Finite Group Databasebeta

← Group #13166389

Character table — Group #13166389

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444444466668888888888888888999912121212121212121212121212121212181818181818363636363636363636363636363654545454108108108108
order1222344666336666661212121212121212121244443366666612121212121212124444121212121212121212121212121212122212121212668888242424242424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1ii−i−i
χ4111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1−i−iii
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111−i−iii
χ81111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111ii−i−i
χ911111-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-11-111-1-111-1-111-1-11-11-1
χ1011111-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-11-1-111-1-11111-1-1-11-11
χ1111111-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111i−i−iiii−i−i−i−iii-1-111i−i−ii
χ1211111-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111−iii−i−i−iiiii−i−i-1-111−iii−i
χ1311111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-11-11-111-1-111-1-1-1-111-11-11
χ1411111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-11-11-1-111-1-111-1-1111-11-1
χ1511111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111i−i−iiii−i−i−i−iii11-1-1−iii−i
χ1611111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111−iii−i−i−iiiii−i−i11-1-1i−i−ii
χ172222-122-1-1-122222222-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ182222-122-1-1-122222222-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022-1-1-1-1-1-1-2-2-2-21111111100000000
χ192222-122-1-1-122222222-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000-2-21111112i2i−2i−2i−i−i−i−iiiii00000000
χ202222-122-1-1-122222222-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000-2-2111111−2i−2i2i2iiiii−i−i−i−i00000000
χ212222-1-2-2-1-1-12222222211-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-11111111122220000000000000000-2-2-1-1-1-1112-22-2-1-111-1-11100000000
χ222222-1-2-2-1-1-12222222211-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-11111111122220000000000000000-2-2-1-1-1-111-22-2211-1-111-1-100000000
χ232222-1-2-2-1-1-12222222211-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-111111111-2-2-2-20000000000000000221111-1-12i−2i−2i2i−i−iiiii−i−i00000000
χ242222-1-2-2-1-1-12222222211-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-111111111-2-2-2-20000000000000000221111-1-1−2i2i2i−2iii−i−i−i−iii00000000
χ2522-2-222-2-2-222222-2-2-2-22-22222-2-2-2-2000022-2-2-2-2222222-2-2-2-222-2-200000000000000002-222-2-22-200000000000000000000
χ2622-2-222-2-2-222222-2-2-2-22-22222-2-2-2-2000022-2-2-2-2222222-2-2-2-2-2-2220000000000000000-22-2-222-2200000000000000000000
χ2722-2-22-22-2-222222-2-2-2-2-22-2-2-2-22222000022-2-2-2-222-2-2-2-2222222-2-20000000000000000-2222-2-2-2200000000000000000000
χ2822-2-22-22-2-222222-2-2-2-2-22-2-2-2-22222000022-2-2-2-222-2-2-2-22222-2-22200000000000000002-2-2-2222-200000000000000000000
