Finite Group Databasebeta

← Group #13165401

Character table — Group #13165401

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222244444444666666888888889999121212121212121212121212121212121212181818181818181824242424242424242424242436363636363636363636363654547272108108
order1222366633666666444444336666662222226666121212121212121212121212444466666666661212121212124444121212121212121244121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1
χ311111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-111
χ71111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
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
χ911-1-111-1-1111-1-1-11-1ii−i−ii−i111-11-1-1-11-1-111-111-1-1ii−i−iii−i−iii−i−i11-1-111-1-11-111-1-1i−iii−i−ii−ii−i11-1-1ii−i−ii−ii−i1-1
χ1011-1-111-1-1111-1-1-11-1ii−i−ii−i111-11-1-1-11-1-11-11-1-111ii−i−iii−i−iii−i−i11-1-111-1-1-11-1-111i−iii−i−i−ii−ii11-1-1−i−iiii−i−ii-11
χ1111-1-111-1-1111-1-1-11-1ii−i−i−ii111-11-1-1-11-1-111-111-1-1ii−i−iii−i−i−i−iii-1-11111-1-11-111-1-1−iiii−i−i−iii−i-1-111ii−i−i−ii−ii-11
χ1211-1-111-1-1111-1-1-11-1ii−i−i−ii111-11-1-1-11-1-11-11-1-111ii−i−iii−i−i−i−iii-1-11111-1-1-11-1-111−iiii−i−ii−i−ii-1-111−i−iii−iii−i1-1
χ1311-1-111-1-1111-1-1-11-1−i−iiii−i111-11-1-1-11-1-111-111-1-1−i−iii−i−iiiii−i−i-1-11111-1-11-111-1-1i−i−i−iiii−i−ii-1-111−i−iiii−ii−i-11
χ1411-1-111-1-1111-1-1-11-1−i−iiii−i111-11-1-1-11-1-11-11-1-111−i−iii−i−iiiii−i−i-1-11111-1-1-11-1-111i−i−i−iii−iii−i-1-111ii−i−ii−i−ii1-1
χ1511-1-111-1-1111-1-1-11-1−i−iii−ii111-11-1-1-11-1-111-111-1-1−i−iii−i−iii−i−iii11-1-111-1-11-111-1-1−ii−i−iii−ii−ii11-1-1−i−iii−ii−ii1-1
χ1611-1-111-1-1111-1-1-11-1−i−iii−ii111-11-1-1-11-1-11-11-1-111−i−iii−i−iii−i−iii11-1-111-1-1-11-1-111−ii−i−iiii−ii−i11-1-1ii−i−i−iii−i-11
χ17222222222222222200002222222222-2-2-2-20000000000000022220000-2-2-2-2000000220000000000000000-2-20000
χ1822222222222222220000-2-222222222-2-2-2-200000000000000-2-2-2-20000-2-2-2-2000000-2-20000000000000000220000
χ192222-1-1-1-122222222222200-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222200000000-1-1-1-122-1-1-1-100-1-1-1-100220000-1-1-1-1000000
χ202222-1-1-1-122222222222200-1-1-1-1-1-1-1-12222-2-21111-1-1-1-1222200000000-1-1-1-1-2-2111100-1-1-1-100-2-200001111000000
χ212222-1-1-1-122222222-2-2-2-200-1-1-1-1-1-1-1-1222222-1-1-1-11111-2-2-2-200000000-1-1-1-122-1-1-1-100111100-2-200001111000000
χ222222-1-1-1-122222222-2-2-2-200-1-1-1-1-1-1-1-12222-2-211111111-2-2-2-200000000-1-1-1-1-2-2111100111100220000-1-1-1-1000000
χ2322-2-222-2-2222-2-2-22-200002i−2i222-22-2-2-2-222-2000000000000002i2i−2i−2i0000-2-2220000002i−2i0000000000000000−2i2i0000
χ2422-2-222-2-2222-2-2-22-20000−2i2i222-22-2-2-2-222-200000000000000−2i−2i2i2i0000-2-222000000−2i2i00000000000000002i−2i0000
