Finite Group Databasebeta

← Group #13165509

Character table — Group #13165509

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222244444444668888888812121212181818181818242424242424242424242424242424242424242427272727363636363636363636365454545472727272
order122236663366666644336666664444448888121212121212121212121212121212121212121244444444121224242424888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1
χ51111111111111111-1-1111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111
χ71111111111111111-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1
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
χ91-1-111-1-1111-1-11-11-1i−i111-1-1-11-1i−i1-1-11ii−i−ii−i1-11-1i−ii−ii−iii−i−i11-1-1ii−i−ii−i1-11-1ii−i−i11-1-11-1i−i
χ101-1-111-1-1111-1-11-11-1i−i111-1-1-11-1i−i-11-11−i−iiii−i-11-11i−ii−ii−iii−i−i-1-111ii−i−i−ii1-11-1−i−iii-1-1111-1−ii
χ111-1-111-1-1111-1-11-11-1i−i111-1-1-11-1−ii1-1-11−i−iii−ii1-11-1i−i−iii−i−i−iii11-1-1ii−i−ii−i-111-1−i−iii-1-111-11i−i
χ121-1-111-1-1111-1-11-11-1i−i111-1-1-11-1−ii-11-11ii−i−i−ii-11-11i−i−iii−i−i−iii-1-111ii−i−i−ii-111-1ii−i−i11-1-1-11−ii
χ131-1-111-1-1111-1-11-11-1−ii111-1-1-11-1i−i1-1-11ii−i−ii−i1-11-1−iii−i−iiii−i−i11-1-1−i−iii−ii-111-1ii−i−i-1-111-11−ii
χ141-1-111-1-1111-1-11-11-1−ii111-1-1-11-1i−i-11-11−i−iiii−i-11-11−iii−i−iiii−i−i-1-111−i−iiii−i-111-1−i−iii11-1-1-11i−i
χ151-1-111-1-1111-1-11-11-1−ii111-1-1-11-1−ii1-1-11−i−iii−ii1-11-1−ii−ii−ii−i−iii11-1-1−i−iii−ii1-11-1−i−iii11-1-11-1−ii
χ161-1-111-1-1111-1-11-11-1−ii111-1-1-11-1−ii-11-11ii−i−i−ii-11-11−ii−ii−ii−i−iii-1-111−i−iiii−i1-11-1ii−i−i-1-1111-1i−i
χ17222222222222222222222222220000-2-2000000000022002200000000-2-2-2-20000-2-2000000000000
χ182222222222222222-2-2222222220000-2-20000000000-2-200-2-20000000022220000-2-2000000000000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-12222222222-1-1-1-122002200-1-1-1-1-1-1-1-100000000-1-1-1-1-1-100000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-222-2-2-2-2-1-111-2-2002200-1-1-1-1111100000000-1-1111100000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-22222-2-2-2-211-1-12200-2-2001111-1-1-1-100000000-1-1111100000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2-2-22222221111-2-200-2-2001111111100000000-1-1-1-1-1-100000000
χ2322-2-222-2-22222-2-2-2-20022-222-2-2-20000002−22−2000000000000000000002-22-20000002−22−22−22−20000
χ2422-2-222-2-22222-2-2-2-20022-222-2-2-20000002−22−200000000000000000000-22-220000002−22−2−22−220000
χ2522-2-222-2-22222-2-2-2-20022-222-2-2-2000000−22−22000000000000000000002-22-2000000−22−22−22−220000
χ2622-2-222-2-22222-2-2-2-20022-222-2-2-2000000−22−2200000000000000000000-22-22000000−22−222−22−20000
