-42−4i4i4i−4i4-2-2022-4000000000−4i4i4i−4i2i−2i−2i2i-22000000000-44000000000002i−2i−2i2i0000000002-200000000000000000000000000000000
χ884-444-20-4-42−4i4i−4i4i4-2-2022-4000000000−4i4i−4i4i2i−2i2i−2i-220000000004-4000000000002i−2i2i−2i000000000-2200000000000000000000000000000000
χ894-44-240-42-4004i−4i-24-20-422000000022−2200−2i2i004i−4i-22000000000000000000000000−2i2i22−22−22000000000−2i22i20000000000−2200000000i2−i2000000
χ904-44-240-42-4004i−4i-24-20-4220000000−222200−2i2i004i−4i-22000000000000000000000000−2i2i−22222−20000000002i2−2i200000000002−200000000−i2i2000000
χ914-44-240-42-400−4i4i-24-20-422000000022−22002i−2i00−4i4i-220000000000000000000000002i−2i22−22−220000000002i2−2i20000000000−2200000000−i2i2000000
χ924-44-240-42-400−4i4i-24-20-4220000000−2222002i−2i00−4i4i-220000000000000000000000002i−2i−22222−2000000000−2i22i200000000002−200000000i2−i2000000
χ934-4-24402-4-44i−4i00-2-2402-42000000022−22−2i2i004i−4i00-220000000000000000000000−2i2i00−2222−220000000−2i22i2000000000000−22000000i2−i200000000
χ944-4-24402-4-44i−4i00-2-2402-420000000−2222−2i2i004i−4i00-220000000000000000000000−2i2i002−2−222200000002i2−2i20000000000002−2000000−i2i200000000
χ954-4-24402-4-4−4i4i00-2-2402-42000000022−222i−2i00−4i4i00-2200000000000000000000002i−2i00−2222−2200000002i2−2i2000000000000−22000000−i2i200000000
χ964-4-24402-4-4−4i4i00-2-2402-420000000−22222i−2i00−4i4i00-2200000000000000000000002i−2i002−2−22220000000−2i22i20000000000002−2000000i2−i200000000
χ9788-4-48-8-4-4800002-4-40-4-42-800440000000000002200440000-20000000000000000000000-20000000000000000000000000000000000000
χ9888-4-4-48-4-4-400002228222-4-4-4-4-4000000000000-1-1-4-422222220000000000000000000002-1-1-100000000000000000000000000000000000
χ9988-4-4-48-4-4-40000222-8222-444-4-4000000000000-1-14422-2-2-2-22000000000000000000000-2-11100000000000000000000000000000000000
χ10088-4-4-4-8-4-4-4000022202224−4i34i344000000000000-1-100-2-22i32i3−2i3−2i3-200000000000000000000001−i3i300000000000000000000000000000000000
χ10188-4-4-4-8-4-4-40000222022244i3−4i344000000000000-1-100-2-2−2i3−2i32i32i3-200000000000000000000001i3−i300000000000000000000000000000000000
χ1028-88-4-40-844008i−8i-4-4204-2400000000000−4i4i00−4i4i2-20000000000000000000000002i−2i0000000000000000000000000000000000000000000
χ1038-88-4-40-84400−8i8i-4-4204-24000000000004i−4i004i−4i2-2000000000000000000000000−2i2i0000000000000000000000000000000000000000000
χ1048-8-48-404-848i−8i00-42-40-244000000000−4i4i00−4i4i002-200000000000000000000002i−2i000000000000000000000000000000000000000000000
χ1058-8-48-404-84−8i8i00-42-40-2440000000004i−4i004i−4i002-20000000000000000000000−2i2i000000000000000000000000000000000000000000000
χ1068-8-4-48044-800002-4-4044-2000000042−42000000002-200000000000000000000000000−2222−22220000000000000000000002−20000000000000000
χ1078-8-4-48044-800002-4-4044-20000000−4242000000002-20000000000000000000000000022−2222−22000000000000000000000−220000000000000000
χ10816-16-8-8-8088800004440-4-4-400000000000000000-22000000000000000000000000000000000000000000000000000000000000000000000

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