Finite Group Databasebeta

← Group #13165513

Character table — Group #13165513

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444466888888881212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363654547272108108
order12223666336666664433666666224466661212121244666666121212121212121212124444881212121212122424242444121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111111111111111-1-111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-11111111111-1-111-1-11-1-1-1-11-1-1-1-11111-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111
χ51111111111111111-1-11111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-11-1-1-1-1-1-11111
χ71111111111111111-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1
χ911-1-11-1-1111-11-1-11-1i−i111-11-1-1-11-1i−i11-1-1ii−i−i-111-111-1-1i−ii−ii−iii−i−ii−i1-1i−i1ii−i−i-1ii−i−ii−i1-11-1
χ1011-1-11-1-1111-11-1-11-1i−i111-11-1-1-11-1−ii11-1-1ii−i−i-111-111-1-1−iii−i−ii−i−iiii−i-11−ii1ii−i−i-1−i−iiii−i-11-11
χ1111-1-11-1-1111-11-1-11-1i−i111-11-1-1-1-11i−i-1-111ii−i−i-11-11-1-111i−ii−ii−iii−i−i−ii1-1−ii1−i−iii-1−i−iiii−i1-1-11
χ1211-1-11-1-1111-11-1-11-1i−i111-11-1-1-1-11−ii-1-111ii−i−i-11-11-1-111−iii−i−ii−i−iii−ii-11i−i1−i−iii-1ii−i−ii−i-111-1
χ1311-1-11-1-1111-11-1-11-1−ii111-11-1-1-11-1i−i11-1-1−i−iii-111-111-1-1i−i−iii−iii−i−i−ii-11i−i1−i−iii-1ii−i−i−ii-11-11
χ1411-1-11-1-1111-11-1-11-1−ii111-11-1-1-11-1−ii11-1-1−i−iii-111-111-1-1−ii−ii−ii−i−iii−ii1-1−ii1−i−iii-1−i−iii−ii1-11-1
χ1511-1-11-1-1111-11-1-11-1−ii111-11-1-1-1-11i−i-1-111−i−iii-11-11-1-111i−i−iii−iii−i−ii−i-11−ii1ii−i−i-1−i−iii−ii-111-1
χ1611-1-11-1-1111-11-1-11-1−ii111-11-1-1-1-11−ii-1-111−i−iii-11-11-1-111−ii−ii−ii−i−iiii−i1-1i−i1ii−i−i-1ii−i−i−ii1-1-11
χ1722222222222222222222222222000000002222-2-20000000022000000000000-20000-20000-2-20000
χ182222222222222222-2-22222222200000000-2-2-2-2-2-200000000-2-2000000000000-20000-20000220000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122222222000022-1-1-1-1-1-1-1-10022-1-1-1-1000022-10000-1-1-1-1-1000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-22222000022-1-1-1-1-1-11100-2-211110000-2-2-10000-11111000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-222-2-2-2-2000022111111-1-10022-1-1-1-10000-2-2-10000-11111000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-20000221111111100-2-21111000022-10000-1-1-1-1-1000000
χ2322-2-22-2-2222-22-2-22-22i−2i222-22-2-2-2000000002i2i−2i−2i2-2000000002i−2i000000000000-2000020000−2i2i0000
χ2422-2-22-2-2222-22-2-22-2−2i2i222-22-2-2-200000000−2i−2i2i2i2-200000000−2i2i000000000000-20000200002i−2i0000
χ2522-2-2-111-122-22-2-22-200-1-1-11-11112-22i−2i22-2-20000-22-11-1-111−ii002i−2i−i−iii00002i−2i-100001−i−iii000000
χ2622-2-2-111-122-22-2-22-200-1-1-11-11112-2−2i2i22-2-20000-22-11-1-111i−i00−2i2iii−i−i0000−2i2i-100001ii−i−i000000