χ2522-2-2-1-111222-2-2-22-22i2i−2i−2i00-1-1-11-11112-2-222-2-1-111−i−iii2i2i−2i−2i00000000-1-1112-2-1-11100−i−iii002i−2i0000−i−iii000000
χ2622-2-2-1-111222-2-2-22-22i2i−2i−2i00-1-1-11-11112-2-22-2211-1-1−i−iii2i2i−2i−2i00000000-1-111-2211-1-100−i−iii00−2i2i0000ii−i−i000000
χ2722-2-2-1-111222-2-2-22-2−2i−2i2i2i00-1-1-11-11112-2-222-2-1-111ii−i−i−2i−2i2i2i00000000-1-1112-2-1-11100ii−i−i00−2i2i0000ii−i−i000000
χ2822-2-2-1-111222-2-2-22-2−2i−2i2i2i00-1-1-11-11112-2-22-2211-1-1ii−i−i−2i−2i2i2i00000000-1-111-2211-1-100ii−i−i002i−2i0000−i−iii000000
χ292-22-22-2-2222-22-2-2-2200000022-2-2-22-2222-2-20000000000000000002i−2i2i−2i2-22-200000000000000002i−2i2i−2i0000000000
χ302-22-22-2-2222-22-2-2-2200000022-2-2-22-2222-2-2000000000000000000−2i2i−2i2i2-22-20000000000000000−2i2i−2i2i0000000000
χ312-22-22-2-2222-22-2-2-222-22-20022-2-2-22-22-2-2220000002-22-22-22-200000000-22-22000000002-22-2000000000000000000
χ322-22-22-2-2222-22-2-2-22-22-220022-2-2-22-22-2-222000000-22-22-22-2200000000-22-2200000000-22-22000000000000000000
χ332-22-2-111-122-22-2-2-222-22-200-1-1111-11-1-2-22200−i3i3−i3i3-11-112-22-2000000001-11-100−i3i3−i3i300-11-1100000000−i3i3−i3i3000000
χ342-22-2-111-122-22-2-2-222-22-200-1-1111-11-1-2-22200i3−i3i3−i3-11-112-22-2000000001-11-100i3−i3i3−i300-11-1100000000i3−i3i3−i3000000
χ352-22-2-111-122-22-2-2-22-22-2200-1-1111-11-1-2-22200−i3i3−i3i31-11-1-22-22000000001-11-100−i3i3−i3i3001-11-100000000i3−i3i3−i3000000
χ362-22-2-111-122-22-2-2-22-22-2200-1-1111-11-1-2-22200i3−i3i3−i31-11-1-22-22000000001-11-100i3−i3i3−i3001-11-100000000−i3i3−i3i3000000
χ372-2-222-22-222-2-222-2-200000022-22-2-22-22-22-20000000000000000002i−2i−2i2i2-2-2200000000000000002i−2i−2i2i0000000000
χ382-2-222-22-222-2-222-2-200000022-22-2-22-22-22-2000000000000000000−2i2i2i−2i2-2-220000000000000000−2i2i2i−2i0000000000
χ392-2-222-22-222-2-222-2-22i−2i−2i2i0022-22-2-22-2-22-220000002i−2i−2i2i2i−2i−2i2i00000000-222-2000000002i−2i−2i2i000000000000000000
χ402-2-222-22-222-2-222-2-2−2i2i2i−2i0022-22-2-22-2-22-22000000−2i2i2i−2i−2i2i2i−2i00000000-222-200000000−2i2i2i−2i000000000000000000
χ412-2-22-11-1122-2-222-2-22i−2i−2i2i00-1-11-111-11-22-2200−i3i3i3−i3−iii−i2i−2i−2i2i000000001-1-1100−i3i3i3−i300−iii−i000000003−3−33000000
χ422-2-22-11-1122-2-222-2-22i−2i−2i2i00-1-11-111-11-22-2200i3−i3−i3i3−iii−i2i−2i−2i2i000000001-1-1100i3−i3−i3i300−iii−i00000000−333−3000000
χ432-2-22-11-1122-2-222-2-2−2i2i2i−2i00-1-11-111-11-22-2200−i3i3i3−i3i−i−ii−2i2i2i−2i000000001-1-1100−i3i3i3−i300i−i−ii00000000−333−3000000
χ442-2-22-11-1122-2-222-2-2−2i2i2i−2i00-1-11-111-11-22-2200i3−i3−i3i3i−i−ii−2i2i2i−2i000000001-1-1100i3−i3−i3i300i−i−ii000000003−3−33000000
χ45444444441-2-211-21-22222441-211-2-2-2100000000002222-1-1-1-1111122220000000000-2-2-1-1-1-10000-1-1-1-10000000000