χ2922-2-2-12-211-12222-2-2-2-2-112222-2-2-2-20000-1-11111-1-1-1-1-1-1111122-2-200000000000000002-2-1-111-1100003−33−33−33−300000000
χ3022-2-2-12-211-12222-2-2-2-2-112222-2-2-2-20000-1-11111-1-1-1-1-1-1111122-2-200000000000000002-2-1-111-110000−33−33−33−3300000000
χ3122-2-2-12-211-12222-2-2-2-2-112222-2-2-2-20000-1-11111-1-1-1-1-1-11111-2-2220000000000000000-2211-1-11-10000−i3i3−i3i3i3−i3i3−i300000000
χ3222-2-2-12-211-12222-2-2-2-2-112222-2-2-2-20000-1-11111-1-1-1-1-1-11111-2-2220000000000000000-2211-1-11-10000i3−i3i3−i3−i3i3−i3i300000000
χ3322-2-2-1-2211-12222-2-2-2-21-1-2-2-2-222220000-1-11111-1-11111-1-1-1-122-2-20000000000000000-22-1-1111-100003−3−333−3−3300000000
χ3422-2-2-1-2211-12222-2-2-2-21-1-2-2-2-222220000-1-11111-1-11111-1-1-1-122-2-20000000000000000-22-1-1111-10000−333−3−333−300000000
χ3522-2-2-1-2211-12222-2-2-2-21-1-2-2-2-222220000-1-11111-1-11111-1-1-1-1-2-22200000000000000002-211-1-1-110000−i3i3i3−i3i3−i3−i3i300000000
χ3622-2-2-1-2211-12222-2-2-2-21-1-2-2-2-222220000-1-11111-1-11111-1-1-1-1-2-22200000000000000002-211-1-1-110000i3−i3−i3i3−i3i3i3−i300000000
χ372-22-22002-2-222-2-222-2-20000000000002i−2i2222-2-2-2-2000000002i−2i2i−2i000000002i2i2i2i−2i−2i−2i−2i002i−2i2i−2i00000000000000002-20000
χ382-22-22002-2-222-2-222-2-20000000000002i−2i2222-2-2-2-200000000−2i2i−2i2i000000002i2i2i2i−2i−2i−2i−2i00−2i2i−2i2i0000000000000000-220000
χ392-22-22002-2-222-2-222-2-2000000000000−2i2i2222-2-2-2-2000000002i−2i2i−2i00000000−2i−2i−2i−2i2i2i2i2i002i−2i2i−2i0000000000000000-220000
χ402-22-22002-2-222-2-222-2-2000000000000−2i2i2222-2-2-2-200000000−2i2i−2i2i00000000−2i−2i−2i−2i2i2i2i2i00−2i2i−2i2i00000000000000002-20000
χ412-2-22200-22-222-2-2-2-22200000000002i−2i0022-2-222-2-2000000002i−2i−2i2i2i2i2i2i−2i−2i−2i−2i00000000002i−2i−2i2i000000000000002-2000000
χ422-2-22200-22-222-2-2-2-22200000000002i−2i0022-2-222-2-200000000−2i2i2i−2i2i2i2i2i−2i−2i−2i−2i0000000000−2i2i2i−2i00000000000000-22000000
χ432-2-22200-22-222-2-2-2-2220000000000−2i2i0022-2-222-2-2000000002i−2i−2i2i−2i−2i−2i−2i2i2i2i2i00000000002i−2i−2i2i00000000000000-22000000
χ442-2-22200-22-222-2-2-2-2220000000000−2i2i0022-2-222-2-200000000−2i2i2i−2i−2i−2i−2i−2i2i2i2i2i0000000000−2i2i2i−2i000000000000002-2000000
χ4544444444441-21-21-21-24411-2-211-2-244441-21-21-21-211-2-211-2-2000011-2-211-2-211-2-211-2-20000000000000000000000000000
χ4644444444441-21-21-21-24411-2-211-2-2-4-4-4-41-21-21-21-211-2-211-2-20000-1-122-1-122-1-122-1-1220000000000000000000000000000
χ474444444444-21-21-21-2144-2-211-2-2114444-21-21-21-21-2-211-2-2110000-2-211-2-211-2-211-2-2110000000000000000000000000000
χ484444444444-21-21-21-2144-2-211-2-211-4-4-4-4-21-21-21-21-2-211-2-211000022-1-122-1-122-1-122-1-10000000000000000000000000000
χ4944444-4-44441-21-21-21-2-4-4-1-122-1-12244-4-41-21-21-21-2-1-122-1-122000011-2-211-2-2-1-122-1-1220000000000000000000000000000
χ5044444-4-44441-21-21-21-2-4-4-1-122-1-122-4-4441-21-21-21-2-1-122-1-1220000-1-122-1-12211-2-211-2-20000000000000000000000000000
