Finite Group Databasebeta

← Group #13165471

Character table — Group #13165471

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444466888888881212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363654547272108108
order1222366633666666223366666622446666666644666666661212121212121212224466668812122424242444121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-1111111-1-1-1-111-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1
χ411111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111
χ51111111111111111-1-1111111111111-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111
χ71111111111111111-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1-1-1-1-1-1-111
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
χ91-1-111-1-111111-1-1-1-11-1111-11-1-1-11-1i−i11-1-111-1-11-11-11-111-1-1i−ii−iii−i−i1-1i−i11-1-1i−i1-1ii−i−i1-1i−ii−i
χ101-1-111-1-111111-1-1-1-11-1111-11-1-1-11-1−ii11-1-111-1-11-11-11-111-1-1−ii−ii−i−iii1-1−ii11-1-1−ii1-1−i−iii1-1−ii−ii
χ111-1-111-1-111111-1-1-1-11-1111-11-1-1-1-11i−i11-1-1-1-1111-1-111-1-1-111i−ii−iii−i−i-11i−i-1-111−ii1-1−i−iii1-1i−i−ii
χ121-1-111-1-111111-1-1-1-11-1111-11-1-1-1-11−ii11-1-1-1-1111-1-111-1-1-111−ii−ii−i−iii-11−ii-1-111i−i1-1ii−i−i1-1−iii−i
χ131-1-111-1-111111-1-1-1-1-11111-11-1-1-11-1i−i-1-11111-1-11-11-1-1111-1-1i−ii−iii−i−i-11−ii-1-111i−i1-1ii−i−i-11−ii−ii
χ141-1-111-1-111111-1-1-1-1-11111-11-1-1-11-1−ii-1-11111-1-11-11-1-1111-1-1−ii−ii−i−iii-11i−i-1-111−ii1-1−i−iii-11i−ii−i
χ151-1-111-1-111111-1-1-1-1-11111-11-1-1-1-11i−i-1-111-1-1111-1-11-11-1-111i−ii−iii−i−i1-1−ii11-1-1−ii1-1−i−iii-11−iii−i
χ161-1-111-1-111111-1-1-1-1-11111-11-1-1-1-11−ii-1-111-1-1111-1-11-11-1-111−ii−ii−i−iii1-1i−i11-1-1i−i1-1ii−i−i-11i−i−ii
χ1722222222222222222222222222000022220000-2-200220000000000000000000000-2-20000-2-20000
χ182222222222222222-2-2222222220000-2-2-2-20000-2-200-2-20000000000000000000000-2-20000220000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122220000222222-1-100-1-1-1-1-1-122-1-1-1-10000000022-1-1-1-1-1-1000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-20000222222-1-100-1-1-1-111-2-2111100000000-2-2-1-11111000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2220000-2-2-2-22211001111-1-122-1-1-1-100000000-2-2-1-11111000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-2221100111111-2-211110000000022-1-1-1-1-1-1000000
χ232-2-222-2-222222-2-2-2-22-2222-22-2-2-2000022-2-20000-22002-20000000000000000000000-220000-220000
χ242-2-222-2-222222-2-2-2-2-22222-22-2-2-20000-2-2220000-2200-220000000000000000000000-2200002-20000
χ252-2-22-111-12222-2-2-2-200-1-1-11-11112-22i−2i000022-2-22-2-1100-1-111−ii2i−2i−i−iii000000002i−2i-11−i−iii000000
χ262-2-22-111-12222-2-2-2-200-1-1-11-11112-2−2i2i000022-2-22-2-1100-1-111i−i−2i2iii−i−i00000000−2i2i-11ii−i−i000000
