Finite Group Databasebeta

← Group #13165404

Character table — Group #13165404

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222244444444666666888888889999121212121212121212121212121212121212181818181818181824242424242424242424242436363636363636363636363654547272108108
order122236663366666644444433666666222244121212121212121212121212121212124444666612121212121212121212121222441212121212121212446644
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ311111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111
χ71111111111111111-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1
χ911-1-11-11-11111-1-1-1-111-1-1i−i111-1-1-11-11-1-11i−i11-1-1ii−i−i11-1-1ii−i−iii−i−i11-1-1i−ii−i11-1-1ii−i−i1-1i−iii−i−iii−i−ii−i1-11-1
χ1011-1-11-11-11111-1-1-1-111-1-1i−i111-1-1-11-11-1-11−ii11-1-1−i−iii11-1-1ii−i−iii−i−i11-1-1i−i−ii11-1-1−i−iii-11−iiii−i−i−i−iiii−i-11-11
χ1111-1-11-11-11111-1-1-1-111-1-1−ii111-1-1-11-11-1-11i−i11-1-1ii−i−i11-1-1−i−iii−i−iii11-1-1−iii−i11-1-1ii−i−i-11i−i−i−iiiii−i−i−ii-11-11
χ1211-1-11-11-11111-1-1-1-111-1-1−ii111-1-1-11-11-1-11−ii11-1-1−i−iii11-1-1−i−iii−i−iii11-1-1−ii−ii11-1-1−i−iii1-1−ii−i−iii−i−iii−ii1-11-1
χ1311-1-11-11-11111-1-1-1-1-1-111i−i111-1-1-11-11-1-11i−i-1-111ii−i−i-1-111ii−i−i−i−iii11-1-1i−ii−i-1-111ii−i−i1-1−ii−i−iii−i−iiii−i1-1-11
χ1411-1-11-11-11111-1-1-1-1-1-111i−i111-1-1-11-11-1-11−ii-1-111−i−iii-1-111ii−i−i−i−iii11-1-1i−i−ii-1-111−i−iii-11i−i−i−iiiii−i−ii−i-111-1
χ1511-1-11-11-11111-1-1-1-1-1-111−ii111-1-1-11-11-1-11i−i-1-111ii−i−i-1-111−i−iiiii−i−i11-1-1−iii−i-1-111ii−i−i-11−iiii−i−i−i−iii−ii-111-1
χ1611-1-11-11-11111-1-1-1-1-1-111−ii111-1-1-11-11-1-11−ii-1-111−i−iii-1-111−i−iiiii−i−i11-1-1−ii−ii-1-111−i−iii1-1i−iii−i−iii−i−i−ii1-1-11
χ17222222222222222200002222222222-2-2-2-20000000000000022220000-2-2-2-2220000000000000000000000-2-20000
χ1822222222222222220000-2-222222222-2-2-2-200000000000000-2-2-2-20000-2-2-2-2-2-20000000000000000000000220000
χ192222-1-1-1-122222222222200-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222200000000-1-1-1-10022-1-1-1-1-1-1-1-100220000-1-1-1-1000000
χ202222-1-1-1-122222222222200-1-1-1-1-1-1-1-12222-2-2-1-1-1-11111222200000000-1-1-1-100-2-2-1-1-1-1111100-2-200001111000000
χ212222-1-1-1-122222222-2-2-2-200-1-1-1-1-1-1-1-12222221111-1-1-1-1-2-2-2-200000000-1-1-1-100221111-1-1-1-100-2-200001111000000
χ222222-1-1-1-122222222-2-2-2-200-1-1-1-1-1-1-1-12222-2-211111111-2-2-2-200000000-1-1-1-100-2-21111111100220000-1-1-1-1000000
χ2322-2-22-22-22222-2-2-2-200002i−2i222-2-2-22-2-222-2000000000000002i2i−2i−2i0000-2-2222i−2i0000000000000000000000−2i2i0000
χ2422-2-22-22-22222-2-2-2-20000−2i2i222-2-2-22-2-222-200000000000000−2i−2i2i2i0000-2-222−2i2i00000000000000000000002i−2i0000