χ5144444-4-4444-21-21-21-21-4-422-1-122-1-144-4-4-21-21-21-2122-1-122-1-10000-2-211-2-21122-1-122-1-10000000000000000000000000000
χ5244444-4-4444-21-21-21-21-4-422-1-122-1-1-4-444-21-21-21-2122-1-122-1-1000022-1-122-1-1-2-211-2-2110000000000000000000000000000
χ5344-4-444-4-4-441-21-2-12-124-411-2-2-1-12200001-2-12-121-211-2-2-1-12200003i−3i003i−3i003i−3i003i−3i000000000000000000000000000000
χ5444-4-444-4-4-441-21-2-12-124-411-2-2-1-12200001-2-12-121-211-2-2-1-1220000−3i3i00−3i3i00−3i3i00−3i3i000000000000000000000000000000
χ5544-4-444-4-4-44-21-212-12-14-4-2-21122-1-10000-212-12-1-21-2-21122-1-10000003i−3i003i−3i003i−3i003i−3i0000000000000000000000000000
χ5644-4-444-4-4-44-21-212-12-14-4-2-21122-1-10000-212-12-1-21-2-21122-1-1000000−3i3i00−3i3i00−3i3i00−3i3i0000000000000000000000000000
χ5744-4-44-44-4-441-21-2-12-12-44-1-12211-2-200001-2-12-121-2-1-12211-2-200003i−3i003i−3i00−3i3i00−3i3i000000000000000000000000000000
χ5844-4-44-44-4-441-21-2-12-12-44-1-12211-2-200001-2-12-121-2-1-12211-2-20000−3i3i00−3i3i003i−3i003i−3i000000000000000000000000000000
χ5944-4-44-44-4-44-21-212-12-1-4422-1-1-2-2110000-212-12-1-2122-1-1-2-2110000003i−3i003i−3i00−3i3i00−3i3i0000000000000000000000000000
χ6044-4-44-44-4-44-21-212-12-1-4422-1-1-2-2110000-212-12-1-2122-1-1-2-211000000−3i3i00−3i3i003i−3i003i−3i0000000000000000000000000000
χ614-44-44004-4-41-2-121-2-12003i−3i003i−3i00004i−4i1-21-2-12-123i−3i003i−3i0000003-300-3300ii−2i−2i−i−i2i2i0000000000000000000000000000
χ624-44-44004-4-41-2-121-2-12003i−3i003i−3i0000−4i4i1-21-2-12-123i−3i003i−3i000000-33003-300−i−i2i2iii−2i−2i0000000000000000000000000000
χ634-44-44004-4-41-2-121-2-1200−3i3i00−3i3i00004i−4i1-21-2-12-12−3i3i00−3i3i000000-33003-300ii−2i−2i−i−i2i2i0000000000000000000000000000
χ644-44-44004-4-41-2-121-2-1200−3i3i00−3i3i0000−4i4i1-21-2-12-12−3i3i00−3i3i0000003-300-3300−i−i2i2iii−2i−2i0000000000000000000000000000
χ654-44-44004-4-4-212-1-212-100003i−3i003i−3i004i−4i-21-212-12-1003i−3i003i−3i0000003-300-33−2i−2iii2i2i−i−i0000000000000000000000000000
χ664-44-44004-4-4-212-1-212-100003i−3i003i−3i00−4i4i-21-212-12-1003i−3i003i−3i000000-33003-32i2i−i−i−2i−2iii0000000000000000000000000000
χ674-44-44004-4-4-212-1-212-10000−3i3i00−3i3i004i−4i-21-212-12-100−3i3i00−3i3i000000-33003-3−2i−2iii2i2i−i−i0000000000000000000000000000
χ684-44-44004-4-4-212-1-212-10000−3i3i00−3i3i00−4i4i-21-212-12-100−3i3i00−3i3i0000003-300-332i2i−i−i−2i−2iii0000000000000000000000000000
χ694-44-4-200-22244-4-444-4-400000000000000-2-2-2-22222000000004i−4i4i−4i000000000000000000−2i2i−2i2i0000000000000000000000
χ704-44-4-200-22244-4-444-4-400000000000000-2-2-2-2222200000000−4i4i−4i4i0000000000000000002i−2i2i−2i0000000000000000000000
χ714-4-44400-44-41-2-12-121-2003i−3i00−3i3i004i−4i001-2-121-2-123i−3i00−3i3i000000ii−2i−2i−i−i2i2i-33003-3000000000000000000000000000000
χ724-4-44400-44-41-2-12-121-2003i−3i00−3i3i00−4i4i001-2-121-2-123i−3i00−3i3i000000−i−i2i2iii−2i−2i3-300-33000000000000000000000000000000
χ734-4-44400-44-41-2-12-121-200−3i3i003i−3i004i−4i001-2-121-2-12−3i3i003i−3i000000ii−2i−2i−i−i2i2i3-300-33000000000000000000000000000000