χ272-22-22-22-222-2-2-22-220022-2-2-22-22000000i2−i2−i2i2000000000000000000002i−2i−2i2i000000i2−i2−i2i22−2−220000
χ282-22-22-22-222-2-2-22-220022-2-2-22-22000000i2−i2−i2i200000000000000000000−2i2i2i−2i000000i2−i2−i2i2−222−20000
χ292-22-22-22-222-2-2-22-220022-2-2-22-22000000−i2i2i2−i2000000000000000000002i−2i−2i2i000000−i2i2i2−i2−222−20000
χ302-22-22-22-222-2-2-22-220022-2-2-22-22000000−i2i2i2−i200000000000000000000−2i2i2i−2i000000−i2i2i2−i22−2−220000
χ312-2-222-2-2222-2-22-22-22i−2i222-2-2-22-200002-200000000002i−2i002i−2i00000000−2i−2i2i2i0000-22000000000000
χ322-2-222-2-2222-2-22-22-2−2i2i222-2-2-22-200002-20000000000−2i2i00−2i2i000000002i2i−2i−2i0000-22000000000000
χ332-2-22-111-122-2-22-22-200-1-1-1111-112i−2i2-2-222i2i−2i−2i−ii-112-2002i−2i00−i−iii-1-11100000000-11−i−iii00000000
χ342-2-22-111-122-2-22-22-200-1-1-1111-112i−2i-22-22−2i−2i2i2i−ii1-1-22002i−2i00−i−iii11-1-100000000-11ii−i−i00000000
χ352-2-22-111-122-2-22-22-200-1-1-1111-11−2i2i2-2-22−2i−2i2i2ii−i-112-200−2i2i00ii−i−i-1-11100000000-11ii−i−i00000000
χ362-2-22-111-122-2-22-22-200-1-1-1111-11−2i2i-22-222i2i−2i−2ii−i1-1-2200−2i2i00ii−i−i11-1-100000000-11−i−iii00000000
χ37444444441-21-21-2-21441-2-21-211-200220000000022-1-1-2-200110000-1-1-1-100002200000000000000-1-1
χ38444444441-21-21-2-21441-2-21-211-200-2-200000000-2-211-2-20011000011110000-2-20000000000000011
χ39444444441-21-21-2-21-4-41-2-21-211-200220000000022-1-12200-1-10000-1-1-1-10000-2-20000000000000011
χ40444444441-21-21-2-21-4-41-2-21-211-200-2-200000000-2-2112200-1-10000111100002200000000000000-1-1
χ4144444444-21-21-211-244-211-21-2-21220000000022000011-1-1-2-2-1-1-1-10000000000220000000000-1-100
χ4244444444-21-21-211-244-211-21-2-21-2-200000000-2-200001111-2-211110000000000-2-200000000001100
χ4344444444-21-21-211-2-4-4-211-21-2-212200000000220000-1-1-1-122-1-1-1-10000000000-2-200000000001100
χ4444444444-21-21-211-2-4-4-211-21-2-21-2-200000000-2-20000-1-1112211110000000000220000000000-1-100
χ454444-2-2-2-24444444400-2-2-2-2-2-2-2-20000-4-40000000000000000000000000000000022000000000000
χ4644-4-4-2-2224444-4-4-4-400-2-22-2-222200000022−2222−22000000000000000000000000000000−22−2200000000
χ4744-4-4-2-2224444-4-4-4-400-2-22-2-2222000000−2222−22220000000000000000000000000000002−22−200000000
χ484-44-4-22-2244-4-4-44-4400-2-2222-22-20000002i2−2i2−2i22i2000000000000000000000000000000−i2i2i2−i200000000
χ494-44-4-22-2244-4-4-44-4400-2-2222-22-2000000−2i22i22i2−2i2000000000000000000000000000000i2−i2−i2i200000000
χ504-4-444-4-441-2-1212-2-14i−4i1-2-2-12-112002-2000000002-2-11−2i2i00i−i0000-1-11100002i−2i00000000000000−ii
χ514-4-444-4-441-2-1212-2-14i−4i1-2-2-12-11200-2200000000-221-1−2i2i00i−i000011-1-10000−2i2i00000000000000i−i
χ524-4-444-4-441-2-1212-2-1−4i4i1-2-2-12-112002-2000000002-2-112i−2i00−ii0000-1-1110000−2i2i00000000000000i−i
