Finite Group Databasebeta

← Group #13165497

Character table — Group #13165497

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11444412121212121218181811444412121212121218181822888824242424242436363622888824242424242436363633121212123636363636365454543312121212363636363636545454
order12336624661212488226666246612124883633666126612121224246666666126612121224244412121212441212121248844121212124412121212488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111-111-1-11-1-11111111-111-1-11-1-11111111-111-1-11-1-11111111-111-1-11-1-11111111-111-1-11-1-11111111-111-1-11-1-1
χ3111111-11-1-1111-1-1111111-11-1-1111-1-1111111-11-1-1111-1-1111111-11-1-1111-1-1111111-11-1-1111-1-1111111-11-1-1111-1-1
χ4111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111
χ5222222000000-200222222000000-200222222000000-200222222000000-200222222000000-200222222000000-200
χ62-222-2-20000000−i2i22-222-2-20000000−i2i22-222-2-20000000−i2i22-222-2-20000000−i2i22-222-2-20000000−i2i22-222-2-20000000−i2i2
χ72-222-2-20000000i2−i22-222-2-20000000i2−i22-222-2-20000000i2−i22-222-2-20000000i2−i22-222-2-20000000i2−i22-222-2-20000000i2−i2
χ8441-2-210200-1-1000441-2-210200-1-1000441-2-210200-1-1000441-2-210200-1-1000441-2-210200-1-1000441-2-210200-1-1000
χ9441-2-210-20011000441-2-210-20011000441-2-210-20011000441-2-210-20011000441-2-210-20011000441-2-210-20011000
χ1044-211-220-1-10000044-211-220-1-10000044-211-220-1-10000044-211-220-1-10000044-211-220-1-10000044-211-220-1-100000
χ1144-211-2-20110000044-211-2-20110000044-211-2-20110000044-211-2-20110000044-211-2-20110000044-211-2-201100000
χ124-41-22-100003−30004-41-22-100003−30004-41-22-100003−30004-41-22-100003−30004-41-22-100003−30004-41-22-100003−3000
χ134-41-22-10000−330004-41-22-10000−330004-41-22-10000−330004-41-22-10000−330004-41-22-10000−330004-41-22-10000−33000
χ144-4-21-1200−i3i3000004-4-21-1200−i3i3000004-4-21-1200−i3i3000004-4-21-1200−i3i3000004-4-21-1200−i3i3000004-4-21-1200−i3i300000
χ154-4-21-1200i3−i3000004-4-21-1200i3−i3000004-4-21-1200i3−i3000004-4-21-1200i3−i3000004-4-21-1200i3−i3000004-4-21-1200i3−i300000
χ16111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ171111111-111-1-11-1-11111111-111-1-11-1-11111111-111-1-11-1-11111111-111-1-11-1-1-1-1-1-1-1-1-11-1-111-111-1-1-1-1-1-1-11-1-111-111
χ18111111-11-1-1111-1-1111111-11-1-1111-1-1111111-11-1-1111-1-1111111-11-1-1111-1-1-1-1-1-1-1-11-111-1-1-111-1-1-1-1-1-11-111-1-1-111
χ19111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111-1-1-1
χ20222222000000-200222222000000-200222222000000-200222222000000-200-2-2-2-2-2-2000000200-2-2-2-2-2-2000000200
χ212-222-2-20000000−i2i22-222-2-20000000−i2i22-222-2-20000000−i2i22-222-2-20000000−i2i2-22-2-2220000000i2−i2-22-2-2220000000i2−i2
χ222-222-2-20000000i2−i22-222-2-20000000i2−i22-222-2-20000000i2−i22-222-2-20000000i2−i2-22-2-2220000000−i2i2-22-2-2220000000−i2i2
