Finite Group Databasebeta

← Group #13165403

Character table — Group #13165403

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122224444444466888888889999121212121212121212121212181818181818181824242424242424242424242424242424363636363636363654545454545472727272
order1222366633666666443366666622222244666612121212444466666666661212121212121212121244441212121244444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1
χ3111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-111
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ51111111111111111-1-111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ81111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ911-1-111-1-111-11-1-11-1i−i111-11-1-1-11-1-111-1i−i11-1-1ii−i−iii−i−i11-1-11-111-1-1i−ii−ii−iii−i−ii−i1-1ii−i−ii−i11-1-1i−i1-1
χ1011-1-111-1-111-11-1-11-1i−i111-11-1-1-11-1-111-1−ii11-1-1−i−iii−i−iii11-1-11-111-1-1i−ii−i−ii−i−iiii−i-11−i−iiii−i-1-111i−i-11
χ1111-1-111-1-111-11-1-11-1i−i111-11-1-1-11-1-11-11i−i-1-111ii−i−i−i−iii11-1-1-11-1-111i−ii−ii−iii−i−i−ii1-1−i−iiii−i-1-111−ii1-1
χ1211-1-111-1-111-11-1-11-1i−i111-11-1-1-11-1-11-11−ii-1-111−i−iiiii−i−i11-1-1-11-1-111i−ii−i−ii−i−iii−ii-11ii−i−ii−i11-1-1−ii-11
χ1311-1-111-1-111-11-1-11-1−ii111-11-1-1-11-1-111-1i−i11-1-1ii−i−iii−i−i11-1-11-111-1-1−ii−iii−iii−i−i−ii-11ii−i−i−ii-1-111−ii-11
χ1411-1-111-1-111-11-1-11-1−ii111-11-1-1-11-1-111-1−ii11-1-1−i−iii−i−iii11-1-11-111-1-1−ii−ii−ii−i−iii−ii1-1−i−iii−ii11-1-1−ii1-1
χ1511-1-111-1-111-11-1-11-1−ii111-11-1-1-11-1-11-11i−i-1-111ii−i−i−i−iii11-1-1-11-1-111−ii−iii−iii−i−ii−i-11−i−iii−ii11-1-1i−i-11
χ1611-1-111-1-111-11-1-11-1−ii111-11-1-1-11-1-11-11−ii-1-111−i−iiiii−i−i11-1-1-11-1-111−ii−ii−ii−i−iiii−i1-1ii−i−i−ii-1-111i−i1-1
χ1722222222222222222222222222-2-2-2-20000000000000000-2-2-2-2000000222200000000000000-2-200000000
χ182222222222222222-2-222222222-2-2-2-20000000000000000-2-2-2-2000000-2-2-2-2000000000000002200000000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1000022-1-1-1-10000-1-1-1-10000000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-1222222-2-2-1-1-1-11111-2-2-2-2-1-1-1-122-1-1-1-10000-2-21111000011110000000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-12222-2-2221111-1-1-1-1-2-2-2-2-1-1-1-1-2-21111000022-1-1-1-1000011110000000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-12222-2-2-2-2111111112222-1-1-1-1-2-211110000-2-211110000-1-1-1-10000000000
χ2322-2-222-2-222-22-2-22-22i−2i222-22-2-2-2-222-20000000000000000-2-2220000002i−2i2i−2i00000000000000−2i2i00000000
χ2422-2-222-2-222-22-2-22-2−2i2i222-22-2-2-2-222-20000000000000000-2-222000000−2i2i−2i2i000000000000002i−2i00000000
χ2522-2-2-1-11122-22-2-22-200-1-1-11-11112-2-222-22i−2i-1-111−i−iii2i2i−2i−2i-1-1112-2-1-11100002i−2i−i−iii0000−i−iii0000000000
χ2622-2-2-1-11122-22-2-22-200-1-1-11-11112-2-222-2−2i2i-1-111ii−i−i−2i−2i2i2i-1-1112-2-1-1110000−2i2iii−i−i0000ii−i−i0000000000
χ2722-2-2-1-11122-22-2-22-200-1-1-11-11112-2-22-222i−2i11-1-1−i−iii−2i−2i2i2i-1-111-2211-1-100002i−2i−i−iii0000ii−i−i0000000000
χ2822-2-2-1-11122-22-2-22-200-1-1-11-11112-2-22-22−2i2i11-1-1ii−i−i2i2i−2i−2i-1-111-2211-1-10000−2i2iii−i−i0000−i−iii0000000000