χ272-2-22-111-12222-2-2-2-200-1-1-11-1111-222i−2i0000-2-2222-21-10011-1-1−ii2i−2i−i−iii00000000−2i2i-11ii−i−i000000
χ282-2-22-111-12222-2-2-2-200-1-1-11-1111-22−2i2i0000-2-2222-21-10011-1-1i−i−2i2iii−i−i000000002i−2i-11−i−iii000000
χ29444444441-21-2-2-211441-211-2-2-210022-2-2-2-20000000011000022-1-1-1-1-1-1002200000000000000-1-100
χ30444444441-21-2-2-211441-211-2-2-2100-2-2-2-2-2-200000000110000-2-211111100-2-2000000000000001100
χ31444444441-21-2-2-211-4-41-211-2-2-210022222200000000-1-1000022-1-1-1-1-1-100-2-2000000000000001100
χ32444444441-21-2-2-211-4-41-211-2-2-2100-2-2222200000000-1-10000-2-2111111002200000000000000-1-100
χ3344444444-21-2111-2-244-21-2-2111-222001111-1-1-1-10022-2-2-1-1-1-1000000002200-1-1-1-100000000000000
χ3444444444-21-2111-2-244-21-2-2111-2-2-2001111111100-2-2-2-2111100000000-2-200111100000000000000
χ3544444444-21-2111-2-2-4-4-21-2-2111-22200-1-1-1-1-1-1-1-1002222-1-1-1-100000000-2-200111100000000000000
χ3644444444-21-2111-2-2-4-4-21-2-2111-2-2-200-1-1-1-1111100-2-2221111000000002200-1-1-1-100000000000000
χ374444-2-2-2-24444444400-2-2-2-2-2-2-2-2000000000000-4-400000000000000000000000000220000000000
χ3844-4-44-44-444-4-44-44-40044-4-4-44-440000000000000000000000000000000000000000000000000000
χ3944-4-44-44-4-212-11-1-2200-2122-11-1-200003-33-3−i3i3−i3i3000000−i3i3−i3i3000000000000−i3i3−i3i300000000000000
χ4044-4-44-44-4-212-11-1-2200-2122-11-1-200003-33-3i3−i3i3−i3000000i3−i3i3−i3000000000000i3−i3i3−i300000000000000
χ4144-4-44-44-4-212-11-1-2200-2122-11-1-20000-33-33−i3i3−i3i3000000−i3i3−i3i3000000000000i3−i3i3−i300000000000000
χ4244-4-44-44-4-212-11-1-2200-2122-11-1-20000-33-33i3−i3i3−i3000000i3−i3i3−i3000000000000−i3i3−i3i300000000000000
χ4344-4-4-22-2244-4-44-44-400-2-2222-22-2000000000000000000000000000000000000000000i6−i6i6−i6000000
χ4444-4-4-22-2244-4-44-44-400-2-2222-22-2000000000000000000000000000000000000000000−i6i6−i6i6000000
χ454-44-444-4-444-4-4-44-440044-44-4-44-40000000000000000000000000000000000000000000000000000
χ464-44-444-4-4-212-1-112-200-212-2-1-11200003-3-33−i3i3i3−i3000000−i3i3i3−i3000000000000−i3i3i3−i300000000000000
χ474-44-444-4-4-212-1-112-200-212-2-1-11200003-3-33i3−i3−i3i3000000i3−i3−i3i3000000000000i3−i3−i3i300000000000000
χ484-44-444-4-4-212-1-112-200-212-2-1-1120000-333-3−i3i3i3−i3000000−i3i3i3−i3000000000000i3−i3−i3i300000000000000
χ494-44-444-4-4-212-1-112-200-212-2-1-1120000-333-3i3−i3−i3i3000000i3−i3−i3i3000000000000−i3i3i3−i300000000000000
χ504-44-4-2-22244-4-4-44-4400-2-22-222-220000000000000000000000000000000000000000006−6−66000000
χ514-44-4-2-22244-4-4-44-4400-2-22-222-22000000000000000000000000000000000000000000−666−6000000
χ524-4-444-4-441-21-222-1-14-41-21-1-222-1002i−2i-2-222000000001-100002i−2i−ii−i−iii002i−2i00000000000000−ii00