χ2722-2-2-111-122-22-2-22-200-1-1-11-1111-222i−2i-2-2220000-221-111-1-1−ii002i−2i−i−iii0000−2i2i-100001ii−i−i000000
χ2822-2-2-111-122-22-2-22-200-1-1-11-1111-22−2i2i-2-2220000-221-111-1-1i−i00−2i2iii−i−i00002i−2i-100001−i−iii000000
χ29444444441-21-2-211-2441-211-2-2-2100220000-2-2-2-2000000002211-1-1-1-1-1-1002200000000000000-1-100
χ30444444441-21-2-211-2441-211-2-2-2100-2-20000-2-2-2-200000000-2-21111111100-2-2000000000000001100
χ31444444441-21-2-211-2-4-41-211-2-2-210022000022220000000022-1-1-1-1-1-1-1-100-2-2000000000000001100
χ32444444441-21-2-211-2-4-41-211-2-2-2100-2-20000222200000000-2-2-1-1111111002200000000000000-1-100
χ3344444444-21-211-2-2144-21-2-2111-22200-1-1-1-111110022-1-1-1-100-2-20000002200000-1-1-1-100000000000
χ3444444444-21-211-2-2144-21-2-2111-2-2-2001111111100-2-2111100-2-2000000-2-200000111100000000000
χ3544444444-21-211-2-21-4-4-21-2-2111-22200-1-1-1-1-1-1-1-10022-1-1-1-10022000000-2-200000111100000000000
χ3644444444-21-211-2-21-4-4-21-2-2111-2-2-2001111-1-1-1-100-2-2111100220000002200000-1-1-1-100000000000
χ374444-2-2-2-24444444400-2-2-2-2-2-2-2-2000000000000-4-400000000000000000000002000020000000000
χ3844-4-44-4-441-2-1-22-1124i−4i1-21-1-222-1002i−2i0000−2i−2i2i2i000000002i−2ii−i−ii−i−iii002-200000000000000-1100
χ3944-4-44-4-441-2-1-22-1124i−4i1-21-1-222-100−2i2i0000−2i−2i2i2i00000000−2i2ii−ii−iii−i−i00-22000000000000001-100
χ4044-4-44-4-441-2-1-22-112−4i4i1-21-1-222-1002i−2i00002i2i−2i−2i000000002i−2i−ii−ii−i−iii00-22000000000000001-100
χ4144-4-44-4-441-2-1-22-112−4i4i1-21-1-222-100−2i2i00002i2i−2i−2i00000000−2i2i−iii−iii−i−i002-200000000000000-1100
χ4244-4-44-4-44-2121-12-2-14i−4i-21-221-1-122-200-1-111ii−i−i002-2-1-11100−2i2i0000002i−2i00000−i−iii00000000000
χ4344-4-44-4-44-2121-12-2-14i−4i-21-221-1-12-220011-1-1ii−i−i00-2211-1-100−2i2i000000−2i2i00000ii−i−i00000000000
χ4444-4-44-4-44-2121-12-2-1−4i4i-21-221-1-122-200-1-111−i−iii002-2-1-111002i−2i000000−2i2i00000ii−i−i00000000000
χ4544-4-44-4-44-2121-12-2-1−4i4i-21-221-1-12-220011-1-1−i−iii00-2211-1-1002i−2i0000002i−2i00000−i−iii00000000000
χ4644-4-4-222-244-44-4-44-400-2-2-22-22220000000000004-4000000000000000000000020000-20000000000
χ474-44-444-4-4444-44-4-4-40044-44-44-4-40000000000000000000000000000000000000000000000000000
χ484-44-444-4-4-21-2-1122-100-212-2-11-120000−i3i3−i3i33i−3i3i−3i0000−i3i3−i3i3000000000000000003−33−300000000000
χ494-44-444-4-4-21-2-1122-100-212-2-11-120000−i3i3−i3i3−3i3i−3i3i0000−i3i3−i3i300000000000000000−33−3300000000000
χ504-44-444-4-4-21-2-1122-100-212-2-11-120000i3−i3i3−i33i−3i3i−3i0000i3−i3i3−i300000000000000000−33−3300000000000
χ514-44-444-4-4-21-2-1122-100-212-2-11-120000i3−i3i3−i3−3i3i−3i3i0000i3−i3i3−i3000000000000000003−33−300000000000
χ524-44-4-2-222444-44-4-4-400-2-22-22-2220000000000000000000000000000000000000000006−66−6000000