χ46444444441-2-211-21-22222-4-41-211-2-2-2100000000002222-1-1-1-1-1-1-1-1-2-2-2-2000000000022-1-1-1-1000011110000000000
χ47444444441-2-211-21-2-2-2-2-2441-211-2-2-210000000000-2-2-2-211111111-2-2-2-20000000000-2-21111000011110000000000
χ48444444441-2-211-21-2-2-2-2-2-4-41-211-2-2-210000000000-2-2-2-21111-1-1-1-1222200000000002211110000-1-1-1-10000000000
χ4944444444-211-2-21-21000044-21-2-2111-2000022222200000000-2-2-2-200000000-1-1-1-1-1-111000022000000000000-1-100
χ5044444444-211-2-21-21000044-21-2-2111-20000-2-2-2-2-2-200000000-2-2-2-200000000111111110000-2-20000000000001100
χ5144444444-211-2-21-210000-4-4-21-2-2111-2000022222200000000222200000000-1-1-1-1-1-1-1-10000-2-20000000000001100
χ5244444444-211-2-21-210000-4-4-21-2-2111-20000-2-2-2-2-2-200000000222200000000111111-1-1000022000000000000-1-100
χ534444-2-2-2-244444444000000-2-2-2-2-2-2-2-2-4-4-4-400000000000000000000002222000000000000000000000000000000
χ5444-4-444-4-41-2-2-1-12122i2i−2i−2i4i−4i1-21-1-222-100000000002i2i−2i−2i−i−iiiii−i−i22-2-20000000000−2i2i−i−iii0000-1-1110000000000
χ5544-4-444-4-41-2-2-1-12122i2i−2i−2i−4i4i1-21-1-222-100000000002i2i−2i−2i−i−iii−i−iii-2-22200000000002i−2i−i−iii000011-1-10000000000
χ5644-4-444-4-41-2-2-1-1212−2i−2i2i2i4i−4i1-21-1-222-10000000000−2i−2i2i2iii−i−iii−i−i-2-2220000000000−2i2iii−i−i000011-1-10000000000
χ5744-4-444-4-41-2-2-1-1212−2i−2i2i2i−4i4i1-21-1-222-10000000000−2i−2i2i2iii−i−i−i−iii22-2-200000000002i−2iii−i−i0000-1-1110000000000
χ5844-4-444-4-4-21122-1-2-100004i−4i-21-221-1-1200002-222-2-200000000−2i−2i2i2i00000000-11-1-111i−i00002i−2i000000000000−ii00
χ5944-4-444-4-4-21122-1-2-100004i−4i-21-221-1-120000-22-2-22200000000−2i−2i2i2i000000001-111-1-1i−i0000−2i2i000000000000i−i00
χ6044-4-444-4-4-21122-1-2-10000−4i4i-21-221-1-1200002-222-2-2000000002i2i−2i−2i00000000-11-1-111−ii0000−2i2i000000000000i−i00
χ6144-4-444-4-4-21122-1-2-10000−4i4i-21-221-1-120000-22-2-222000000002i2i−2i−2i000000001-111-1-1−ii00002i−2i000000000000−ii00
χ6244-4-4-2-222444-4-4-44-4000000-2-2-22-2222-444-4000000000000000000000022-2-2000000000000000000000000000000
χ634-44-44-4-441-221-12-1-22-22-2001-2-1-12-22100000000002-22-2-11-113i−3i3i−3i2i−2i2i−2i000000000000-11-110000−ii−ii0000000000
χ644-44-44-4-441-221-12-1-22-22-2001-2-1-12-22100000000002-22-2-11-11−3i3i−3i3i−2i2i−2i2i000000000000-11-110000i−ii−i0000000000
χ654-44-44-4-441-221-12-1-2-22-22001-2-1-12-2210000000000-22-221-11-13i−3i3i−3i−2i2i−2i2i0000000000001-11-10000i−ii−i0000000000
χ664-44-44-4-441-221-12-1-2-22-22001-2-1-12-2210000000000-22-221-11-1−3i3i−3i3i2i−2i2i−2i0000000000001-11-10000−ii−ii0000000000
χ674-44-4-222-244-44-4-4-44000000-2-2222-22-244-4-40000000000000000000000-22-22000000000000000000000000000000
χ684-4-444-44-41-22-11-2-122i−2i−2i2i001-2-1122-2-100000000002i−2i−2i2i−iii−i3-3-33−2i2i2i−2i000000000000−iii−i0000i−i−ii0000000000