χ2522-2-2-11-112222-2-2-2-222-2-200-1-1-1111-112-2-222i−2i-1-111−i−iii22-2-200000000-1-111002i−2i-1-111−i−iii002i−2i0000−i−iii000000
χ2622-2-2-11-112222-2-2-2-222-2-200-1-1-1111-112-2-22−2i2i-1-111ii−i−i22-2-200000000-1-11100−2i2i-1-111ii−i−i00−2i2i0000ii−i−i000000
χ2722-2-2-11-112222-2-2-2-2-2-22200-1-1-1111-112-2-222i−2i11-1-1−i−iii-2-22200000000-1-111002i−2i11-1-1−i−iii00−2i2i0000ii−i−i000000
χ2822-2-2-11-112222-2-2-2-2-2-22200-1-1-1111-112-2-22−2i2i11-1-1ii−i−i-2-22200000000-1-11100−2i2i11-1-1ii−i−i002i−2i0000−i−iii000000
χ292-22-22-2-2222-2-2-22-2200000022-22-2-2-22-2-2220000000000000000002-22-22-2-2200000000000000002-22-20000000000
χ302-22-22-2-2222-2-2-22-2200000022-22-2-2-22-2-222000000000000000000-22-222-2-220000000000000000-22-220000000000
χ312-22-22-2-2222-2-2-22-222i−2i2i−2i0022-22-2-2-2222-2-2002i−2i2i−2i00002i−2i2i−2i00000000-222-200002i−2i2i−2i0000000000000000000000
χ322-22-22-2-2222-2-2-22-22−2i2i−2i2i0022-22-2-2-2222-2-200−2i2i−2i2i0000−2i2i−2i2i00000000-222-20000−2i2i−2i2i0000000000000000000000
χ332-22-2-111-122-2-2-22-222i−2i2i−2i00-1-11-1111-122-2-200−ii−ii−i3i3−i3i32i−2i2i−2i000000001-1-110000−ii−ii−i3i3−i3i3000000003−33−3000000
χ342-22-2-111-122-2-2-22-222i−2i2i−2i00-1-11-1111-122-2-200−ii−iii3−i3i3−i32i−2i2i−2i000000001-1-110000−ii−iii3−i3i3−i300000000−33−33000000
χ352-22-2-111-122-2-2-22-22−2i2i−2i2i00-1-11-1111-122-2-200i−ii−i−i3i3−i3i3−2i2i−2i2i000000001-1-110000i−ii−i−i3i3−i3i300000000−33−33000000
χ362-22-2-111-122-2-2-22-22−2i2i−2i2i00-1-11-1111-122-2-200i−ii−ii3−i3i3−i3−2i2i−2i2i000000001-1-110000i−ii−ii3−i3i3−i3000000003−33−3000000
χ372-2-2222-2-222-2-22-22-200000022-2-222-2-2-22-220000000000000000002i−2i−2i2i2-22-200000000000000002i−2i−2i2i0000000000
χ382-2-2222-2-222-2-22-22-200000022-2-222-2-2-22-22000000000000000000−2i2i2i−2i2-22-20000000000000000−2i2i2i−2i0000000000
χ392-2-2222-2-222-2-22-22-22i−2i−2i2i0022-2-222-2-22-22-2002i−2i−2i2i00002i−2i−2i2i00000000-22-2200002i−2i−2i2i0000000000000000000000
χ402-2-2222-2-222-2-22-22-2−2i2i2i−2i0022-2-222-2-22-22-200−2i2i2i−2i0000−2i2i2i−2i00000000-22-220000−2i2i2i−2i0000000000000000000000
χ412-2-22-1-11122-2-22-22-22i−2i−2i2i00-1-111-1-1112-22-200−iii−i3−3−332i−2i−2i2i000000001-11-10000−iii−i3−3−3300000000i3−i3−i3i3000000
χ422-2-22-1-11122-2-22-22-22i−2i−2i2i00-1-111-1-1112-22-200−iii−i−333−32i−2i−2i2i000000001-11-10000−iii−i−333−300000000−i3i3i3−i3000000
χ432-2-22-1-11122-2-22-22-2−2i2i2i−2i00-1-111-1-1112-22-200i−i−ii3−3−33−2i2i2i−2i000000001-11-10000i−i−ii3−3−3300000000−i3i3i3−i3000000
χ442-2-22-1-11122-2-22-22-2−2i2i2i−2i00-1-111-1-1112-22-200i−i−ii−333−3−2i2i2i−2i000000001-11-10000i−i−ii−333−300000000i3−i3−i3i3000000
χ45444444441-2-211-2-212222441-2-211-21-200000022220000-1-1-1-1111122220000-2-200-1-1-1-100000000-1-1-1-10000000000