χ292-22-22-22-2222-2-2-2-220022-22-22-2-22-22-200000000000000002-2-22000000000000000000000000002i−2i2i−2i0000
χ302-22-22-22-2222-2-2-2-220022-22-22-2-22-22-200000000000000002-2-2200000000000000000000000000−2i2i−2i2i0000
χ312-22-22-22-2222-2-2-2-220022-22-22-2-2-22-220000000000002i−2i2i−2i-222-2000000000000000000002i−2i2i−2i0000000000
χ322-22-22-22-2222-2-2-2-220022-22-22-2-2-22-22000000000000−2i2i−2i2i-222-200000000000000000000−2i2i−2i2i0000000000
χ332-22-2-11-11222-2-2-2-2200-1-11-11-111-22-220000−i3i3−i3i33−33−32i−2i2i−2i1-1-1100−i3i3−i3i30000003−33−30000−ii−ii0000000000
χ342-22-2-11-11222-2-2-2-2200-1-11-11-111-22-220000−i3i3−i3i3−33−33−2i2i−2i2i1-1-1100−i3i3−i3i3000000−33−330000i−ii−i0000000000
χ352-22-2-11-11222-2-2-2-2200-1-11-11-111-22-220000i3−i3i3−i33−33−3−2i2i−2i2i1-1-1100i3−i3i3−i30000003−33−30000i−ii−i0000000000
χ362-22-2-11-11222-2-2-2-2200-1-11-11-111-22-220000i3−i3i3−i3−33−332i−2i2i−2i1-1-1100i3−i3i3−i3000000−33−330000−ii−ii0000000000
χ372-2-222-2-2222-2-222-2-20022-2-2-2-22222-2-200000000000000002-22-2000000000000000000000000002i−2i−2i2i0000
χ382-2-222-2-2222-2-222-2-20022-2-2-2-22222-2-200000000000000002-22-200000000000000000000000000−2i2i2i−2i0000
χ392-2-222-2-2222-2-222-2-20022-2-2-2-222-2-2220000000000002-2-22-22-22000000000000000000002-2-220000000000
χ402-2-222-2-2222-2-222-2-20022-2-2-2-222-2-222000000000000-222-2-22-2200000000000000000000-222-20000000000
χ412-2-22-111-122-2-222-2-200-1-11111-1-1-2-2220000−i3i3i3−i3−i3i3i3−i32-2-221-11-100−i3i3i3−i3000000−i3i3i3−i30000-111-10000000000
χ422-2-22-111-122-2-222-2-200-1-11111-1-1-2-2220000−i3i3i3−i3i3−i3−i3i3-222-21-11-100−i3i3i3−i3000000i3−i3−i3i300001-1-110000000000
χ432-2-22-111-122-2-222-2-200-1-11111-1-1-2-2220000i3−i3−i3i3−i3i3i3−i3-222-21-11-100i3−i3−i3i3000000−i3i3i3−i300001-1-110000000000
χ442-2-22-111-122-2-222-2-200-1-11111-1-1-2-2220000i3−i3−i3i3i3−i3−i3i32-2-221-11-100i3−i3−i3i3000000i3−i3−i3i30000-111-10000000000
χ45444444441-21-2-211-2441-211-2-2-21000000220000222200000000000000-2-211-1-1-1-1-1-10022000000000000-1-1
χ46444444441-21-2-211-2441-211-2-2-21000000-2-20000-2-2-2-200000000000000-2-21111111100-2-200000000000011
χ47444444441-21-2-211-2-4-41-211-2-2-2100000022000022220000000000000022-1-1-1-1-1-1-1-100-2-200000000000011
χ48444444441-21-2-211-2-4-41-211-2-2-21000000-2-20000-2-2-2-20000000000000022-1-11111110022000000000000-1-1
χ4944444444-21-211-2-2144-21-2-2111-2000022002222000000000000-1-1-1-1-1-111-2-200000022000000000000-1-100
χ5044444444-21-211-2-2144-21-2-2111-20000-2-200-2-2-2-200000000000011111111-2-2000000-2-20000000000001100
χ5144444444-21-211-2-21-4-4-21-2-2111-2000022002222000000000000-1-1-1-1-1-1-1-122000000-2-20000000000001100
χ5244444444-21-211-2-21-4-4-21-2-2111-20000-2-200-2-2-2-2000000000000111111-1-12200000022000000000000-1-100
χ534444-2-2-2-24444444400-2-2-2-2-2-2-2-2-4-4-4-4000000000000000022220000000000000000000000000000000000
χ5444-4-444-4-41-2-1-22-1124i−4i1-21-1-222-10000002i−2i00002i2i−2i−2i00000000000000−2i2ii−i−ii−i−iii002-2000000000000-11
χ5544-4-444-4-41-2-1-22-1124i−4i1-21-1-222-1000000−2i2i0000−2i−2i2i2i00000000000000−2i2ii−ii−iii−i−i00-220000000000001-1
χ5644-4-444-4-41-2-1-22-112−4i4i1-21-1-222-10000002i−2i00002i2i−2i−2i000000000000002i−2i−ii−ii−i−iii00-220000000000001-1