χ534-4-444-4-441-2-1212-2-1−4i4i1-2-2-12-11200-2200000000-221-12i−2i00−ii000011-1-100002i−2i00000000000000−ii
χ544-4-444-4-44-212-1-2-1124i−4i-2112-12-2-12i−2i000000002i−2i0000i−i−ii−2i2i−i−iii00000000002-20000000000-1100
χ554-4-444-4-44-212-1-2-1124i−4i-2112-12-2-1−2i2i00000000−2i2i0000i−ii−i−2i2iii−i−i0000000000-2200000000001-100
χ564-4-444-4-44-212-1-2-112−4i4i-2112-12-2-12i−2i000000002i−2i0000−ii−ii2i−2i−i−iii0000000000-2200000000001-100
χ574-4-444-4-44-212-1-2-112−4i4i-2112-12-2-1−2i2i00000000−2i2i0000−iii−i2i−2iii−i−i00000000002-20000000000-1100
χ584-4-44-222-244-4-44-44-400-2-2-2222-2200004-4000000000000000000000000000000002-2000000000000
χ598888-4-4-4-42-42-42-4-4200-122-12-1-12004400000000-2-2-2-2000000000011110000000000000000000000
χ608888-4-4-4-42-42-42-4-4200-122-12-1-1200-4-40000000022220000000000-1-1-1-10000000000000000000000
χ618888-4-4-4-4-42-42-422-4002-1-12-122-14400000000-2-2000000-2-200111100000000000000000000000000
χ628888-4-4-4-4-42-42-422-4002-1-12-122-1-4-400000000220000002200-1-1-1-100000000000000000000000000
χ6388-8-888-8-82-42-4-244-2002-442-4-2-240000000000000000000000000000000000000000000000000000
χ6488-8-888-8-8-42-424-2-2400-42-2-4244-20000000000000000000000000000000000000000000000000000
χ6588-8-8-4-4442-42-4-244-200-12-2-1211-2000000000000000000000000003i−3i3i−3i0000000000000000000000
χ6688-8-8-4-4442-42-4-244-200-12-2-1211-200000000000000000000000000−3i3i−3i3i0000000000000000000000
χ6788-8-8-4-444-42-424-2-24002-112-1-2-2100000000000000000000003i−3i3i−3i00000000000000000000000000
χ6888-8-8-4-444-42-424-2-24002-112-1-2-210000000000000000000000−3i3i−3i3i00000000000000000000000000
χ698-88-88-88-82-4-24-2-442002-44-242-2-40000000000000000000000000000000000000000000000000000
χ708-88-88-88-8-424-242-2-400-42-24-2-4420000000000000000000000000000000000000000000000000000
χ718-88-8-44-442-4-24-2-44200-12-21-2-112000000000000000000000000003i−3i−3i3i0000000000000000000000
χ728-88-8-44-442-4-24-2-44200-12-21-2-11200000000000000000000000000−3i3i3i−3i0000000000000000000000
χ738-88-8-44-44-424-242-2-4002-11-212-2-100000000000000000000003-3-3300000000000000000000000000
χ748-88-8-44-44-424-242-2-4002-11-212-2-10000000000000000000000-333-300000000000000000000000000
χ758-8-88-444-42-4-2424-4-200-1221-21-1-2004-400000000-22-22000000000011-1-10000000000000000000000
χ768-8-88-444-42-4-2424-4-200-1221-21-1-200-44000000002-22-20000000000-1-1110000000000000000000000
χ778-8-88-444-4-424-2-4-224002-1-1-21-2214i−4i00000000−2i2i000000−2i2i00ii−i−i00000000000000000000000000
χ788-8-88-444-4-424-2-4-224002-1-1-21-221−4i4i000000002i−2i0000002i−2i00−i−iii00000000000000000000000000

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