χ46444444441-2-211-2-212222-4-41-2-211-21-200000022220000-1-1-1-1-1-1-1-1-2-2-2-200002200-1-1-1-10000000011110000000000
χ47444444441-2-211-2-21-2-2-2-2441-2-211-21-2000000-2-2-2-2000011111111-2-2-2-20000-2-20011110000000011110000000000
χ48444444441-2-211-2-21-2-2-2-2-4-41-2-211-21-2000000-2-2-2-200001111-1-1-1-1222200002200111100000000-1-1-1-10000000000
χ4944444444-211-2-211-2000044-211-2-21-21000022000022220000-2-2-2-20000000011-1-10000-1-1-1-122000000000000-1-100
χ5044444444-211-2-211-2000044-211-2-21-210000-2-20000-2-2-2-20000-2-2-2-200000000111100001111-2-20000000000001100
χ5144444444-211-2-211-20000-4-4-211-2-21-21000022000022220000222200000000-1-1-1-10000-1-1-1-1-2-20000000000001100
χ5244444444-211-2-211-20000-4-4-211-2-21-210000-2-20000-2-2-2-20000222200000000-1-1110000111122000000000000-1-100
χ534444-2-2-2-244444444000000-2-2-2-2-2-2-2-2-4-4-4-400000000000000000000002222000000000000000000000000000000
χ5444-4-44-44-41-2-21-122-122-2-24i−4i1-2-2-1-121200000022-2-20000-1-111ii−i−i2i2i−2i−2i0000−2i2i00-1-11100000000−i−iii0000000000
χ5544-4-44-44-41-2-21-122-122-2-2−4i4i1-2-2-1-121200000022-2-20000-1-111−i−iii−2i−2i2i2i00002i−2i00-1-11100000000ii−i−i0000000000
χ5644-4-44-44-41-2-21-122-1-2-2224i−4i1-2-2-1-1212000000-2-222000011-1-1ii−i−i−2i−2i2i2i0000−2i2i0011-1-100000000ii−i−i0000000000
χ5744-4-44-44-41-2-21-122-1-2-222−4i4i1-2-2-1-1212000000-2-222000011-1-1−i−iii2i2i−2i−2i00002i−2i0011-1-100000000−i−iii0000000000
χ5844-4-44-44-4-211-22-1-1200004i−4i-21122-1-2-100002i−2i00002i2i−2i−2i0000−2i−2i2i2i00000000i−i−ii0000−i−iii2-2000000000000-1100
χ5944-4-44-44-4-211-22-1-1200004i−4i-21122-1-2-10000−2i2i0000−2i−2i2i2i0000−2i−2i2i2i00000000i−ii−i0000ii−i−i-220000000000001-100
χ6044-4-44-44-4-211-22-1-120000−4i4i-21122-1-2-100002i−2i00002i2i−2i−2i00002i2i−2i−2i00000000−ii−ii0000−i−iii-220000000000001-100
χ6144-4-44-44-4-211-22-1-120000−4i4i-21122-1-2-10000−2i2i0000−2i−2i2i2i00002i2i−2i−2i00000000−iii−i0000ii−i−i2-2000000000000-1100
χ6244-4-4-22-224444-4-4-4-4000000-2-2-2222-22-444-4000000000000000000000022-2-2000000000000000000000000000000
χ634-44-44-4-441-22-1-1-2212i−2i2i−2i001-221-12-1-20000002i−2i2i−2i0000−ii−ii3i−3i3i−3i2-22-200000000−ii−ii00000000-11-110000000000
χ644-44-44-4-441-22-1-1-2212i−2i2i−2i001-221-12-1-20000002i−2i2i−2i0000−ii−ii−3i3i−3i3i-22-2200000000−ii−ii000000001-11-10000000000
χ654-44-44-4-441-22-1-1-221−2i2i−2i2i001-221-12-1-2000000−2i2i−2i2i0000i−ii−i3i−3i3i−3i-22-2200000000i−ii−i000000001-11-10000000000
χ664-44-44-4-441-22-1-1-221−2i2i−2i2i001-221-12-1-2000000−2i2i−2i2i0000i−ii−i−3i3i−3i3i2-22-200000000i−ii−i00000000-11-110000000000
χ674-44-4-222-244-4-4-44-44000000-2-22-2222-2-4-4440000000000000000000000-222-2000000000000000000000000000000
χ684-4-4444-4-41-22-112-2-12i−2i−2i2i001-22-11-2-120000002i−2i−2i2i0000−iii−i3-3-33−2i2i2i−2i00000000−iii−i00000000i−i−ii0000000000