χ5744-4-444-4-41-2-1-22-112−4i4i1-21-1-222-1000000−2i2i0000−2i−2i2i2i000000000000002i−2i−iii−iii−i−i002-2000000000000-11
χ5844-4-444-4-4-2121-12-2-14i−4i-21-221-1-1200002-20022-2-2000000000000-11-1-111i−i−2i2i0000002i−2i000000000000−ii00
χ5944-4-444-4-4-2121-12-2-14i−4i-21-221-1-120000-2200-2-2220000000000001-111-1-1i−i−2i2i000000−2i2i000000000000i−i00
χ6044-4-444-4-4-2121-12-2-1−4i4i-21-221-1-1200002-20022-2-2000000000000-11-1-111−ii2i−2i000000−2i2i000000000000i−i00
χ6144-4-444-4-4-2121-12-2-1−4i4i-21-221-1-120000-2200-2-2220000000000001-111-1-1−ii2i−2i0000002i−2i000000000000−ii00
χ6244-4-4-2-22244-44-4-44-400-2-2-22-2222-444-4000000000000000022-2-20000000000000000000000000000000000
χ634-44-4-22-22444-4-4-4-4400-2-22-22-2224-44-40000000000000000-222-20000000000000000000000000000000000
χ644-4-44-222-244-4-444-4-400-2-22222-2-244-4-40000000000000000-22-220000000000000000000000000000000000
χ658888-4-4-4-42-42-4-422-400-12-1-1222-1000000440000-2-2-2-2000000000000000000-2-21111000000000000000000
χ668888-4-4-4-42-42-4-422-400-12-1-1222-1000000-4-40000222200000000000000000022-1-1-1-1000000000000000000
χ678888-4-4-4-4-42-422-4-42002-122-1-1-1200004400-2-2-2-2000000000000-2-211110000000000000000000000000000
χ688888-4-4-4-4-42-422-4-42002-122-1-1-120000-4-400222200000000000022-1-1-1-10000000000000000000000000000
χ6988-8-8-4-4442-4-2-44-22400-12-112-2-210000004i−4i0000−2i−2i2i2i000000000000000000−2i2iii−i−i000000000000000000
χ7088-8-8-4-4442-4-2-44-22400-12-112-2-21000000−4i4i00002i2i−2i−2i0000000000000000002i−2i−i−iii000000000000000000
χ7188-8-8-4-444-4242-24-4-2002-12-2-111-200004-400-2-222000000000000-2211-1-10000000000000000000000000000
χ7288-8-8-4-444-4242-24-4-2002-12-2-111-20000-440022-2-20000000000002-2-1-1110000000000000000000000000000
χ738-88-88-88-82-4244-2-2-4002-4-224-44-20000000000000000000000000000000000000000000000000000000000
χ748-88-88-88-8-42-4-2-244200-424-4-22-240000000000000000000000000000000000000000000000000000000000
χ758-88-8-44-442-4244-2-2-400-121-1-22-2100000000000023−2323−2300000000000000000000−33−33000000000000000000
χ768-88-8-44-442-4244-2-2-400-121-1-22-21000000000000−2323−2323000000000000000000003−33−3000000000000000000
χ778-88-8-44-44-42-4-2-2442002-1-221-11-200000000−2i32i3−2i32i300000000000000i3−i3i3−i30000000000000000000000000000
χ788-88-8-44-44-42-4-2-2442002-1-221-11-2000000002i3−2i32i3−2i300000000000000−i3i3−i3i30000000000000000000000000000
χ798-8-888-8-882-4-24-42-24002-4-2-244-420000000000000000000000000000000000000000000000000000000000
χ808-8-888-8-88-424-22-44-200-4244-2-22-40000000000000000000000000000000000000000000000000000000000
χ818-8-88-444-42-4-24-42-2400-1211-2-22-1000000000000−2i32i32i3−2i300000000000000000000i3−i3−i3i3000000000000000000
χ828-8-88-444-42-4-24-42-2400-1211-2-22-10000000000002i3−2i3−2i32i300000000000000000000−i3i3i3−i3000000000000000000
χ838-8-88-444-4-424-22-44-2002-1-2-211-1200000000−2i32i32i3−2i300000000000000i3−i3−i3i30000000000000000000000000000
χ848-8-88-444-4-424-22-44-2002-1-2-211-12000000002i3−2i3−2i32i300000000000000−i3i3i3−i30000000000000000000000000000

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