Finite Group Databasebeta

← Group #13165496

Character table — Group #13165496

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222244444444668888888812121212181818181818242424242424242424242424242424242424242427272727363636363636363636365454545472727272
order12223666336666664433666666444444888812121212121212121212121212121212121212124444222212122424242488886666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-111-1-1111111-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1
χ51111111111111111-1-11111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ71111111111111111-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1111111-1-1
χ81111111111111111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ91-11-11-11-11111-1-1-1-1i−i1111-1-1-1-1i−ii−i1-111-1-1i−ii−iii−i−ii−ii−iii−i−iii−i−iii−i−i1-11-1-1111-1-1ii−i−i1-11-1
χ101-11-11-11-11111-1-1-1-1i−i1111-1-1-1-1i−i−ii1-1-1-111i−i−iiii−i−ii−i−iiii−i−i−i−iiiii−i−i1-1-11-11-1-111−i−iii1-1-11
χ111-11-11-11-11111-1-1-1-1i−i1111-1-1-1-1−iii−i1-1-1-111−iii−iii−i−i−iii−i−i−iiiii−i−iii−i−i-111-1-11-1-111−i−iii-111-1
χ121-11-11-11-11111-1-1-1-1i−i1111-1-1-1-1−ii−ii1-111-1-1−ii−iiii−i−i−ii−ii−i−iii−i−iiiii−i−i-11-11-1111-1-1ii−i−i-11-11
χ131-11-11-11-11111-1-1-1-1−ii1111-1-1-1-1i−ii−i1-111-1-1i−ii−i−i−iiii−ii−iii−i−iii−i−i−i−iii-11-11-1111-1-1−i−iii-11-11
χ141-11-11-11-11111-1-1-1-1−ii1111-1-1-1-1i−i−ii1-1-1-111i−i−ii−i−iiii−i−iiii−i−i−i−iii−i−iii-111-1-11-1-111ii−i−i-111-1
χ151-11-11-11-11111-1-1-1-1−ii1111-1-1-1-1−iii−i1-1-1-111−iii−i−i−iii−iii−i−i−iiiii−i−i−i−iii1-1-11-11-1-111ii−i−i1-1-11
χ161-11-11-11-11111-1-1-1-1−ii1111-1-1-1-1−ii−ii1-111-1-1−ii−ii−i−iii−ii−ii−i−iii−i−iii−i−iii1-11-1-1111-1-1−i−iii1-11-1
χ17222222222222222222222222220000-2-2000000002222000000000000-2-2-2-20000-2-2000000000000
χ182222222222222222-2-2222222220000-2-200000000-2-2-2-200000000000022220000-2-2000000000000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-12222222222-1-1-1-100002222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-100000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-222-2-2-2-2-1-111000022-2-2-1-1-1-1111100000000-1-1111100000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-22222-2-2-2-211-1-10000-2-2221111-1-1-1-100000000-1-1111100000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2-2-222222211110000-2-2-2-21111111100000000-1-1-1-1-1-100000000
χ2322-2-222-2-222-2-222-2-20022-2-222-2-20000002−22−2000000000000000000002i−2i2i−2i0000002−22−2i2−i2i2−i20000
χ2422-2-222-2-222-2-222-2-20022-2-222-2-20000002−22−200000000000000000000−2i2i−2i2i0000002−22−2−i2i2−i2i20000
χ2522-2-222-2-222-2-222-2-20022-2-222-2-2000000−22−22000000000000000000002i−2i2i−2i000000−22−22−i2i2−i2i20000