χ534-4-444-4-441-21-222-1-14-41-21-1-222-100−2i2i-2-222000000001-10000−2i2ii−iii−i−i00−2i2i00000000000000i−i00
χ544-4-444-4-441-21-222-1-1-441-21-1-222-1002i−2i22-2-200000000-1100002i−2i−ii−i−iii00−2i2i00000000000000i−i00
χ554-4-444-4-441-21-222-1-1-441-21-1-222-100−2i2i22-2-200000000-110000−2i2ii−iii−i−i002i−2i00000000000000−ii00
χ564-4-444-4-44-21-21-1-1224-4-21-221-1-122-20011-1-1-1-111002-2-22-1-111000000002-200-1-11100000000000000
χ574-4-444-4-44-21-21-1-1224-4-21-221-1-12-220011-1-111-1-100-22-2211-1-100000000-220011-1-100000000000000
χ584-4-444-4-44-21-21-1-122-44-21-221-1-122-200-1-111-1-111002-22-2-1-11100000000-220011-1-100000000000000
χ594-4-444-4-44-21-21-1-122-44-21-221-1-12-2200-1-11111-1-100-222-211-1-1000000002-200-1-11100000000000000
χ604-4-44-222-24444-4-4-4-400-2-2-22-2222000000000000-44000000000000000000000000002-20000000000
χ618888-4-4-4-42-42-4-4-42200-12-1-1222-10044000000000000000000-2-2-2-211110000000000000000000000
χ628888-4-4-4-42-42-4-4-42200-12-1-1222-100-4-40000000000000000002222-1-1-1-10000000000000000000000
χ638888-4-4-4-4-42-4222-4-4002-122-1-1-1244000000-2-2-2-200-2-2001111000000000000000000000000000000
χ648888-4-4-4-4-42-4222-4-4002-122-1-1-12-4-40000002222002200-1-1-1-1000000000000000000000000000000
χ6588-8-88-88-82-4-24-442-2002-4-2-24-4420000000000000000000000000000000000000000000000000000
χ6688-8-8-44-442-4-24-442-200-1211-22-2-1000000000000000000000000003-33-30000000000000000000000
χ6788-8-8-44-442-4-24-442-200-1211-22-2-100000000000000000000000000-33-330000000000000000000000
χ6888-8-8-44-44-424-22-2-44002-1-2-21-11200000000−2i32i3−2i32i3000000i3−i3i3−i3000000000000000000000000000000
χ6988-8-8-44-44-424-22-2-44002-1-2-21-112000000002i3−2i32i3−2i3000000−i3i3−i3i3000000000000000000000000000000
χ708-88-888-8-82-4-244-4-22002-4-2244-4-20000000000000000000000000000000000000000000000000000
χ718-88-8-4-4442-4-244-4-2200-121-1-2-221000000000000000000000000003i−3i−3i3i0000000000000000000000
χ728-88-8-4-4442-4-244-4-2200-121-1-2-22100000000000000000000000000−3i3i3i−3i0000000000000000000000
χ738-88-8-4-444-424-2-224-4002-1-2211-1-200000000−2i32i32i3−2i3000000i3−i3−i3i3000000000000000000000000000000
χ748-88-8-4-444-424-2-224-4002-1-2211-1-2000000002i3−2i3−2i32i3000000−i3i3i3−i3000000000000000000000000000000
χ758-8-88-444-42-42-444-2-200-12-112-2-21004i−4i000000000000000000−2i2i−2i2iii−i−i0000000000000000000000
χ768-8-88-444-42-42-444-2-200-12-112-2-2100−4i4i0000000000000000002i−2i2i−2i−i−iii0000000000000000000000
χ778-8-88-444-4-42-42-2-244002-12-2-111-24-4000000-2-22200-220011-1-1000000000000000000000000000000
χ788-8-88-444-4-42-42-2-244002-12-2-111-2-4400000022-2-2002-200-1-111000000000000000000000000000000

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