χ694-4-4444-4-41-22-112-2-12i−2i−2i2i001-22-11-2-120000002i−2i−2i2i0000−iii−i-333-32i−2i−2i2i00000000−iii−i00000000−iii−i0000000000
χ704-4-4444-4-41-22-112-2-1−2i2i2i−2i001-22-11-2-12000000−2i2i2i−2i0000i−i−ii3-3-332i−2i−2i2i00000000i−i−ii00000000−iii−i0000000000
χ714-4-4444-4-41-22-112-2-1−2i2i2i−2i001-22-11-2-12000000−2i2i2i−2i0000i−i−ii-333-3−2i2i2i−2i00000000i−i−ii00000000i−i−ii0000000000
χ724-4-44-2-22244-4-44-44-4000000-2-222-2-222-44-440000000000000000000000-22-22000000000000000000000000000000
χ738888-4-4-4-42-4-422-4-42444400-122-1-12-12000000-2-2-2-20000-2-2-2-2000000000000000011110000000000000000000000
χ748888-4-4-4-42-4-422-4-42-4-4-4-400-122-1-12-120000002222000022220000000000000000-1-1-1-10000000000000000000000
χ758888-4-4-4-4-422-4-422-40000002-1-122-12-10000440000-2-2-2-2000000000000000000-2-200001111000000000000000000
χ768888-4-4-4-4-422-4-422-40000002-1-122-12-10000-4-400002222000000000000000000220000-1-1-1-1000000000000000000
χ7788-8-8-44-442-4-42-244-244-4-400-12211-2-1-2000000-2-2220000-2-222000000000000000011-1-10000000000000000000000
χ7888-8-8-44-442-4-42-244-2-4-44400-12211-2-1-200000022-2-2000022-2-20000000000000000-1-1110000000000000000000000
χ7988-8-8-44-44-422-44-2-240000002-1-1-2-212100004i−4i0000−2i−2i2i2i000000000000000000−2i2i0000ii−i−i000000000000000000
χ8088-8-8-44-44-422-44-2-240000002-1-1-2-21210000−4i4i00002i2i−2i−2i0000000000000000002i−2i0000−i−iii000000000000000000
χ818-88-88-8-88-42-2442-2-4000000-42-2-44-242000000000000000000000000000000000000000000000000000000000000
χ828-88-8-444-42-44-2-2-4424i−4i4i−4i00-12-2-11-212000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000i−ii−i0000000000000000000000
χ838-88-8-444-42-44-2-2-442−4i4i−4i4i00-12-2-11-2120000002i−2i2i−2i00002i−2i2i−2i0000000000000000−ii−ii0000000000000000000000
χ848-88-8-444-4-42-2442-2-40000002-112-21-2-10000000000−2i32i3−2i32i3000000000000000000000000i3−i3i3−i3000000000000000000
χ858-88-8-444-4-42-2442-2-40000002-112-21-2-100000000002i3−2i32i3−2i3000000000000000000000000−i3i3−i3i3000000000000000000
χ868-8-8888-8-8-42-24-4-224000000-42-24-424-2000000000000000000000000000000000000000000000000000000000000
χ878-8-88-4-4442-44-224-4-24i−4i−4i4i00-12-21-121-2000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000i−i−ii0000000000000000000000
χ888-8-88-4-4442-44-224-4-2−4i4i4i−4i00-12-21-121-20000002i−2i−2i2i00002i−2i−2i2i0000000000000000−iii−i0000000000000000000000
χ898-8-88-4-444-42-24-4-2240000002-11-22-1-21000000000023−23−2323000000000000000000000000−333−3000000000000000000
χ908-8-88-4-444-42-24-4-2240000002-11-22-1-210000000000−232323−230000000000000000000000003−3−33000000000000000000

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