χ23441-2-210200-1-1000441-2-210200-1-1000441-2-210200-1-1000441-2-210200-1-1000-4-4-122-10-20011000-4-4-122-10-20011000
χ24441-2-210-20011000441-2-210-20011000441-2-210-20011000441-2-210-20011000-4-4-122-10200-1-1000-4-4-122-10200-1-1000
χ2544-211-220-1-10000044-211-220-1-10000044-211-220-1-10000044-211-220-1-100000-4-42-1-12-201100000-4-42-1-12-201100000
χ2644-211-2-20110000044-211-2-20110000044-211-2-20110000044-211-2-201100000-4-42-1-1220-1-100000-4-42-1-1220-1-100000
χ274-41-22-100003−30004-41-22-100003−30004-41-22-100003−30004-41-22-100003−3000-44-12-210000−33000-44-12-210000−33000
χ284-41-22-10000−330004-41-22-10000−330004-41-22-10000−330004-41-22-10000−33000-44-12-2100003−3000-44-12-2100003−3000
χ294-4-21-1200−i3i3000004-4-21-1200−i3i3000004-4-21-1200−i3i3000004-4-21-1200−i3i300000-442-11-200i3−i300000-442-11-200i3−i300000
χ304-4-21-1200i3−i3000004-4-21-1200i3−i3000004-4-21-1200i3−i3000004-4-21-1200i3−i300000-442-11-200−i3i300000-442-11-200−i3i300000
χ31111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ321111111-111-1-11-1-1-1-1-1-1-1-1-11-1-111-1111111111-111-1-11-1-1-1-1-1-1-1-1-11-1-111-111iiiiiii−iii−i−ii−i−i−i−i−i−i−i−i−ii−i−iii−iii
χ33111111-11-1-1111-1-1-1-1-1-1-1-11-111-1-1-111111111-11-1-1111-1-1-1-1-1-1-1-11-111-1-1-111iiiiii−ii−i−iiii−i−i−i−i−i−i−i−ii−iii−i−i−iii
χ34111111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1iiiiii−i−i−i−i−i−iiii−i−i−i−i−i−iiiiiii−i−i−i
χ35222222000000-200-2-2-2-2-2-2000000200222222000000-200-2-2-2-2-2-20000002002i2i2i2i2i2i000000−2i00−2i−2i−2i−2i−2i−2i0000002i00
χ362-222-2-20000000−i2i2-22-2-2220000000i2−i22-222-2-20000000−i2i2-22-2-2220000000i2−i22i−2i2i2i−2i−2i00000002−2−2i2i−2i−2i2i2i0000000−22
χ372-222-2-20000000i2−i2-22-2-2220000000−i2i22-222-2-20000000i2−i2-22-2-2220000000−i2i22i−2i2i2i−2i−2i0000000−22−2i2i−2i−2i2i2i00000002−2
χ38441-2-210200-1-1000-4-4-122-10-20011000441-2-210200-1-1000-4-4-122-10-200110004i4ii−2i−2ii02i00−i−i000−4i−4i−i2i2i−i0−2i00ii000
χ39441-2-210-20011000-4-4-122-10200-1-1000441-2-210-20011000-4-4-122-10200-1-10004i4ii−2i−2ii0−2i00ii000−4i−4i−i2i2i−i02i00−i−i000
χ4044-211-220-1-100000-4-42-1-12-20110000044-211-220-1-100000-4-42-1-12-2011000004i4i−2iii−2i2i0−i−i00000−4i−4i2i−i−i2i−2i0ii00000
χ4144-211-2-201100000-4-42-1-1220-1-10000044-211-2-201100000-4-42-1-1220-1-1000004i4i−2iii−2i−2i0ii00000−4i−4i2i−i−i2i2i0−i−i00000
χ424-41-22-100003−3000-44-12-210000−330004-41-22-100003−3000-44-12-210000−330004i−4ii−2i2i−i0000i3−i3000−4i4i−i2i−2ii0000−i3i3000
χ434-41-22-10000−33000-44-12-2100003−30004-41-22-10000−33000-44-12-2100003−30004i−4ii−2i2i−i0000−i3i3000−4i4i−i2i−2ii0000i3−i3000
χ444-4-21-1200−i3i300000-442-11-200i3−i3000004-4-21-1200−i3i300000-442-11-200i3−i3000004i−4i−2ii−i2i003−300000−4i4i2i−ii−2i00−3300000