χ694-4-444-44-41-22-11-2-122i−2i−2i2i001-2-1122-2-100000000002i−2i−2i2i−iii−i-333-32i−2i−2i2i000000000000−iii−i0000−iii−i0000000000
χ704-4-444-44-41-22-11-2-12−2i2i2i−2i001-2-1122-2-10000000000−2i2i2i−2ii−i−ii3-3-332i−2i−2i2i000000000000i−i−ii0000−iii−i0000000000
χ714-4-444-44-41-22-11-2-12−2i2i2i−2i001-2-1122-2-10000000000−2i2i2i−2ii−i−ii-333-3−2i2i2i−2i000000000000i−i−ii0000i−i−ii0000000000
χ724-4-44-22-2244-4-444-4-4000000-2-22-222-224-44-40000000000000000000000-222-2000000000000000000000000000000
χ738888-4-4-4-42-4-422-42-4444400-12-1-1222-10000000000-2-2-2-2-2-2-2-2000000000000000000001111000000000000000000
χ748888-4-4-4-42-4-422-42-4-4-4-4-400-12-1-1222-100000000002222222200000000000000000000-1-1-1-1000000000000000000
χ758888-4-4-4-4-422-4-42-420000002-122-1-1-12000044-2-2-2-200000000000000000000-2-21111000000000000000000000000
χ768888-4-4-4-4-422-4-42-420000002-122-1-1-120000-4-422220000000000000000000022-1-1-1-1000000000000000000000000
χ7788-8-8-4-4442-4-4-2-24244i4i−4i−4i00-12-112-2-210000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000ii−i−i000000000000000000
χ7888-8-8-4-4442-4-4-2-2424−4i−4i4i4i00-12-112-2-2100000000002i2i−2i−2i2i2i−2i−2i00000000000000000000−i−iii000000000000000000
χ7988-8-8-4-444-42244-2-4-20000002-12-2-111-200004-4-2-22200000000000000000000-2211-1-1000000000000000000000000
χ8088-8-8-4-444-42244-2-4-20000002-12-2-111-20000-4422-2-2000000000000000000002-2-1-111000000000000000000000000
χ818-88-88-8-88-42-2-44-242000000-4244-22-2-4000000000000000000000000000000000000000000000000000000000000
χ828-88-8-444-42-442-24-2-44-44-400-1211-22-2-10000000000-22-22-22-22000000000000000000001-11-1000000000000000000
χ838-88-8-444-42-442-24-2-4-44-4400-1211-22-2-100000000002-22-22-22-200000000000000000000-11-11000000000000000000
χ848-88-8-444-4-42-2-44-2420000002-1-2-21-112000000−2i32i3−2i32i30000000000000000000000i3−i3i3−i3000000000000000000000000
χ858-88-8-444-4-42-2-44-2420000002-1-2-21-1120000002i3−2i32i3−2i30000000000000000000000−i3i3−i3i3000000000000000000000000
χ868-8-888-88-8-42-24-424-2000000-424-4-2-224000000000000000000000000000000000000000000000000000000000000
χ878-8-88-44-442-44-22-4-244i−4i−4i4i00-121-1-2-2210000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000i−i−ii000000000000000000
χ888-8-88-44-442-44-22-4-24−4i4i4i−4i00-121-1-2-22100000000002i−2i−2i2i2i−2i−2i2i00000000000000000000−iii−i000000000000000000
χ898-8-88-44-44-42-24-424-20000002-1-2211-1-2000000−2i32i32i3−2i30000000000000000000000i3−i3−i3i3000000000000000000000000
χ908-8-88-44-44-42-24-424-20000002-1-2211-1-20000002i3−2i3−2i32i30000000000000000000000−i3i3i3−i3000000000000000000000000

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