χ744-4-44400-44-41-2-12-121-200−3i3i003i−3i00−4i4i001-2-121-2-12−3i3i003i−3i000000−i−i2i2iii−2i−2i-33003-3000000000000000000000000000000
χ754-4-44400-44-4-212-12-1-2100003i−3i00−3i3i4i−4i00-212-1-212-1003i−3i00−3i3i0000−2i−2iii2i2i−i−i00-33003-30000000000000000000000000000
χ764-4-44400-44-4-212-12-1-2100003i−3i00−3i3i−4i4i00-212-1-212-1003i−3i00−3i3i00002i2i−i−i−2i−2iii003-300-330000000000000000000000000000
χ774-4-44400-44-4-212-12-1-210000−3i3i003i−3i4i−4i00-212-1-212-100−3i3i003i−3i0000−2i−2iii2i2i−i−i003-300-330000000000000000000000000000
χ784-4-44400-44-4-212-12-1-210000−3i3i003i−3i−4i4i00-212-1-212-100−3i3i003i−3i00002i2i−i−i−2i−2iii00-33003-30000000000000000000000000000
χ794-4-44-2002-2244-4-4-4-44400000000000000-2-222-2-222000000004i−4i−4i4i000000000000000000−2i2i2i−2i0000000000000000000000
χ804-4-44-2002-2244-4-4-4-44400000000000000-2-222-2-22200000000−4i4i4i−4i0000000000000000002i−2i−2i2i0000000000000000000000
χ818888-488-4-4-42-42-42-42-4-4-422-4-422-4-40000-12-12-12-12-1-122-1-122000000000000000000000000000000000000000000000000
χ828888-488-4-4-4-42-42-42-42-4-4-4-422-4-42200002-12-12-12-122-1-122-1-1000000000000000000000000000000000000000000000000
χ838888-4-8-8-4-4-42-42-42-42-444-2-244-2-2440000-12-12-12-1211-2-211-2-2000000000000000000000000000000000000000000000000
χ848888-4-8-8-4-4-4-42-42-42-424444-2-244-2-200002-12-12-12-1-2-211-2-211000000000000000000000000000000000000000000000000
χ8588-8-8-48-844-42-42-4-24-24-4422-4-4-2-2440000-121-21-2-12-1-12211-2-2000000000000000000000000000000000000000000000000
χ8688-8-8-48-844-4-42-424-24-2-44-4-42244-2-200002-1-21-212-122-1-1-2-211000000000000000000000000000000000000000000000000
χ8788-8-8-4-8844-42-42-4-24-244-4-2-24422-4-40000-121-21-2-1211-2-2-1-122000000000000000000000000000000000000000000000000
χ8888-8-8-4-8844-4-42-424-24-24-444-2-2-4-42200002-1-21-212-1-2-21122-1-1000000000000000000000000000000000000000000000000
χ898-88-8-400-4442-4-242-4-24006i−6i006i−6i000000-12-121-21-2−3i3i00−3i3i00000000000000000000000000000000000000000000000000
χ908-88-8-400-4442-4-242-4-2400−6i6i00−6i6i000000-12-121-21-23i−3i003i−3i00000000000000000000000000000000000000000000000000
χ918-88-8-400-444-424-2-424-200006i−6i006i−6i00002-12-1-21-2100−3i3i00−3i3i000000000000000000000000000000000000000000000000
χ928-88-8-400-444-424-2-424-20000−6i6i00−6i6i00002-12-1-21-21003i−3i003i−3i000000000000000000000000000000000000000000000000
χ938-8-88-4004-442-4-24-242-4006i−6i00−6i6i000000-121-2-121-2−3i3i003i−3i00000000000000000000000000000000000000000000000000
χ948-8-88-4004-442-4-24-242-400−6i6i006i−6i000000-121-2-121-23i−3i00−3i3i00000000000000000000000000000000000000000000000000
χ958-8-88-4004-44-424-24-2-4200006i−6i00−6i6i00002-1-212-1-2100−3i3i003i−3i000000000000000000000000000000000000000000000000
χ968-8-88-4004-44-424-24-2-420000−6i6i006i−6i00002-1-212-1-21003i−3i00−3i3i000000000000000000000000000000000000000000000000

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