χ454-4-21-1200i3−i300000-442-11-200−i3i3000004-4-21-1200i3−i300000-442-11-200−i3i3000004i−4i−2ii−i2i00−3300000−4i4i2i−ii−2i003−300000
χ46111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiii
χ471111111-111-1-11-1-1-1-1-1-1-1-1-11-1-111-1111111111-111-1-11-1-1-1-1-1-1-1-1-11-1-111-111−i−i−i−i−i−i−ii−i−iii−iiiiiiiiii−iii−i−ii−i−i
χ48111111-11-1-1111-1-1-1-1-1-1-1-11-111-1-1-111111111-11-1-1111-1-1-1-1-1-1-1-11-111-1-1-111−i−i−i−i−i−ii−iii−i−i−iiiiiiiii−ii−i−iiii−i−i
χ49111111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1−i−i−i−i−i−iiiiiii−i−i−iiiiiii−i−i−i−i−i−iiii
χ50222222000000-200-2-2-2-2-2-2000000200222222000000-200-2-2-2-2-2-2000000200−2i−2i−2i−2i−2i−2i0000002i002i2i2i2i2i2i000000−2i00
χ512-222-2-20000000−i2i2-22-2-2220000000i2−i22-222-2-20000000−i2i2-22-2-2220000000i2−i2−2i2i−2i−2i2i2i0000000−222i−2i2i2i−2i−2i00000002−2
χ522-222-2-20000000i2−i2-22-2-2220000000−i2i22-222-2-20000000i2−i2-22-2-2220000000−i2i2−2i2i−2i−2i2i2i00000002−22i−2i2i2i−2i−2i0000000−22
χ53441-2-210200-1-1000-4-4-122-10-20011000441-2-210200-1-1000-4-4-122-10-20011000−4i−4i−i2i2i−i0−2i00ii0004i4ii−2i−2ii02i00−i−i000
χ54441-2-210-20011000-4-4-122-10200-1-1000441-2-210-20011000-4-4-122-10200-1-1000−4i−4i−i2i2i−i02i00−i−i0004i4ii−2i−2ii0−2i00ii000
χ5544-211-220-1-100000-4-42-1-12-20110000044-211-220-1-100000-4-42-1-12-201100000−4i−4i2i−i−i2i−2i0ii000004i4i−2iii−2i2i0−i−i00000
χ5644-211-2-201100000-4-42-1-1220-1-10000044-211-2-201100000-4-42-1-1220-1-100000−4i−4i2i−i−i2i2i0−i−i000004i4i−2iii−2i−2i0ii00000
χ574-41-22-100003−3000-44-12-210000−330004-41-22-100003−3000-44-12-210000−33000−4i4i−i2i−2ii0000−i3i30004i−4ii−2i2i−i0000i3−i3000
χ584-41-22-10000−33000-44-12-2100003−30004-41-22-10000−33000-44-12-2100003−3000−4i4i−i2i−2ii0000i3−i30004i−4ii−2i2i−i0000−i3i3000
χ594-4-21-1200−i3i300000-442-11-200i3−i3000004-4-21-1200−i3i300000-442-11-200i3−i300000−4i4i2i−ii−2i00−33000004i−4i−2ii−i2i003−300000
χ604-4-21-1200i3−i300000-442-11-200−i3i3000004-4-21-1200i3−i300000-442-11-200−i3i300000−4i4i2i−ii−2i003−3000004i−4i−2ii−i2i00−3300000
χ61222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000
χ622222222-222-2-22-2-22222222-222-2-22-2-2-1-1-1-1-1-1-11-1-111-111-1-1-1-1-1-1-11-1-111-111000000000000000000000000000000
χ63222222-22-2-2222-2-2222222-22-2-2222-2-2-1-1-1-1-1-11-111-1-1-111-1-1-1-1-1-11-111-1-1-111000000000000000000000000000000
χ64222222-2-2-2-2-2-2222222222-2-2-2-2-2-2222-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111-1-1-1000000000000000000000000000000
χ65444444000000-400444444000000-400-2-2-2-2-2-2000000200-2-2-2-2-2-2000000200000000000000000000000000000000
χ664-444-4-40000000−2i22i24-444-4-40000000−2i22i2-22-2-2220000000i2−i2-22-2-2220000000i2−i2000000000000000000000000000000