χ2622-2-222-2-222-2-222-2-20022-2-222-2-2000000−22−2200000000000000000000−2i2i−2i2i000000−22−22i2−i2i2−i20000
χ272-22-22-22-22222-2-2-2-22i−2i2222-2-2-2-20000-22000000002i2i−2i−2i000000000000−2i−2i2i2i00002-2000000000000
χ282-22-22-22-22222-2-2-2-2−2i2i2222-2-2-2-20000-2200000000−2i−2i2i2i0000000000002i2i−2i−2i00002-2000000000000
χ292-22-2-11-112222-2-2-2-200-1-1-1-111112i−2i2i−2i2-222-2-2−ii−ii00002i−2i2i−2i−i−iii−i−iii000000001-1-1-11100000000
χ302-22-2-11-112222-2-2-2-200-1-1-1-111112i−2i−2i2i2-2-2-222−iii−i00002i−2i−2i2i−i−iiiii−i−i000000001-111-1-100000000
χ312-22-2-11-112222-2-2-2-200-1-1-1-11111−2i2i2i−2i2-2-2-222i−i−ii0000−2i2i2i−2iii−i−i−i−iii000000001-111-1-100000000
χ322-22-2-11-112222-2-2-2-200-1-1-1-11111−2i2i−2i2i2-222-2-2i−ii−i0000−2i2i−2i2iii−i−iii−i−i000000001-1-1-11100000000
χ332-2-222-2-2222-2-2-2-2220022-2-2-2-2220000002−2−22000000000000000000002-2-220000002−2−222−2−220000
χ342-2-222-2-2222-2-2-2-2220022-2-2-2-2220000002−2−2200000000000000000000-222-20000002−2−22−222−20000
χ352-2-222-2-2222-2-2-2-2220022-2-2-2-222000000−222−2000000000000000000002-2-22000000−222−2−222−20000
χ362-2-222-2-2222-2-2-2-2220022-2-2-2-222000000−222−200000000000000000000-222-2000000−222−22−2−220000
χ37444444441-21-21-21-2441-21-21-21-2002200000000221-21-200-1-10000-1-1-1-100000022000000000000-1-1
χ38444444441-21-21-21-2441-21-21-21-200-2-200000000-2-21-21-2001100001111000000-2-200000000000011
χ39444444441-21-21-21-2-4-41-21-21-21-200220000000022-12-1200-1-10000-1-1-1-1000000-2-200000000000011
χ40444444441-21-21-21-2-4-41-21-21-21-200-2-200000000-2-2-12-1200110000111100000022000000000000-1-1
χ4144444444-21-21-21-2144-21-21-21-2122000000002200-21-21-1-100-1-1-1-10000000022000000000000-1-100
χ4244444444-21-21-21-2144-21-21-21-21-2-200000000-2-200-21-211100111100000000-2-20000000000001100
χ4344444444-21-21-21-21-4-4-21-21-21-21220000000022002-12-1-1-100-1-1-1-100000000-2-20000000000001100
χ4444444444-21-21-21-21-4-4-21-21-21-21-2-200000000-2-2002-12-1110011110000000022000000000000-1-100
χ454444-2-2-2-24444444400-2-2-2-2-2-2-2-20000-4-40000000000000000000000000000000022000000000000
χ4644-4-4-2-22244-4-444-4-400-2-222-2-22200000022−2222−22000000000000000000000000000000−22−2200000000
χ4744-4-4-2-22244-4-444-4-400-2-222-2-222000000−2222−22220000000000000000000000000000002−22−200000000
χ484-44-44-44-41-21-2-12-124i−4i1-21-2-12-12002i−2i000000002i−2ii−2i−i2i00−ii0000−i−iii0000002-2000000000000-11
χ494-44-44-44-41-21-2-12-124i−4i1-21-2-12-1200−2i2i00000000−2i2ii−2i−i2i00i−i0000ii−i−i000000-220000000000001-1
χ504-44-44-44-41-21-2-12-12−4i4i1-21-2-12-12002i−2i000000002i−2i−i2ii−2i00−ii0000−i−iii000000-220000000000001-1
χ514-44-44-44-41-21-2-12-12−4i4i1-21-2-12-1200−2i2i00000000−2i2i−i2ii−2i00i−i0000ii−i−i0000002-2000000000000-11