χ534-44-4-2-222444-44-4-4-400-2-22-22-222000000000000000000000000000000000000000000−66−66000000
χ544-4-444-44-444-4-4-44-440044-4-4-4-4440000000000000000000000000000000000000000000000000000
χ554-4-444-44-4-212-1-1-22100-2122-1-11-20000−i3i3i3−i33-3-330000−i3i3i3−i300000000000000000−i3i3i3−i300000000000
χ564-4-444-44-4-212-1-1-22100-2122-1-11-20000−i3i3i3−i3-333-30000−i3i3i3−i300000000000000000i3−i3−i3i300000000000
χ574-4-444-44-4-212-1-1-22100-2122-1-11-20000i3−i3−i3i33-3-330000i3−i3−i3i300000000000000000i3−i3−i3i300000000000
χ584-4-444-44-4-212-1-1-22100-2122-1-11-20000i3−i3−i3i3-333-30000i3−i3−i3i300000000000000000−i3i3i3−i300000000000
χ594-4-44-22-2244-4-4-44-4400-2-22222-2-2000000000000000000000000000000000000000000i6−i6−i6i6000000
χ604-4-44-22-2244-4-4-44-4400-2-22222-2-2000000000000000000000000000000000000000000−i6i6i6−i6000000
χ618888-4-4-4-42-42-4-422-400-12-1-1222-100440000000000000000-2-200-2-211110000000000000000000000
χ628888-4-4-4-42-42-4-422-400-12-1-1222-100-4-40000000000000000220022-1-1-1-10000000000000000000000
χ638888-4-4-4-4-42-422-4-42002-122-1-1-124400-2-2-2-2000000-2-2111100000000000000000000000000000000
χ648888-4-4-4-4-42-422-4-42002-122-1-1-12-4-400222200000022-1-1-1-100000000000000000000000000000000
χ6588-8-8-444-42-4-2-44-22400-12-112-2-21004i−4i0000000000000000−2i2i00−2i2iii−i−i0000000000000000000000
χ6688-8-8-444-42-4-2-44-22400-12-112-2-2100−4i4i00000000000000002i−2i002i−2i−i−iii0000000000000000000000
χ6788-8-8-444-4-4242-24-4-2002-12-2-111-24-400-2-222000000-2211-1-100000000000000000000000000000000
χ6888-8-8-444-4-4242-24-4-2002-12-2-111-2-440022-2-20000002-2-1-11100000000000000000000000000000000
χ698-88-888-8-82-424-4-2-24002-4-224-44-20000000000000000000000000000000000000000000000000000
χ708-88-8-4-4442-424-4-2-2400-121-1-22-21000000000000000000000000003i−3i3i−3i0000000000000000000000
χ718-88-8-4-4442-424-4-2-2400-121-1-22-2100000000000000000000000000−3i3i−3i3i0000000000000000000000
χ728-88-8-4-444-42-4-2244-2002-1-221-11-20000−2i32i3−2i32i300000000i3−i3i3−i300000000000000000000000000000000
χ738-88-8-4-444-42-4-2244-2002-1-221-11-200002i3−2i32i3−2i300000000−i3i3−i3i300000000000000000000000000000000
χ748-8-888-88-82-4-2442-2-4002-4-2-244-420000000000000000000000000000000000000000000000000000
χ758-8-88-44-442-4-2442-2-400-1211-2-22-1000000000000000000000000003-3-330000000000000000000000
χ768-8-88-44-442-4-2442-2-400-1211-2-22-100000000000000000000000000-333-30000000000000000000000
χ778-8-88-44-44-424-2-2-442002-1-2-211-120000−2i32i32i3−2i300000000i3−i3−i3i300000000000000000000000000000000
χ788-8-88-44-44-424-2-2-442002-1-2-211-1200002i3−2i3−2i32i300000000−i3i3i3−i300000000000000000000000000000000

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