χ674-444-4-400000002i2−2i24-444-4-400000002i2−2i2-22-2-2220000000−i2i2-22-2-2220000000−i2i2000000000000000000000000000000
χ68882-4-420400-2-2000882-4-420400-2-2000-4-4-122-10-20011000-4-4-122-10-20011000000000000000000000000000000000
χ69882-4-420-40022000882-4-420-40022000-4-4-122-10200-1-1000-4-4-122-10200-1-1000000000000000000000000000000000
χ7088-422-440-2-20000088-422-440-2-200000-4-42-1-12-201100000-4-42-1-12-201100000000000000000000000000000000000
χ7188-422-4-40220000088-422-4-402200000-4-42-1-1220-1-100000-4-42-1-1220-1-100000000000000000000000000000000000
χ728-82-44-2000023−230008-82-44-2000023−23000-44-12-210000−33000-44-12-210000−33000000000000000000000000000000000
χ738-82-44-20000−23230008-82-44-20000−2323000-44-12-2100003−3000-44-12-2100003−3000000000000000000000000000000000
χ748-8-42-2400−2i32i3000008-8-42-2400−2i32i300000-442-11-200i3−i300000-442-11-200i3−i300000000000000000000000000000000000
χ758-8-42-24002i3−2i3000008-8-42-24002i3−2i300000-442-11-200−i3i300000-442-11-200−i3i300000000000000000000000000000000000
χ76222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111000000000000000000000000000000
χ772222222-222-2-22-2-2-2-2-2-2-2-2-22-2-222-222-1-1-1-1-1-1-11-1-111-1111111111-111-1-11-1-1000000000000000000000000000000
χ78222222-22-2-2222-2-2-2-2-2-2-2-22-222-2-2-222-1-1-1-1-1-11-111-1-1-111111111-11-1-1111-1-1000000000000000000000000000000
χ79222222-2-2-2-2-2-2222-2-2-2-2-2-2222222-2-2-2-1-1-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1111000000000000000000000000000000
χ80444444000000-400-4-4-4-4-4-4000000400-2-2-2-2-2-2000000200222222000000-200000000000000000000000000000000
χ814-444-4-40000000−2i22i2-44-4-44400000002i2−2i2-22-2-2220000000i2−i22-222-2-20000000−i2i2000000000000000000000000000000
χ824-444-4-400000002i2−2i2-44-4-4440000000−2i22i2-22-2-2220000000−i2i22-222-2-20000000i2−i2000000000000000000000000000000
χ83882-4-420400-2-2000-8-8-244-20-40022000-4-4-122-10-20011000441-2-210200-1-1000000000000000000000000000000000
χ84882-4-420-40022000-8-8-244-20400-2-2000-4-4-122-10200-1-1000441-2-210-20011000000000000000000000000000000000
χ8588-422-440-2-200000-8-84-2-24-402200000-4-42-1-12-20110000044-211-220-1-100000000000000000000000000000000000
χ8688-422-4-402200000-8-84-2-2440-2-200000-4-42-1-1220-1-10000044-211-2-201100000000000000000000000000000000000
χ878-82-44-2000023−23000-88-24-420000−2323000-44-12-210000−330004-41-22-100003−3000000000000000000000000000000000
χ888-82-44-20000−2323000-88-24-42000023−23000-44-12-2100003−30004-41-22-10000−33000000000000000000000000000000000
χ898-8-42-2400−2i32i300000-884-22-4002i3−2i300000-442-11-200i3−i3000004-4-21-1200−i3i300000000000000000000000000000000000
χ908-8-42-24002i3−2i300000-884-22-400−2i32i300000-442-11-200−i3i3000004-4-21-1200i3−i300000000000000000000000000000000000

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