χ524-44-44-44-4-21-212-12-14i−4i-21-212-12-12i−2i000000002i−2i00−2ii2i−i−ii00−i−iii000000002-2000000000000-1100
χ534-44-44-44-4-21-212-12-14i−4i-21-212-12-1−2i2i00000000−2i2i00−2ii2i−ii−i00ii−i−i00000000-220000000000001-100
χ544-44-44-44-4-21-212-12-1−4i4i-21-212-12-12i−2i000000002i−2i002i−i−2ii−ii00−i−iii00000000-220000000000001-100
χ554-44-44-44-4-21-212-12-1−4i4i-21-212-12-1−2i2i00000000−2i2i002i−i−2iii−i00ii−i−i000000002-2000000000000-1100
χ564-44-4-22-224444-4-4-4-400-2-2-2-222220000-4400000000000000000000000000000000-22000000000000
χ574-4-44-222-244-4-4-4-44400-2-22222-2-200000022−22−2222000000000000000000000000000000−222−200000000
χ584-4-44-222-244-4-4-4-44400-2-22222-2-2000000−222222−220000000000000000000000000000002−2−2200000000
χ598888-4-4-4-42-42-42-42-400-12-12-12-12004400000000-2-2000000-2-2000011110000000000000000000000
χ608888-4-4-4-42-42-42-42-400-12-12-12-1200-4-40000000022000000220000-1-1-1-10000000000000000000000
χ618888-4-4-4-4-42-42-42-42002-12-12-12-14400000000-2-2000000-2-200111100000000000000000000000000
χ628888-4-4-4-4-42-42-42-42002-12-12-12-1-4-400000000220000002200-1-1-1-100000000000000000000000000
χ6388-8-888-8-82-4-242-4-24002-4-242-4-240000000000000000000000000000000000000000000000000000
χ6488-8-888-8-8-424-2-424-200-424-2-424-20000000000000000000000000000000000000000000000000000
χ6588-8-8-4-4442-4-242-4-2400-121-2-121-2000000000000000000000000003i−3i3i−3i0000000000000000000000
χ6688-8-8-4-4442-4-242-4-2400-121-2-121-200000000000000000000000000−3i3i−3i3i0000000000000000000000
χ6788-8-8-4-444-424-2-424-2002-1-212-1-2100000000000000000000003i−3i3i−3i00000000000000000000000000
χ6888-8-8-4-444-424-2-424-2002-1-212-1-210000000000000000000000−3i3i−3i3i00000000000000000000000000
χ698-88-8-44-442-42-4-24-2400-12-121-21-2004i−4i00000000−2i2i000000−2i2i0000ii−i−i0000000000000000000000
χ708-88-8-44-442-42-4-24-2400-12-121-21-200−4i4i000000002i−2i0000002i−2i0000−i−iii0000000000000000000000
χ718-88-8-44-44-42-424-24-2002-12-1-21-214i−4i00000000−2i2i000000−2i2i00ii−i−i00000000000000000000000000
χ728-88-8-44-44-42-424-24-2002-12-1-21-21−4i4i000000002i−2i0000002i−2i00−i−iii00000000000000000000000000
χ738-8-888-8-882-4-24-242-4002-4-24-242-40000000000000000000000000000000000000000000000000000
χ748-8-888-8-88-424-24-2-4200-424-24-2-420000000000000000000000000000000000000000000000000000
χ758-8-88-444-42-4-24-242-400-121-21-2-12000000000000000000000000003-3-330000000000000000000000
χ768-8-88-444-42-4-24-242-400-121-21-2-1200000000000000000000000000-333-30000000000000000000000
χ778-8-88-444-4-424-24-2-42002-1-21-212-100000000000000000000003-3-3300000000000000000000000000
χ788-8-88-444-4-424-24-2-42002-1-21-212-10000000000000000000000-333-300000000000000000000000000

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